Daily Papers

Autoregressive large language models (LLMs) have unified a vast range of language tasks, inspiring preliminary efforts in autoregressive video generation. Existing autoregressive video generators either diverge from standard LLM architectures, depend on bulky external text encoders, or incur prohibitive latency due to next-token decoding. In this paper, we introduce Lumos-1, an autoregressive video generator that retains the LLM architecture with minimal architectural modifications. To inject spatiotemporal correlations in LLMs, we identify the efficacy of incorporating 3D RoPE and diagnose its imbalanced frequency spectrum ranges. Therefore, we propose MM-RoPE, a RoPE scheme that preserves the original textual RoPE while providing comprehensive frequency spectra and scaled 3D positions for modeling multimodal spatiotemporal data. Moreover, Lumos-1 resorts to a token dependency strategy that obeys intra-frame bidirectionality and inter-frame temporal causality. Based on this dependency strategy, we identify the issue of frame-wise loss imbalance caused by spatial information redundancy and solve it by proposing Autoregressive Discrete Diffusion Forcing (AR-DF). AR-DF introduces temporal tube masking during training with a compatible inference-time masking policy to avoid quality degradation. By using memory-efficient training techniques, we pre-train Lumos-1 on only 48 GPUs, achieving performance comparable to EMU3 on GenEval, COSMOS-Video2World on VBench-I2V, and OpenSoraPlan on VBench-T2V. Code and models are available at https://github.com/alibaba-damo-academy/Lumos.

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to autoregressive (AR) LLMs for text generation, with the potential to decode multiple tokens in a single iteration. However, none of the existing open-source dLLMs have achieved superior inference speed over AR LLMs of similar size. This paper breaks this barrier based on a simple and effective strategy named discrete diffusion forcing (D2F). D2F equips dLLMs with two key capabilities: (1) block-wise autoregressive generation to enable KV cache utilization; (2) prediction of following tokens without requiring completion of prior blocks for inter-block parallel decoding. In this way, the vanilla dLLMs are refurbished into an AR-diffusion hybrid paradigm for efficient inference. D2F can be implemented with an asymmetric distillation process based on pre-trained dLLMs. We further propose a pipelined parallel decoding algorithm, which enables a trade-off between efficiency and efficacy. Empirically, D2F dLLMs achieve more than 2.5times inference speed than LLaMA3 and Qwen2.5 on GSM8K. Compared to vanilla dLLMs like LLaDA and Dream, the acceleration can be more than 50times while maintaining comparable output quality. The code is available at https://github.com/zhijie-group/Discrete-Diffusion-Forcing.

Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot vectors and cannot be propagated across steps, forcing subsequent steps to operate with limited information. To mitigate this problem, we introduce Loopholing, a novel and simple mechanism that preserves this information via a deterministic latent pathway, leading to Loopholing Discrete Diffusion Models (LDDMs). Trained efficiently with a self-conditioning strategy, LDDMs achieve substantial gains-reducing generative perplexity by up to 61% over prior baselines, closing (and in some cases surpassing) the gap with autoregressive models, and producing more coherent text. Applied to reasoning tasks, LDDMs also improve performance on arithmetic benchmarks such as Countdown and Game of 24. These results also indicate that loopholing mitigates idle steps and oscillations, providing a scalable path toward high-quality non-autoregressive text generation.

Autoregressive video diffusion with causal diffusion transformers has emerged as a major paradigm for real-time streaming video generation and action-conditioned interactive world models. In this work, we extend rCM, an advanced diffusion distillation framework, to autoregressive video diffusion. The core philosophy of rCM lies in the complementarity between forward and reverse divergences, represented by consistency models (CMs) and distribution matching distillation (DMD), respectively, in diffusion distillation. This philosophy naturally carries over to the autoregressive setting, where teacher-forcing (TF) provides an offline, forward-divergence causal training paradigm, while self-forcing (SF) corresponds to an on-policy, reverse-divergence refinement. Our contributions are: (1) through extensive experiments, we show that teacher-forcing CM is currently the best complement to self-forcing DMD as an initialization strategy (2) we present the first implementation of teacher-forcing-based continuous-time CMs (e.g., sCM/MeanFlow) for autoregressive video diffusion, enabled by our custom-mask FlashAttention-2 JVP kernel, achieving 10times faster convergence compared to discrete-time CMs (dCMs) (3) we introduce Causal-rCM, a leading, unified, and scalable algorithm-infrastructure open recipe for diffusion distillation and causal training (4) we achieve state-of-the-art streaming video generation performance in both frame-wise and chunk-wise settings, using only synthetic data for training. Notably, our distilled 2-step causal Wan2.1-1.3B model achieves a VBench-T2V score of 84.63 with only 1 or 2 sampling steps. We further apply Causal-rCM to Cosmos 3, an advanced omnimodal world foundation model for physical AI with action-conditioned generation capability, enabling an interactive world model.

Autoregressive video diffusion models hold promise for world simulation but are vulnerable to exposure bias arising from the train-test mismatch. While recent works address this via post-training, they typically rely on a bidirectional teacher model or online discriminator. To achieve an end-to-end solution, we introduce Resampling Forcing, a teacher-free framework that enables training autoregressive video models from scratch and at scale. Central to our approach is a self-resampling scheme that simulates inference-time model errors on history frames during training. Conditioned on these degraded histories, a sparse causal mask enforces temporal causality while enabling parallel training with frame-level diffusion loss. To facilitate efficient long-horizon generation, we further introduce history routing, a parameter-free mechanism that dynamically retrieves the top-k most relevant history frames for each query. Experiments demonstrate that our approach achieves performance comparable to distillation-based baselines while exhibiting superior temporal consistency on longer videos owing to native-length training.

We introduce Self Forcing, a novel training paradigm for autoregressive video diffusion models. It addresses the longstanding issue of exposure bias, where models trained on ground-truth context must generate sequences conditioned on their own imperfect outputs during inference. Unlike prior methods that denoise future frames based on ground-truth context frames, Self Forcing conditions each frame's generation on previously self-generated outputs by performing autoregressive rollout with key-value (KV) caching during training. This strategy enables supervision through a holistic loss at the video level that directly evaluates the quality of the entire generated sequence, rather than relying solely on traditional frame-wise objectives. To ensure training efficiency, we employ a few-step diffusion model along with a stochastic gradient truncation strategy, effectively balancing computational cost and performance. We further introduce a rolling KV cache mechanism that enables efficient autoregressive video extrapolation. Extensive experiments demonstrate that our approach achieves real-time streaming video generation with sub-second latency on a single GPU, while matching or even surpassing the generation quality of significantly slower and non-causal diffusion models. Project website: http://self-forcing.github.io/

Real-time talking avatar generation requires low latency and minute-level temporal stability. Autoregressive (AR) forcing enables streaming inference but suffers from exposure bias, which causes errors to accumulate and become irreversible over long rollouts. In contrast, full-sequence diffusion transformers mitigate drift but remain computationally prohibitive for real-time long-form synthesis. We present AvatarForcing, a one-step streaming diffusion framework that denoises a fixed local-future window with heterogeneous noise levels and emits one clean block per step under constant per-step cost. To stabilize unbounded streams, the method introduces dual-anchor temporal forcing: a style anchor that re-indexes RoPE to maintain a fixed relative position with respect to the active window and applies anchor-audio zero-padding, and a temporal anchor that reuses recently emitted clean blocks to ensure smooth transitions. Real-time one-step inference is enabled by two-stage streaming distillation with offline ODE backfill and distribution matching. Experiments on standard benchmarks and a new 400-video long-form benchmark show strong visual quality and lip synchronization at 34 ms/frame using a 1.3B-parameter student model for realtime streaming. Our page is available at: https://cuiliyuan121.github.io/AvatarForcing/

We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special cases of ARDMs under mild assumptions. ARDMs are simple to implement and easy to train. Unlike standard ARMs, they do not require causal masking of model representations, and can be trained using an efficient objective similar to modern probabilistic diffusion models that scales favourably to highly-dimensional data. At test time, ARDMs support parallel generation which can be adapted to fit any given generation budget. We find that ARDMs require significantly fewer steps than discrete diffusion models to attain the same performance. Finally, we apply ARDMs to lossless compression, and show that they are uniquely suited to this task. Contrary to existing approaches based on bits-back coding, ARDMs obtain compelling results not only on complete datasets, but also on compressing single data points. Moreover, this can be done using a modest number of network calls for (de)compression due to the model's adaptable parallel generation.

Autoregressive (AR) video diffusion models adopt a streaming generation framework, enabling long-horizon video generation with real-time responsiveness, as exemplified by the Self Forcing training paradigm. However, existing AR video diffusion models still suffer from significant attention complexity and severe memory overhead due to the redundant key-value (KV) caches across historical frames, which limits scalability. In this paper, we tackle this challenge by introducing KV cache compression into autoregressive video diffusion. We observe that attention heads in mainstream AR diffusion models exhibit markedly distinct attention patterns and functional roles that remain stable across samples and denoising steps. Building on our empirical study of head-wise functional specialization, we divide the attention heads into two categories: static heads, which focus on transitions across autoregressive chunks and intra-frame fidelity, and dynamic heads, which govern inter-frame motion and consistency. We then propose Forcing-KV, a hybrid KV cache compression strategy that performs structured static pruning for static heads and dynamic pruning based on segment-wise similarity for dynamic heads. While maintaining output quality, our method achieves a generation speed of over 29 frames per second on a single NVIDIA H200 GPU along with 30% cache memory reduction, delivering up to 1.35x and 1.50x speedups on LongLive and Self Forcing at 480P resolution, and further scaling to 2.82x speedup at 1080P resolution. Code and demo videos are provided at https://zju-jiyicheng.github.io/Forcing-KV-Page.

Autoregressive (AR) diffusion models offer a promising framework for sequential generation tasks such as video synthesis by combining diffusion modeling with causal inference. Although they support streaming generation, existing AR diffusion methods struggle to scale efficiently. In this paper, we identify two key challenges in hour-scale real-time human animation. First, most forcing strategies propagate sample-level representations with mismatched diffusion states, causing inconsistent learning signals and unstable convergence. Second, historical representations grow unbounded and lack structure, preventing effective reuse of cached states and severely limiting inference efficiency. To address these challenges, we propose Neighbor Forcing, a diffusion-step-consistent AR formulation that propagates temporally adjacent frames as latent neighbors under the same noise condition. This design provides a distribution-aligned and stable learning signal while preserving drifting throughout the AR chain. Building upon this, we introduce a structured ConvKV memory mechanism that compresses the keys and values in causal attention into a fixed-length representation, enabling constant-memory inference and truly infinite video generation without relying on short-term motion-frame memory. Extensive experiments demonstrate that our approach significantly improves training convergence, hour-scale generation quality, and inference efficiency compared to existing AR diffusion methods. Numerically, LiveAct enables hour-scale real-time human animation and supports 20 FPS real-time streaming inference on as few as two NVIDIA H100 or H200 GPUs. Quantitative results demonstrate that our method attains state-of-the-art performance in lip-sync accuracy, human animation quality, and emotional expressiveness, with the lowest inference cost.

This paper presents Diffusion Forcing, a new training paradigm where a diffusion model is trained to denoise a set of tokens with independent per-token noise levels. We apply Diffusion Forcing to sequence generative modeling by training a causal next-token prediction model to generate one or several future tokens without fully diffusing past ones. Our approach is shown to combine the strengths of next-token prediction models, such as variable-length generation, with the strengths of full-sequence diffusion models, such as the ability to guide sampling to desirable trajectories. Our method offers a range of additional capabilities, such as (1) rolling-out sequences of continuous tokens, such as video, with lengths past the training horizon, where baselines diverge and (2) new sampling and guiding schemes that uniquely profit from Diffusion Forcing's variable-horizon and causal architecture, and which lead to marked performance gains in decision-making and planning tasks. In addition to its empirical success, our method is proven to optimize a variational lower bound on the likelihoods of all subsequences of tokens drawn from the true joint distribution. Project website: https://boyuan.space/diffusion-forcing/

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. Yet diffusion models that directly work on discrete data space do not fully exploit the power of iterative refinement, as the signals are lost during the transition between discrete states. Existing continuous diffusion models for discrete data have limited performance compared to discrete approaches, and the unclear link between them restricts the development of diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on the analogy, we introduce a simple design for the diffusion process that generalizes previous discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry and a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models. Codes available at https://github.com/harryjo97/RDLM{https://github.com/harryjo97/RDLM}.

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.

Discrete diffusion models are promising alternatives to autoregressive approaches for text generation, yet their decoding methods remain under-studied. Standard autoregressive search procedures, such as beam search, do not directly apply to iterative denoising, where hypotheses are complete intermediate sequences rather than left-to-right prefixes. Furthermore, existing diffusion decoding procedures only provide limited control over the diversity and coverage of retained hypotheses. In this work, we introduce D5P4, a beam-style decoding method tailored to discrete diffusion models, which casts intermediate beam selection as MAP inference under a partitioned Determinantal Point Process. This yields a model-internal batch objective that balances quality and diversity without external verifiers. Experiments on open-ended generation, question answering, and mathematical reasoning show that D5P4 improves diversity and pass@k coverage while matching or surpassing baseline quality and fidelity

Real-time interactive video generation requires low-latency, streaming, and controllable rollout. Existing autoregressive (AR) diffusion distillation methods have achieved strong results in the chunk-wise 4-step regime by distilling bidirectional base models into few-step AR students, but they remain limited by coarse response granularity and non-negligible sampling latency. In this paper, we study a more aggressive setting: frame-wise autoregression with only 1--2 sampling steps. In this regime, we identify the initialization of a few-step AR student as the key bottleneck: existing strategies are either target-misaligned, incapable of few-step generation, or too costly to scale. We propose Causal Forcing++, a principled and scalable pipeline that uses causal consistency distillation (causal CD) for few-step AR initialization. The core idea is that causal CD learns the same AR-conditional flow map as causal ODE distillation, but obtains supervision from a single online teacher ODE step between adjacent timesteps, avoiding the need to precompute and store full PF-ODE trajectories. This makes the initialization both more efficient and easier to optimize. The resulting pipeline, \ours, surpasses the SOTA 4-step chunk-wise Causal Forcing under the \textbf{frame-wise 2-step setting} by 0.1 in VBench Total, 0.3 in VBench Quality, and 0.335 in VisionReward, while reducing first-frame latency by 50\% and Stage 2 training cost by sim4times. We further extend the pipeline to action-conditioned world model generation in the spirit of Genie3. Project Page: https://github.com/thu-ml/Causal-Forcing and https://github.com/shengshu-ai/minWM .

This paper presents Diffusion via Autoregressive models (D-AR), a new paradigm recasting the image diffusion process as a vanilla autoregressive procedure in the standard next-token-prediction fashion. We start by designing the tokenizer that converts images into sequences of discrete tokens, where tokens in different positions can be decoded into different diffusion denoising steps in the pixel space. Thanks to the diffusion properties, these tokens naturally follow a coarse-to-fine order, which directly lends itself to autoregressive modeling. Therefore, we apply standard next-token prediction on these tokens, without modifying any underlying designs (either causal masks or training/inference strategies), and such sequential autoregressive token generation directly mirrors the diffusion procedure in image space. That is, once the autoregressive model generates an increment of tokens, we can directly decode these tokens into the corresponding diffusion denoising step in the streaming manner. Our pipeline naturally reveals several intriguing properties, for example, it supports consistent previews when generating only a subset of tokens and enables zero-shot layout-controlled synthesis. On the standard ImageNet benchmark, our method achieves 2.09 FID using a 775M Llama backbone with 256 discrete tokens. We hope our work can inspire future research on unified autoregressive architectures of visual synthesis, especially with large language models. Code and models will be available at https://github.com/showlab/D-AR

We introduce Sparse Forcing, a training-and-inference paradigm for autoregressive video diffusion models that improves long-horizon generation quality while reducing decoding latency. Sparse Forcing is motivated by an empirical observation in autoregressive diffusion rollouts: attention concentrates on a persistent subset of salient visual blocks, forming an implicit spatiotemporal memory in the KV cache, and exhibits a locally structured block-sparse pattern within sliding windows. Building on this observation, we propose a trainable native sparsity mechanism that learns to compress, preserve, and update these persistent blocks while restricting computation within each local window to a dynamically selected local neighborhood. To make the approach practical at scale for both training and inference, we further propose Persistent Block-Sparse Attention (PBSA), an efficient GPU kernel that accelerates sparse attention and memory updates for low-latency, memory-efficient decoding. Experiments show that Sparse Forcing improves the VBench score by +0.26 over Self-Forcing on 5-second text-to-video generation while delivering a 1.11-1.17x decoding speedup and 42% lower peak KV-cache footprint. The gains are more pronounced on longer-horizon rollouts, delivering improved visual quality with +0.68 and +2.74 VBench improvements, and 1.22x and 1.27x speedups on 20-second and 1-minute generations, respectively.

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps. In continuous domains, consistency training along the probability-flow ODE is a popular recipe to accelerate diffusion. For discrete diffusion, no analogous sample-space ODE exists, making direct adaptation ill-defined. We argue that the natural discrete substitute is not a deterministic trajectory but its stochastic counterpart: the exact posterior bridge, available in closed form for broad corruption families including masked and uniform diffusion. Building on this observation, we introduce Multi-Path Discrete Consistency (MPDC), a new principle that trains a denoiser to be path-invariant in expectation across these stochastic bridges, and instantiate it as the Consistent Diffusion Language Model (CDLM), a single-stage, teacher-free training framework. A single CDLM objective unifies masked diffusion, continuous consistency models, and progressive/discrete distillation as analytic limits or empirical approximations of one common view. Empirically, CDLM establishes a new state of the art on both conditional and unconditional text-generation, consistently outperforming strong base discrete diffusion models and often even multi-stage distilled baselines across sampling budgets, with the largest gains in the few-step regime. Together, these results position CDLM as a principled and scalable foundation for the next generation of fast, high-fidelity discrete generative modeling.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

We introduce Causal Diffusion as the autoregressive (AR) counterpart of Diffusion models. It is a next-token(s) forecasting framework that is friendly to both discrete and continuous modalities and compatible with existing next-token prediction models like LLaMA and GPT. While recent works attempt to combine diffusion with AR models, we show that introducing sequential factorization to a diffusion model can substantially improve its performance and enables a smooth transition between AR and diffusion generation modes. Hence, we propose CausalFusion - a decoder-only transformer that dual-factorizes data across sequential tokens and diffusion noise levels, leading to state-of-the-art results on the ImageNet generation benchmark while also enjoying the AR advantage of generating an arbitrary number of tokens for in-context reasoning. We further demonstrate CausalFusion's multimodal capabilities through a joint image generation and captioning model, and showcase CausalFusion's ability for zero-shot in-context image manipulations. We hope that this work could provide the community with a fresh perspective on training multimodal models over discrete and continuous data.

Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single continuous Gaussian distribution arguably represents an unnecessarily challenging learning problem. We propose Discrete-Continuous Latent Variable Diffusion Models (DisCo-Diff) to simplify this task by introducing complementary discrete latent variables. We augment DMs with learnable discrete latents, inferred with an encoder, and train DM and encoder end-to-end. DisCo-Diff does not rely on pre-trained networks, making the framework universally applicable. The discrete latents significantly simplify learning the DM's complex noise-to-data mapping by reducing the curvature of the DM's generative ODE. An additional autoregressive transformer models the distribution of the discrete latents, a simple step because DisCo-Diff requires only few discrete variables with small codebooks. We validate DisCo-Diff on toy data, several image synthesis tasks as well as molecular docking, and find that introducing discrete latents consistently improves model performance. For example, DisCo-Diff achieves state-of-the-art FID scores on class-conditioned ImageNet-64/128 datasets with ODE sampler.

Discrete diffusion has achieved state-of-the-art performance, outperforming or approaching autoregressive models on standard benchmarks. In this work, we introduce Discrete Diffusion with Planned Denoising (DDPD), a novel framework that separates the generation process into two models: a planner and a denoiser. At inference time, the planner selects which positions to denoise next by identifying the most corrupted positions in need of denoising, including both initially corrupted and those requiring additional refinement. This plan-and-denoise approach enables more efficient reconstruction during generation by iteratively identifying and denoising corruptions in the optimal order. DDPD outperforms traditional denoiser-only mask diffusion methods, achieving superior results on language modeling benchmarks such as text8, OpenWebText, and token-based generation on ImageNet 256 times 256. Notably, in language modeling, DDPD significantly reduces the performance gap between diffusion-based and autoregressive methods in terms of generative perplexity. Code is available at https://github.com/liusulin/DDPD.

We present FloodDiffusion, a new framework for text-driven, streaming human motion generation. Given time-varying text prompts, FloodDiffusion generates text-aligned, seamless motion sequences with real-time latency. Unlike existing methods that rely on chunk-by-chunk or auto-regressive model with diffusion head, we adopt a diffusion forcing framework to model this time-series generation task under time-varying control events. We find that a straightforward implementation of vanilla diffusion forcing (as proposed for video models) fails to model real motion distributions. We demonstrate that to guarantee modeling the output distribution, the vanilla diffusion forcing must be tailored to: (i) train with a bi-directional attention instead of casual attention; (ii) implement a lower triangular time scheduler instead of a random one; (iii) utilize a continues time-varying way to introduce text conditioning. With these improvements, we demonstrate in the first time that the diffusion forcing-based framework achieves state-of-the-art performance on the streaming motion generation task, reaching an FID of 0.057 on the HumanML3D benchmark. Models, code, and weights are available. https://shandaai.github.io/FloodDiffusion/

MRI reconstruction is an inherently ill-posed inverse problem, since incomplete measurements admit many plausible solutions. This ambiguity becomes more severe under high acceleration, where pixel-domain continuous predictors tend to average over feasible reconstructions and suppress high-frequency anatomy. We address this limitation by moving reconstruction to discrete multi-scale latent space and posing it as autoregressive next-acceleration-scale prediction. Leveraging discrete priors proven effective in visual autoregressive modeling, our method restricts the solution to compact sequences of codebook tokens, enabling sharp reconstructions even from extremely sparse measurements. This discrete autoregressive formulation also aligns naturally with modern large language model post-training techniques. Building on this observation, we introduce on-policy privileged information distillation for visual autoregressive modeling, where a teacher is provided training only privileged context that is unavailable at inference, in our case fully sampled acquisitions, and supervises a student trained on its own rollouts, leading to consistent reconstruction gains. Through extensive experiments on the fastMRI benchmark, we show that our approach delivers improved reconstruction performance across diverse sampling patterns under extreme undersampling. Project website is https://yilmazkorkmaz1.github.io/discrete-mri-reconstruction-opd/{here}.

Autoregressive (AR) models have long dominated the landscape of large language models, driving progress across a wide range of tasks. Recently, diffusion-based language models have emerged as a promising alternative, though their advantages over AR models remain underexplored. In this paper, we systematically study masked diffusion models in data-constrained settings-where training involves repeated passes over limited data-and find that they significantly outperform AR models when compute is abundant but data is scarce. Diffusion models make better use of repeated data, achieving lower validation loss and superior downstream performance. We interpret this advantage as implicit data augmentation: masked diffusion exposes the model to a diverse distribution of token orderings and prediction tasks, unlike AR's fixed left-to-right factorization. We find new scaling laws for diffusion models and derive a closed-form expression for the critical compute threshold at which diffusion begins to outperform AR. These results suggest that when data, not compute, is the bottleneck, diffusion models offer a compelling alternative to the standard AR paradigm. Our code is available at: https://diffusion-scaling.github.io.

We study the problem of posterior sampling using pretrained discrete diffusion foundation models, aiming to recover images from noisy measurements without retraining task-specific models. While diffusion models have achieved remarkable success in generative modeling, most advances rely on continuous Gaussian diffusion. In contrast, discrete diffusion offers a unified framework for jointly modeling categorical data such as text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and principled training-free Bayesian inference, making it particularly well-suited for posterior sampling. However, existing approaches to discrete diffusion posterior sampling face severe challenges: derivative-free guidance yields sparse signals, continuous relaxations limit applicability, and split Gibbs samplers suffer from the curse of dimensionality. To overcome these limitations, we introduce Anchored Posterior Sampling (APS) for masked diffusion foundation models, built on two key innovations -- quantized expectation for gradient-like guidance in discrete embedding space, and anchored remasking for adaptive decoding. Our approach achieves state-of-the-art performance among discrete diffusion samplers across linear and nonlinear inverse problems on the standard benchmarks. We further demonstrate the benefits of our approach in training-free stylization and text-guided editing.

Autoregressive models (ARMs) are hindered by slow sequential inference. While masked diffusion models (MDMs) offer a parallel alternative, they suffer from critical drawbacks: high computational overhead from precluding Key-Value (KV) caching, and incoherent generation arising from learning dependencies over an intractable space of token combinations. To address these limitations, we introduce ReFusion, a novel masked diffusion model that achieves superior performance and efficiency by elevating parallel decoding from the token level to a higher slot level, where each slot is a fixed-length, contiguous sub-sequence. This is achieved through an iterative ``plan-and-infill'' decoding process: a diffusion-based planning step first identifies a set of weakly dependent slots, and an autoregressive infilling step then decodes these selected slots in parallel. The slot-based design simultaneously unlocks full KV cache reuse with a unified causal framework and reduces the learning complexity from the token combination space to a manageable slot-level permutation space. Extensive experiments on seven diverse benchmarks show that ReFusion not only overwhelmingly surpasses prior MDMs with 34% performance gains and an over 18times speedup on average, but also bridges the performance gap to strong ARMs while maintaining a 2.33times average speedup.

To achieve real-time interactive video generation, current methods distill pretrained bidirectional video diffusion models into few-step autoregressive (AR) models, facing an architectural gap when full attention is replaced by causal attention. However, existing approaches do not bridge this gap theoretically. They initialize the AR student via ODE distillation, which requires frame-level injectivity, where each noisy frame must map to a unique clean frame under the PF-ODE of an AR teacher. Distilling an AR student from a bidirectional teacher violates this condition, preventing recovery of the teacher's flow map and instead inducing a conditional-expectation solution, which degrades performance. To address this issue, we propose Causal Forcing that uses an AR teacher for ODE initialization, thereby bridging the architectural gap. Empirical results show that our method outperforms all baselines across all metrics, surpassing the SOTA Self Forcing by 19.3\% in Dynamic Degree, 8.7\% in VisionReward, and 16.7\% in Instruction Following. Project page and the code: https://thu-ml.github.io/CausalForcing.github.io/{https://thu-ml.github.io/CausalForcing.github.io/}

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Recent studies have explored autoregressive models for image generation, with promising results, and have combined diffusion models with autoregressive frameworks to optimize image generation via diffusion losses. In this study, we present a theoretical analysis of diffusion and autoregressive models with diffusion loss, highlighting the latter's advantages. We present a theoretical comparison of conditional diffusion and autoregressive diffusion with diffusion loss, demonstrating that patch denoising optimization in autoregressive models effectively mitigates condition errors and leads to a stable condition distribution. Our analysis also reveals that autoregressive condition generation refines the condition, causing the condition error influence to decay exponentially. In addition, we introduce a novel condition refinement approach based on Optimal Transport (OT) theory to address ``condition inconsistency''. We theoretically demonstrate that formulating condition refinement as a Wasserstein Gradient Flow ensures convergence toward the ideal condition distribution, effectively mitigating condition inconsistency. Experiments demonstrate the superiority of our method over diffusion and autoregressive models with diffusion loss methods.

Pixel-space diffusion models are trained on full-bandwidth noisy images, yet the useful signal available to the denoiser is strongly frequency dependent. Under rectified-flow diffusion and natural-image power-law spectra, the per-band data-to-noise contour k^{*}(t) = (1-t)^{-2/α} separates a signal-bearing low-frequency region from a noise-dominated high-frequency region at each time t. We show that this implicit coarse-to-fine structure is not merely descriptive: it induces a capacity-allocation problem. A standard pixel-space denoiser must discover the moving bandwidth boundary internally and can spend computation on frequency-time regions where the optimal prediction collapses to deterministic baselines rather than data-distribution modeling. To make this boundary explicit, we introduce Spectral Forcing, a parameter-free, time-conditional 2D-DCT low-pass operator applied to the noisy input before the patch embedder. Its cutoff expands monotonically with the diffusion time and becomes the identity at the data endpoint. Through controlled synthetic experiments, we identify the regime in which the operator is beneficial: coarse patch tokenization and data whose high-frequency content is predominantly noise rather than essential signal. On ImageNet-256 with JiT-700M/32, Spectral Forcing consistently improves both FID and Inception Score across different training epochs, demonstrating robust gains throughout training; at finer tokenization, the spectral forcing is still competitive. We further insert the unchanged operator into SenseNova-U1, a unified text-to-image model, where it improves DPG-Bench and GenEval, showing that the input-side spectral prior transfers beyond class-conditional generation. These results suggest a route to capacity-efficient pixel-space diffusion by showing the signal and hiding the noise.

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser (x-prediction) and noise-prediction (epsilon-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers considerably improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Single-cell RNA-seq profiles are high-dimensional, sparse, and unordered, causing autoregressive generation to impose an artificial ordering bias and suffer from error accumulation. To address this, we propose scDiVa, a masked discrete diffusion foundation model that aligns generation with the dropout-like corruption process by defining a continuous-time forward masking mechanism in token space. ScDiVa features a bidirectional denoiser that jointly models discrete gene identities and continuous values, utilizing entropy-normalized serialization and a latent anchor token to maximize information efficiency and preserve global cell identity. The model is trained via depth-invariant time sampling and a dual denoising objective to simulate varying sparsity levels while ensuring precise recovery of both identity and magnitude. Pre-trained on 59 million cells, scDiVa achieves strong transfer performance across major benchmarks, including batch integration, cell type annotation, and perturbation response prediction. These results suggest that masked discrete diffusion serves as a biologically coherent and effective alternative to autoregression.

Diffusion-based lip synchronization models achieve strong visual quality and audio-visual alignment, but full-sequence bidirectional attention and many denoising steps make them impractical for real-time inference. We present Lip Forcing, to our knowledge the first autoregressive diffusion method for video-to-video (V2V) lip synchronization, which distills a 14B audio-conditioned bidirectional video diffusion teacher into causal students. At inference, the students generate each chunk in only two denoising steps without inference-time CFG, enabling real-time lip synchronization. A lip-sync-specific teacher-trajectory analysis reveals a CFG fidelity-sync tradeoff: no-CFG predictions favor reference fidelity, whereas CFG-guided predictions favor synchronization within a mid-trajectory band. Lip Forcing translates this finding into three analysis-derived components: Sync-Window DMD, a two-step inference schedule, and a SyncNet-based reward. We validate Lip Forcing at two student scales, both distilled from the 14B teacher. The 1.3B student crosses into real-time streaming at 31 FPS, 17.6times faster than its same-scale bidirectional model. The 14B student, the largest diffusion model reported for V2V lip synchronization, runs 39.8times faster than its teacher at comparable reference fidelity. Time-to-first-frame is sub-millisecond at both scales, far below every diffusion baseline.

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the development of efficient inference algorithms. Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as tau-leaping. While exact methods suffer from unpredictable inference time and redundant function evaluations, tau-leaping is limited by its first-order accuracy. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models, enabling larger step sizes while reducing error. We rigorously analyze the proposed schemes and establish the second-order accuracy of the theta-trapezoidal method in KL divergence. Empirical evaluations on GPT-2 level text and ImageNet-level image generation tasks demonstrate that our method achieves superior sample quality compared to existing approaches under equivalent computational constraints.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing discrete diffusion approaches, while allowing significantly greater flexibility in the choice of corruption dynamics. The forward noising process relies on uniformization and enables fast arbitrary corruption. For the reverse process, we derive a simple evidence lower bound (ELBO) based on snapshot latents, instead of the entire noising path, that allows efficient training of standard generative modeling architectures with clear probabilistic interpretation. Our experiments on large-vocabulary discrete generation tasks suggest that the proposed framework outperforms existing discrete diffusion methods in terms of training efficiency and generation quality, and beats autoregressive models for the first time at this scale. We provide the code along with a blog post on the project page : https://oussamazekri.fr/gdds{https://oussamazekri.fr/gdds}.

Recently, denoising diffusion models have led to significant breakthroughs in the generation of images, audio and text. However, it is still an open question on how to adapt their strong modeling ability to model time series. In this paper, we propose TimeDiff, a non-autoregressive diffusion model that achieves high-quality time series prediction with the introduction of two novel conditioning mechanisms: future mixup and autoregressive initialization. Similar to teacher forcing, future mixup allows parts of the ground-truth future predictions for conditioning, while autoregressive initialization helps better initialize the model with basic time series patterns such as short-term trends. Extensive experiments are performed on nine real-world datasets. Results show that TimeDiff consistently outperforms existing time series diffusion models, and also achieves the best overall performance across a variety of the existing strong baselines (including transformers and FiLM).

Autoregressive (AR) diffusion offers a promising framework for generating videos of theoretically infinite length. However, a major challenge is maintaining temporal continuity while preventing the progressive quality degradation caused by error accumulation. To ensure continuity, existing methods typically condition on highly denoised contexts; yet, this practice propagates prediction errors with high certainty, thereby exacerbating degradation. In this paper, we argue that a highly clean context is unnecessary. Drawing inspiration from bidirectional diffusion models, which denoise frames at a shared noise level while maintaining coherence, we propose that conditioning on context at the same noise level as the current block provides sufficient signal for temporal consistency while effectively mitigating error propagation. Building on this insight, we propose HiAR, a hierarchical denoising framework that reverses the conventional generation order: instead of completing each block sequentially, it performs causal generation across all blocks at every denoising step, so that each block is always conditioned on context at the same noise level. This hierarchy naturally admits pipelined parallel inference, yielding a 1.8 wall-clock speedup in our 4-step setting. We further observe that self-rollout distillation under this paradigm amplifies a low-motion shortcut inherent to the mode-seeking reverse-KL objective. To counteract this, we introduce a forward-KL regulariser in bidirectional-attention mode, which preserves motion diversity for causal inference without interfering with the distillation loss. On VBench (20s generation), HiAR achieves the best overall score and the lowest temporal drift among all compared methods.

Latent diffusion models excel at generating high-quality images but lose the benefits of end-to-end modeling. They discard information during image encoding, require a separately trained decoder, and model an auxiliary distribution to the raw data. In this paper, we propose Latent Forcing, a simple modification to existing architectures that achieves the efficiency of latent diffusion while operating on raw natural images. Our approach orders the denoising trajectory by jointly processing latents and pixels with separately tuned noise schedules. This allows the latents to act as a scratchpad for intermediate computation before high-frequency pixel features are generated. We find that the order of conditioning signals is critical, and we analyze this to explain differences between REPA distillation in the tokenizer and the diffusion model, conditional versus unconditional generation, and how tokenizer reconstruction quality relates to diffusability. Applied to ImageNet, Latent Forcing achieves a new state-of-the-art for diffusion transformer-based pixel generation at our compute scale.

The integration of Vector Quantised Variational AutoEncoder (VQ-VAE) with autoregressive models as generation part has yielded high-quality results on image generation. However, the autoregressive models will strictly follow the progressive scanning order during the sampling phase. This leads the existing VQ series models to hardly escape the trap of lacking global information. Denoising Diffusion Probabilistic Models (DDPM) in the continuous domain have shown a capability to capture the global context, while generating high-quality images. In the discrete state space, some works have demonstrated the potential to perform text generation and low resolution image generation. We show that with the help of a content-rich discrete visual codebook from VQ-VAE, the discrete diffusion model can also generate high fidelity images with global context, which compensates for the deficiency of the classical autoregressive model along pixel space. Meanwhile, the integration of the discrete VAE with the diffusion model resolves the drawback of conventional autoregressive models being oversized, and the diffusion model which demands excessive time in the sampling process when generating images. It is found that the quality of the generated images is heavily dependent on the discrete visual codebook. Extensive experiments demonstrate that the proposed Vector Quantised Discrete Diffusion Model (VQ-DDM) is able to achieve comparable performance to top-tier methods with low complexity. It also demonstrates outstanding advantages over other vectors quantised with autoregressive models in terms of image inpainting tasks without additional training.

Diffusion language models offer unique benefits over autoregressive models due to their potential for parallelized generation and controllability, yet they lag in likelihood modeling and are limited to fixed-length generation. In this work, we introduce a class of block diffusion language models that interpolate between discrete denoising diffusion and autoregressive models. Block diffusion overcomes key limitations of both approaches by supporting flexible-length generation and improving inference efficiency with KV caching and parallel token sampling. We propose a recipe for building effective block diffusion models that includes an efficient training algorithm, estimators of gradient variance, and data-driven noise schedules to minimize the variance. Block diffusion sets a new state-of-the-art performance among diffusion models on language modeling benchmarks and enables generation of arbitrary-length sequences. We provide the code, along with the model weights and blog post on the project page: https://m-arriola.com/bd3lms/

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

The autoregressive video diffusion model has recently gained considerable research interest due to its causal modeling and iterative denoising. In this work, we identify that the multi-head self-attention in these models under-utilizes historical frames: approximately 25% heads attend almost exclusively to the current frame, and discarding their KV caches incurs only minor performance degradation. Building upon this, we propose Dummy Forcing, a simple yet effective method to control context accessibility across different heads. Specifically, the proposed heterogeneous memory allocation reduces head-wise context redundancy, accompanied by dynamic head programming to adaptively classify head types. Moreover, we develop a context packing technique to achieve more aggressive cache compression. Without additional training, our Dummy Forcing delivers up to 2.0x speedup over the baseline, supporting video generation at 24.3 FPS with less than 0.5% quality drop. Project page is available at https://csguoh.github.io/project/DummyForcing/.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval. Empirically, RADD is up to 3.5 times faster while achieving similar performance with the strongest baseline. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

We introduce Interleaved Gibbs Diffusion (IGD), a novel generative modeling framework for mixed continuous-discrete data, focusing on constrained generation problems. Prior works on discrete and continuous-discrete diffusion models assume factorized denoising distribution for fast generation, which can hinder the modeling of strong dependencies between random variables encountered in constrained generation. IGD moves beyond this by interleaving continuous and discrete denoising algorithms via a discrete time Gibbs sampling type Markov chain. IGD provides flexibility in the choice of denoisers, allows conditional generation via state-space doubling and inference time scaling via the ReDeNoise method. Empirical evaluations on three challenging tasks-solving 3-SAT, generating molecule structures, and generating layouts-demonstrate state-of-the-art performance. Notably, IGD achieves a 7% improvement on 3-SAT out of the box and achieves state-of-the-art results in molecule generation without relying on equivariant diffusion or domain-specific architectures. We explore a wide range of modeling, and interleaving strategies along with hyperparameters in each of these problems.

Although autoregressive models have dominated language modeling in recent years, there has been a growing interest in exploring alternative paradigms to the conventional next-token prediction framework. Diffusion-based language models have emerged as a compelling alternative due to their powerful parallel generation capabilities and inherent editability. However, these models are often constrained by fixed-length generation. A promising direction is to combine the strengths of both paradigms, segmenting sequences into blocks, modeling autoregressive dependencies across blocks while leveraging discrete diffusion to estimate the conditional distribution within each block given the preceding context. Nevertheless, their practical application is often hindered by two key limitations: rigid fixed-length outputs and a lack of flexible control mechanisms. In this work, we address the critical limitations of fixed granularity and weak controllability in current large diffusion language models. We propose CtrlDiff, a dynamic and controllable semi-autoregressive framework that adaptively determines the size of each generation block based on local semantics using reinforcement learning. Furthermore, we introduce a classifier-guided control mechanism tailored to discrete diffusion, which significantly reduces computational overhead while facilitating efficient post-hoc conditioning without retraining. Extensive experiments demonstrate that CtrlDiff sets a new standard among hybrid diffusion models, narrows the performance gap to state-of-the-art autoregressive approaches, and enables effective conditional text generation across diverse tasks.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Autoregressive language models, despite their impressive capabilities, struggle with complex reasoning and long-term planning tasks. We introduce discrete diffusion models as a novel solution to these challenges. Through the lens of subgoal imbalance, we demonstrate how diffusion models effectively learn difficult subgoals that elude autoregressive approaches. We propose Multi-granularity Diffusion Modeling (MDM), which prioritizes subgoals based on difficulty during learning. On complex tasks like Countdown, Sudoku, and Boolean Satisfiability Problems, MDM significantly outperforms autoregressive models without using search techniques. For instance, MDM achieves 91.5\% and 100\% accuracy on Countdown and Sudoku, respectively, compared to 45.8\% and 20.7\% for autoregressive models. Our work highlights the potential of diffusion-based approaches in advancing AI capabilities for sophisticated language understanding and problem-solving tasks.

Autoregressive (AR) Large Language Models (LLMs) have demonstrated significant success across numerous tasks. However, the AR modeling paradigm presents certain limitations; for instance, contemporary autoregressive LLMs are trained to generate one token at a time, which can result in noticeable latency. Recent advances have indicated that search and repeated sampling can enhance performance in various applications, such as theorem proving, code generation, and alignment, by utilizing greater computational resources during inference. In this study, we demonstrate that diffusion language models are capable of generating at least 32 tokens simultaneously, while exceeding the performance of AR models in text quality and on the LAMBADA natural language understanding benchmark. This outcome is achieved through a novel distillation method for discrete diffusion models, which reduces the number of inference steps by a factor of 32-64. Practically, our models, even without caching, can generate tokens at a rate that is up to 8 times faster than AR models employing KV caching, and we anticipate further improvements with the inclusion of caching. Moreover, we demonstrate the efficacy of our approach for diffusion language models with up to 860M parameters.

Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform Diffusion Models (UDM) they do not. We show that the standard plug-in bridge parameterization for UDM is not optimized by the denoising posterior, but by a leave-one-out posterior that predicts each clean token without using its own noisy observation. This identifies a mismatch between the plug-in ELBO and the usual cross-entropy denoising objective. We characterize the leave-one-out target and derive exact conversions between the denoiser, the leave-one-out posterior, and the score. These conversions allow us to disentangle parameterization and training objective. Our results also lead to inference improvements without any additional training through an informed predictor-corrector sampler and improved temperature sampling based on the leave-one-out predictor. We further introduce an absorbing-state reformulation of uniform diffusion that preserves the UDM joint law while decomposing it into masked-diffusion-like sampling operations, with simpler denoising posteriors, carry-over unmasking, and a natural remasking mechanism. On language modeling, leave-one-out parameterizations consistently improve UDM generation, while the absorbing construction matches or surpasses masked diffusion. These results suggest that the empirical gap between masked and uniform diffusion is driven less by the choice of marginals themselves than by parameterization and sampling design. The code and models can be found at https://github.com/samsongourevitch/rev_udm.

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have recently emerged as a promising alternative. Unfortunately, these models still underperform the autoregressive counterparts, with the performance gap increasing when reducing the number of sampling steps. Our analysis reveals that this degradation is a consequence of an imperfect approximation used by diffusion models. In this work, we propose Energy-based Diffusion Language Model (EDLM), an energy-based model operating at the full sequence level for each diffusion step, introduced to improve the underlying approximation used by diffusion models. More specifically, we introduce an EBM in a residual form, and show that its parameters can be obtained by leveraging a pretrained autoregressive model or by finetuning a bidirectional transformer via noise contrastive estimation. We also propose an efficient generation algorithm via parallel important sampling. Comprehensive experiments on language modeling benchmarks show that our model can consistently outperform state-of-the-art diffusion models by a significant margin, and approaches autoregressive models' perplexity. We further show that, without any generation performance drop, our framework offers a 1.3times sampling speedup over existing diffusion models.

Autoregressive (AR) transformers have emerged as a powerful paradigm for visual generation, largely due to their scalability, computational efficiency and unified architecture with language and vision. Among them, next scale prediction Visual Autoregressive Generation (VAR) has recently demonstrated remarkable performance, even surpassing diffusion-based models. In this work, we revisit VAR and uncover a theoretical insight: when equipped with a Markovian attention mask, VAR is mathematically equivalent to a discrete diffusion. We term this reinterpretation as Scalable Visual Refinement with Discrete Diffusion (SRDD), establishing a principled bridge between AR transformers and diffusion models. Leveraging this new perspective, we show how one can directly import the advantages of diffusion such as iterative refinement and reduce architectural inefficiencies into VAR, yielding faster convergence, lower inference cost, and improved zero-shot reconstruction. Across multiple datasets, we show that the diffusion based perspective of VAR leads to consistent gains in efficiency and generation.

Multimodal generative models that can understand and generate across multiple modalities are dominated by autoregressive (AR) approaches, which process tokens sequentially from left to right, or top to bottom. These models jointly handle images, text, video, and audio for various tasks such as image captioning, question answering, and image generation. In this work, we explore discrete diffusion models as a unified generative formulation in the joint text and image domain, building upon their recent success in text generation. Discrete diffusion models offer several advantages over AR models, including improved control over quality versus diversity of generated samples, the ability to perform joint multimodal inpainting (across both text and image domains), and greater controllability in generation through guidance. Leveraging these benefits, we present the first Unified Multimodal Discrete Diffusion (UniDisc) model which is capable of jointly understanding and generating text and images for a variety of downstream tasks. We compare UniDisc to multimodal AR models, performing a scaling analysis and demonstrating that UniDisc outperforms them in terms of both performance and inference-time compute, enhanced controllability, editability, inpainting, and flexible trade-off between inference time and generation quality. Code and additional visualizations are available at https://unidisc.github.io.

We introduce Hybrid Autoregressive Transformer (HART), an autoregressive (AR) visual generation model capable of directly generating 1024x1024 images, rivaling diffusion models in image generation quality. Existing AR models face limitations due to the poor image reconstruction quality of their discrete tokenizers and the prohibitive training costs associated with generating 1024px images. To address these challenges, we present the hybrid tokenizer, which decomposes the continuous latents from the autoencoder into two components: discrete tokens representing the big picture and continuous tokens representing the residual components that cannot be represented by the discrete tokens. The discrete component is modeled by a scalable-resolution discrete AR model, while the continuous component is learned with a lightweight residual diffusion module with only 37M parameters. Compared with the discrete-only VAR tokenizer, our hybrid approach improves reconstruction FID from 2.11 to 0.30 on MJHQ-30K, leading to a 31% generation FID improvement from 7.85 to 5.38. HART also outperforms state-of-the-art diffusion models in both FID and CLIP score, with 4.5-7.7x higher throughput and 6.9-13.4x lower MACs. Our code is open sourced at https://github.com/mit-han-lab/hart.

Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional generative approaches such as VAEs and GANs, diffusion models employ a progressive denoising process that transforms noise into meaningful data over multiple iterative steps. This gradual approach enhances their expressiveness and generation quality. Not only that, diffusion models have also been shown to extract meaningful representations from data while learning to generate samples. Despite their success, the application of diffusion models to graph-structured data remains relatively unexplored, primarily due to the discrete nature of graphs, which necessitates discrete diffusion processes distinct from the continuous methods used in other domains. In this work, we leverage the representational capabilities of diffusion models to learn meaningful embeddings for graph data. By training a discrete diffusion model within an autoencoder framework, we enable both effective autoencoding and representation learning tailored to the unique characteristics of graph-structured data. We only need the encoder at the end to extract representations. Our approach demonstrates the potential of discrete diffusion models to be used for graph representation learning.

Recent advances in autoregressive video diffusion have enabled real-time frame streaming, yet existing solutions still suffer from temporal repetition, drift, and motion deceleration. We find that naively applying StreamingLLM-style attention sinks to video diffusion leads to fidelity degradation and motion stagnation. To overcome this, we introduce Deep Forcing, which consists of two training-free mechanisms that address this without any fine-tuning. Specifically, 1) Deep Sink dedicates half of the sliding window to persistent sink tokens and re-aligns their temporal RoPE phase to the current timeline, stabilizing global context during long rollouts. 2) Participative Compression performs importance-aware KV cache pruning that preserves only tokens actively participating in recent attention while safely discarding redundant and degraded history, minimizing error accumulation under out-of-distribution length generation. Together, these components enable over 12x extrapolation (e.g. 5s-trained to 60s+ generation) with better imaging quality than LongLive, better aesthetic quality than RollingForcing, almost maintaining overall consistency, and substantial gains in dynamic degree, all while maintaining real-time generation. Our results demonstrate that training-free KV-cache management can match or exceed training-based approaches for autoregressively streaming long-video generation.

Vision-Language-Action (VLA) models offer a unified framework for robotic manipulation by integrating visual perception, language understanding, and control generation. Yet existing VLA models still struggle to generalize across diverse tasks, scenes, and camera viewpoints, and often produce coarse or unstable actions. We introduce E0, a continuized discrete diffusion framework that formulates action generation as iterative denoising over quantized action tokens. Compared with continuous diffusion policies, E0 offers two key advantages: (1) discrete action tokens align naturally with the symbolic structure of pretrained VLM/VLA backbones, enabling stronger semantic conditioning; and 2. discrete diffusion matches the true quantized nature of real-world robot control-whose hardware constraints (e.g., encoder resolution, control frequency, actuation latency) inherently discretize continuous signals-and therefore benefits from a Bayes-optimal denoiser that models the correct discrete action distribution, leading to stronger generalization. Compared with discrete autoregressive and mask-based discrete diffusion models, E0 supports a significantly larger and finer-grained action vocabulary and avoids the distributional mismatch introduced by masking-based corruptions-yielding more accurate fine-grained action control. We further introduce a spherical viewpoint perturbation augmentation method to improve robustness to camera shifts without additional data. Experiments on LIBERO, VLABench, and ManiSkill show that E0 achieves state-of-the-art performance across 14 diverse environments, outperforming strong baselines by 10.7% on average. Real-world evaluation on a Franka arm confirms that E0 delivers precise, robust, and transferable manipulation, establishing discrete diffusion as a promising direction for generalizable VLA policy learning.

Autoregressive video diffusion is emerging as a promising paradigm for streaming video synthesis, with step distillation serving as the primary means of accelerating inference. Whether speculative decoding, the dominant acceleration strategy for large language models, can be effectively adapted to autoregressive video generation remains an open question, because video blocks are continuous spatiotemporal tensors with no token-level distribution for exact rejection sampling. We introduce SDVG, which brings speculative decoding to block-based autoregressive video diffusion by replacing token verification with an image-quality router. A 1.3B drafter proposes candidate blocks via four denoising steps; each block is VAE-decoded and scored by ImageReward using worst-frame aggregation--taking the minimum per-frame reward to catch single-frame artifacts that averaging would mask. Blocks scoring above a fixed threshold tau are accepted into the 14B target's KV cache; the rest are regenerated by the target. Two additional design choices prove critical: the first block is always force-rejected to anchor scene composition, and tau serves as a single knob that traces a smooth quality-speed Pareto frontier. On 1003 MovieGenVideoBench prompts (832x480), SDVG retains 98.1% of target-only VisionReward quality (0.0773 vs. 0.0788) at a 1.59x speedup with tau=-0.7, and reaches 2.09x at 95.7% quality retention--while consistently outperforming draft-only generation by over +17%. The framework is training-free, requires no architectural changes, and can be seamlessly integrated into existing autoregressive video generation pipelines.

We propose an Authentic Discrete Diffusion (ADD) framework that fundamentally redefines prior pseudo-discrete approaches by preserving core diffusion characteristics directly in the one-hot space through a suite of coordinated mechanisms. Unlike conventional "pseudo" discrete diffusion (PDD) methods, ADD reformulates the diffusion input by directly using float-encoded one-hot class data, without relying on diffusing in the continuous latent spaces or masking policies. At its core, a timestep-conditioned cross-entropy loss is introduced between the diffusion model's outputs and the original one-hot labels. This synergistic design establishes a bridge between discriminative and generative learning. Our experiments demonstrate that ADD not only achieves superior performance on classification tasks compared to the baseline, but also exhibits excellent text generation capabilities on Image captioning. Extensive ablations validate the measurable gains of each component.

Masked (or absorbing) diffusion is actively explored as an alternative to autoregressive models for generative modeling of discrete data. However, existing work in this area has been hindered by unnecessarily complex model formulations and unclear relationships between different perspectives, leading to suboptimal parameterization, training objectives, and ad hoc adjustments to counteract these issues. In this work, we aim to provide a simple and general framework that unlocks the full potential of masked diffusion models. We show that the continuous-time variational objective of masked diffusion models is a simple weighted integral of cross-entropy losses. Our framework also enables training generalized masked diffusion models with state-dependent masking schedules. When evaluated by perplexity, our models trained on OpenWebText surpass prior diffusion language models at GPT-2 scale and demonstrate superior performance on 4 out of 5 zero-shot language modeling tasks. Furthermore, our models vastly outperform previous discrete diffusion models on pixel-level image modeling, achieving 2.78~(CIFAR-10) and 3.42 (ImageNet 64times64) bits per dimension that are comparable or better than autoregressive models of similar sizes.

Autoregressive models have demonstrated remarkable success in sequential data generation, particularly in NLP, but their extension to continuous-domain image generation presents significant challenges. Recent work, the masked autoregressive model (MAR), bypasses quantization by modeling per-token distributions in continuous spaces using a diffusion head but suffers from slow inference due to the high computational cost of the iterative denoising process. To address this, we propose the Fast AutoRegressive model (FAR), a novel framework that replaces MAR's diffusion head with a lightweight shortcut head, enabling efficient few-step sampling while preserving autoregressive principles. Additionally, FAR seamlessly integrates with causal Transformers, extending them from discrete to continuous token generation without requiring architectural modifications. Experiments demonstrate that FAR achieves 2.3times faster inference than MAR while maintaining competitive FID and IS scores. This work establishes the first efficient autoregressive paradigm for high-fidelity continuous-space image generation, bridging the critical gap between quality and scalability in visual autoregressive modeling.

Block-diffusion language models offer a promising path toward faster-than-autoregressive generation by combining block-wise autoregressive decoding with within-block parallel denoising. However, in the few-step regime needed for practical acceleration, standard confidence-thresholded decoding is often brittle: aggressive thresholds hurt quality, while conservative thresholds require unnecessary denoising steps. Existing approaches that address this issue either require additional training or incur extra test-time compute. We present S2D2, a training-free self-speculative decoding framework for block-diffusion language models. Our key observation is that a block-diffusion model becomes autoregressive when the block size is reduced to one, allowing the same pretrained model to act as both drafter and verifier. S2D2 inserts a speculative verification step into standard block-diffusion decoding and uses lightweight routing policies to decide when verification is worth its cost. This yields a hybrid decoding trajectory in which diffusion proposes tokens in parallel, while the autoregressive mode acts as a local sequence-level critic. Across three mainstream block-diffusion families, S2D2 consistently improves the accuracy-speed tradeoff over strong confidence-thresholding baselines. On SDAR, we observe up to 4.7times speedup over autoregressive decoding, and up to 1.57times over a tuned dynamic decoding baseline while improving accuracy by up to 4.5 points. On LLaDA2.1-Mini, S2D2 remains complementary to built-in self-correction, including a conservative setting where it is 4.4times faster than the static baseline with slightly higher accuracy.

We propose SDAR, a Synergistic Diffusion-Autoregression paradigm that unifies the training efficiency of autoregressive models with the parallel inference capability of diffusion. Instead of costly end-to-end diffusion training, SDAR performs a lightweight paradigm conversion that transforms a well-trained autoregressive (AR) model into a blockwise diffusion model through brief, data-efficient adaptation. During inference, SDAR generates sequences autoregressively across blocks for global coherence while decoding all tokens within each block in parallel via a discrete diffusion process. Extensive experiments show that AR models remain substantially more compute-efficient than masked diffusion models, providing a strong foundation for adaptation. Building on this insight, SDAR achieves efficient AR-to-diffusion conversion with minimal cost, preserving AR-level performance while enabling parallel generation. Scaling studies across dense and Mixture-of-Experts architectures confirm that SDAR scales without compromise: larger models exhibit stronger robustness to block size and decoding thresholds, yielding greater speedups without accuracy loss. Beyond efficiency, SDAR demonstrates enhanced reasoning and domain adaptability. Our 30B MoE model surpasses its AR counterpart on challenging scientific reasoning benchmarks such as GPQA and ChemBench, and gains further improvements under test-time scaling methods like majority voting and pass@k. Together, these results establish SDAR as a practical paradigm that combines the strengths of autoregression and diffusion for scalable, high-throughput reasoning.

Diffusion-based neural solvers have shown strong promise for combinatorial optimization (CO), but existing methods typically rely on supervised training with large collections of near-optimal solutions. In this work, we extend adjoint-based trajectory optimization methods to discrete combinatorial domains. We formulate diffusion-based CO as a stochastic control problem over Continuous-Time Markov Chains and introduce discrete adjoint dynamics for propagating optimization signals through discrete generative trajectories. Building on this formulation, we propose Combinatorial Adjoint Matching (CAM), an unsupervised training framework for discrete diffusion solvers with structured and low-variance trajectory-level optimization signals. Empirically, CAM consistently outperforms existing unsupervised diffusion baselines and achieves performance competitive with strong supervised diffusion solvers and even traditional solvers across diverse combinatorial optimization problems. Our code is available at https://github.com/Shengyu-Feng/CAM.

Time series forecasting has been a widely explored task of great importance in many applications. However, it is common that real-world time series data are recorded in a short time period, which results in a big gap between the deep model and the limited and noisy time series. In this work, we propose to address the time series forecasting problem with generative modeling and propose a bidirectional variational auto-encoder (BVAE) equipped with diffusion, denoise, and disentanglement, namely D3VAE. Specifically, a coupled diffusion probabilistic model is proposed to augment the time series data without increasing the aleatoric uncertainty and implement a more tractable inference process with BVAE. To ensure the generated series move toward the true target, we further propose to adapt and integrate the multiscale denoising score matching into the diffusion process for time series forecasting. In addition, to enhance the interpretability and stability of the prediction, we treat the latent variable in a multivariate manner and disentangle them on top of minimizing total correlation. Extensive experiments on synthetic and real-world data show that D3VAE outperforms competitive algorithms with remarkable margins. Our implementation is available at https://github.com/PaddlePaddle/PaddleSpatial/tree/main/research/D3VAE.

Continuous-valued Autoregressive (AR) image generation models have demonstrated notable superiority over their discrete-token counterparts, showcasing considerable reconstruction quality and higher generation fidelity. However, the computational demands of the autoregressive framework result in significant inference overhead. While speculative decoding has proven effective in accelerating Large Language Models (LLMs), their adaptation to continuous-valued visual autoregressive models remains unexplored. This work generalizes the speculative decoding algorithm from discrete tokens to continuous space. By analyzing the intrinsic properties of output distribution, we establish a tailored acceptance criterion for the diffusion distributions prevalent in such models. To overcome the inconsistency that occurred in speculative decoding output distributions, we introduce denoising trajectory alignment and token pre-filling methods. Additionally, we identify the hard-to-sample distribution in the rejection phase. To mitigate this issue, we propose a meticulous acceptance-rejection sampling method with a proper upper bound, thereby circumventing complex integration. Experimental results show that our continuous speculative decoding achieves a remarkable 2.33times speed-up on off-the-shelf models while maintaining the output distribution. Codes will be available at https://github.com/MarkXCloud/CSpD

Current end-to-end autonomous driving systems are fundamentally limited by a mismatch between temporal causal reasoning and global trajectory consistency. Autoregressive (AR) models capture interaction-aware temporal dependencies via causal factorization, but their step-wise decoding leads to error accumulation and suboptimal global structure. In contrast, diffusion models optimize trajectories globally but lack explicit causal constraints, making them unreliable in interactive and safety-critical scenarios. This dichotomy reveals a deeper issue: existing methods treat causal modeling and global optimization as separate paradigms, without a principled way to unify them within a single trajectory distribution. To address this, we propose ChainFlow-VLA, which unifies causal generation and global refinement within a unified probabilistic framework. We formulate planning as a mixture over AR-induced modes and learn Vision-Language Model (VLM)-conditioned residual distributions over these modes. An autoregressive generator (Chain) produces a discrete set of causal trajectory modes, followed by a diffusion-based refiner (Flow) that leverages VLM hidden states as semantic priors to perform mode-conditioned correction in residual space while preserving causal structure. This straightforward conditioning seamlessly injects high-level scene understanding into fine-grained trajectory adjustments. Experiments demonstrate that ChainFlow-VLA achieves robust planning in ambiguous and long-tail scenarios, achieving a state-of-the-art score of 94.85 on the NAVSIM v1 leaderboard, matching human-level performance (94.8). Code will be available at https://github.com/AFARI-Research/ChainFlow-VLA.

We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete diffusion models remain challenging. In this work, we introduce a principled plug-and-play discrete diffusion posterior sampling algorithm based on split Gibbs sampling, which we call SG-DPS. Our algorithm enables reward-guided generation and solving inverse problems in discrete-state spaces. We demonstrate that SG-DPS converges to the true posterior distribution on synthetic benchmarks, and enjoys state-of-the-art posterior sampling performance on a range of benchmarks for discrete data, achieving up to 2x improved performance compared to existing baselines.

Autoregressive (AR) diffusion enables streaming, interactive long-video generation by producing frames causally, yet maintaining coherence over minute-scale horizons remains challenging due to accumulated errors, motion drift, and content repetition. We approach this problem from a memory perspective, treating video synthesis as a recurrent dynamical process that requires coordinated short- and long-term context. We propose VideoSSM, a Long Video Model that unifies AR diffusion with a hybrid state-space memory. The state-space model (SSM) serves as an evolving global memory of scene dynamics across the entire sequence, while a context window provides local memory for motion cues and fine details. This hybrid design preserves global consistency without frozen, repetitive patterns, supports prompt-adaptive interaction, and scales in linear time with sequence length. Experiments on short- and long-range benchmarks demonstrate state-of-the-art temporal consistency and motion stability among autoregressive video generator especially at minute-scale horizons, enabling content diversity and interactive prompt-based control, thereby establishing a scalable, memory-aware framework for long video generation.

Designing biological sequences is an important challenge that requires satisfying complex constraints and thus is a natural problem to address with deep generative modeling. Diffusion generative models have achieved considerable success in many applications. Score-based generative stochastic differential equations (SDE) model is a continuous-time diffusion model framework that enjoys many benefits, but the originally proposed SDEs are not naturally designed for modeling discrete data. To develop generative SDE models for discrete data such as biological sequences, here we introduce a diffusion process defined in the probability simplex space with stationary distribution being the Dirichlet distribution. This makes diffusion in continuous space natural for modeling discrete data. We refer to this approach as Dirchlet diffusion score model. We demonstrate that this technique can generate samples that satisfy hard constraints using a Sudoku generation task. This generative model can also solve Sudoku, including hard puzzles, without additional training. Finally, we applied this approach to develop the first human promoter DNA sequence design model and showed that designed sequences share similar properties with natural promoter sequences.

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been revealed, and several new variants of SDEs are proposed (e.g., sub-VP, critically-damped Langevin) along this line. Despite the empirical success of the hand-crafted fixed forward SDEs, a great quantity of proper forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing the diffusion model, especially the spatial part of the forward SDE. An abstract formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. We demonstrate the theoretical advantage of our method from an optimization perspective. Numerical experiments on synthetic datasets, MINIST and CIFAR10 are also presented to validate the effectiveness of our framework.

Autoregressive video models offer distinct advantages over bidirectional diffusion models in creating interactive video content and supporting streaming applications with arbitrary duration. In this work, we present Next-Frame Diffusion (NFD), an autoregressive diffusion transformer that incorporates block-wise causal attention, enabling iterative sampling and efficient inference via parallel token generation within each frame. Nonetheless, achieving real-time video generation remains a significant challenge for such models, primarily due to the high computational cost associated with diffusion sampling and the hardware inefficiencies inherent to autoregressive generation. To address this, we introduce two innovations: (1) We extend consistency distillation to the video domain and adapt it specifically for video models, enabling efficient inference with few sampling steps; (2) To fully leverage parallel computation, motivated by the observation that adjacent frames often share the identical action input, we propose speculative sampling. In this approach, the model generates next few frames using current action input, and discard speculatively generated frames if the input action differs. Experiments on a large-scale action-conditioned video generation benchmark demonstrate that NFD beats autoregressive baselines in terms of both visual quality and sampling efficiency. We, for the first time, achieves autoregressive video generation at over 30 Frames Per Second (FPS) on an A100 GPU using a 310M model.

One of the most compelling features of global discrete diffusion language models is their global bidirectional contextual capability. However, existing block-based diffusion studies tend to introduce autoregressive priors, which, while offering benefits, can cause models to lose this global coherence at the macro level. To regain global contextual understanding while preserving the advantages of the semi-autoregressive paradigm, we propose Diffusion in Diffusion, a 'draft-then-refine' framework designed to overcome the irreversibility and myopia problems inherent in block diffusion models. Our approach first employs block diffusion to generate rapid drafts using small blocks, then refines these drafts through global bidirectional diffusion with a larger bidirectional receptive field. We utilize snapshot confidence remasking to identify the most critical tokens that require modification, and apply mix-scale training to expand the block diffusion model's global capabilities. Empirical results demonstrate that our approach sets a new benchmark for discrete diffusion models on the OpenWebText dataset. Using only 26% of the fine-tuning budget of baseline models, we reduce generative perplexity from 25.7 to 21.9, significantly narrowing the performance gap with autoregressive models.

Uniform-state discrete diffusion models excel at few-step generation and guidance due to their ability to self-correct, making them preferred over autoregressive or Masked diffusion models in these settings. However, their sampling quality plateaus with ancestral samplers as the number of steps increases. We introduce a family of Predictor-Corrector (PC) samplers for discrete diffusion that generalize prior methods and apply to arbitrary noise processes. When paired with uniform-state diffusion, our samplers outperform ancestral sampling on both language and image modeling, achieving lower generative perplexity at matched unigram entropy on OpenWebText and better FID/IS scores on CIFAR10. Crucially, unlike conventional samplers, our PC methods continue to improve with more sampling steps. Taken together, these findings call into question the assumption that Masked diffusion is the inevitable future of diffusion-based language modeling. Beyond sampling, we develop a memory-efficient curriculum for the Gaussian relaxation training phase, reducing training time by 25% and memory by 33% compared to Duo while maintaining comparable perplexity on OpenWebText and LM1B and strong downstream performance. We release code, checkpoints, and a video-tutorial on: https://s-sahoo.com/duo-ch2

Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized distribution, which is less expressive than AR. Recent Flow Language Models (FLMs) apply continuous flows to language, transporting noise to data with a deterministic ODE that avoids factorized sampling. FLMs operate on one-hot vectors whose dimension scales with the vocabulary size, making FLMs costly to train. Moreover, since all distinct one-hot embeddings are equidistant in ell_2, adding Gaussian noise does not have a clear semantic interpretation (unlike images, where Gaussian noise progressively degrades structure). We introduce S-FLM, a latent FLM in the hypersphere. S-FLM generates sequences by rotating vectors in S^{d-1} along a velocity field learned with cross-entropy, avoiding the overhead of materializing one-hot vectors. Previous FLMs match AR in Generative Perplexity (Gen.\ PPL), but samples with high likelihood are not necessarily correct in verifiable domains such as math and code. S-FLM substantially improves continuous flow language models on large-vocabulary reasoning and closes the gap to masked diffusion under standard-temperature sampling (T=1), while a gap remains under optimized low-temperature (T=0.1) decoding.

Diffusion models have gained significant attention in the realm of image generation due to their exceptional performance. Their success has been recently expanded to text generation via generating all tokens within a sequence concurrently. However, natural language exhibits a far more pronounced sequential dependency in comparison to images, and the majority of existing language models are trained utilizing a left-to-right auto-regressive approach. To account for the inherent sequential characteristic of natural language, we introduce Auto-Regressive Diffusion (AR-Diffusion). AR-Diffusion ensures that the generation of tokens on the right depends on the generated ones on the left, a mechanism achieved through employing a dynamic number of denoising steps that vary based on token position. This results in tokens on the left undergoing fewer denoising steps than those on the right, thereby enabling them to generate earlier and subsequently influence the generation of tokens on the right. In a series of experiments on various text generation tasks including text summarization, machine translation, and common sense generation, AR-Diffusion clearly demonstrated the superiority over existing diffusion language models and that it can be 100timessim600times faster when achieving comparable results. Our code will be publicly released.

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated with the forward diffusion process admits a characterization as the backward component of a forward--backward stochastic differential equation (FBSDE). This result provides a structural description of the score function and clarifies how score estimation errors propagate along the reverse-time dynamics. As a by-product, we also obtain a system of semilinear parabolic PDEs for the score function. Second, we use tools from Schrödinger's problem to relate distributional errors arising in reverse time to corresponding errors in forward time. This approach allows us to control the reverse-time sampling error in a systematic way. Third, combining these results, we derive an explicit upper bound for the total variation distance between the sampling distribution of the discrete-time DDPM algorithm and the target data distribution under general finite noise schedules. The resulting bound separates the contributions of the learning error and the time discretization error. Our analysis highlights the intrinsic probabilistic structure underlying discrete-time DDPMs and provides a clearer understanding of the sources of error in their sampling procedure.

While inference-time scaling through search has revolutionized Large Language Models, translating these gains to image generation has proven difficult. Recent attempts to apply search strategies to continuous diffusion models show limited benefits, with simple random sampling often performing best. We demonstrate that the discrete, sequential nature of visual autoregressive models enables effective search for image generation. We show that beam search substantially improves text-to-image generation, enabling a 2B parameter autoregressive model to outperform a 12B parameter diffusion model across benchmarks. Systematic ablations show that this advantage comes from the discrete token space, which allows early pruning and computational reuse, and our verifier analysis highlights trade-offs between speed and reasoning capability. These findings suggest that model architecture, not just scale, is critical for inference-time optimization in visual generation.

Recent progress in multimodal generation has increasingly combined autoregressive (AR) and diffusion-based approaches, leveraging their complementary strengths: AR models capture long-range dependencies and produce fluent, context-aware outputs, while diffusion models operate in continuous latent spaces to refine high-fidelity visual details. However, existing hybrids often lack systematic guidance on how and why to allocate model capacity between these paradigms. In this work, we introduce MADFormer, a Mixed Autoregressive and Diffusion Transformer that serves as a testbed for analyzing AR-diffusion trade-offs. MADFormer partitions image generation into spatial blocks, using AR layers for one-pass global conditioning across blocks and diffusion layers for iterative local refinement within each block. Through controlled experiments on FFHQ-1024 and ImageNet, we identify two key insights: (1) block-wise partitioning significantly improves performance on high-resolution images, and (2) vertically mixing AR and diffusion layers yields better quality-efficiency balances--improving FID by up to 75% under constrained inference compute. Our findings offer practical design principles for future hybrid generative models.

Discrete diffusion has recently emerged as a promising paradigm in discrete data modeling. However, existing methods typically rely on a fixed rate transition matrix during training, which not only limits the expressiveness of latent representations, a fundamental strength of variational methods, but also constrains the overall design space. To address these limitations, we propose Discrete Markov Bridge, a novel framework specifically designed for discrete representation learning. Our approach is built upon two key components: Matrix Learning and Score Learning. We conduct a rigorous theoretical analysis, establishing formal performance guarantees for Matrix Learning and proving the convergence of the overall framework. Furthermore, we analyze the space complexity of our method, addressing practical constraints identified in prior studies. Extensive empirical evaluations validate the effectiveness of the proposed Discrete Markov Bridge, which achieves an Evidence Lower Bound (ELBO) of 1.38 on the Text8 dataset, outperforming established baselines. Moreover, the proposed model demonstrates competitive performance on the CIFAR-10 dataset, achieving results comparable to those obtained by image-specific generation approaches.

Post-training pretrained autoregressive models (ARMs) into masked diffusion models (MDMs) has emerged as a cost-effective way to overcome the limitations of sequential generation. Yet the internal algorithmic changes induced by this shift remain poorly understood, leaving it unclear whether post-trained MDMs acquire genuine bidirectional reasoning or merely repackage autoregressive heuristics. We address this question through a comparative circuit analysis of ARMs and their MDM counterparts. Our analysis reveals a systematic "mechanism shift" that depends on the structural nature of the task. MDMs largely preserve autoregressive circuitry for tasks driven by local causal dependencies, but for global planning tasks they abandon initialized pathways and exhibit distinct rewiring with increased early-layer processing. At the semantic level, we observe a transition from sharp, localized specialization in ARMs to distributed integration in MDMs. These findings show that diffusion post-training does not simply adjust model parameters, but reorganizes internal computation to support non-sequential global planning.

Diffusion language models are a promising alternative to autoregressive models due to their potential for faster generation. Among discrete diffusion approaches, Masked diffusion currently dominates, largely driven by strong perplexity on language modeling benchmarks. In this work, we present the first scaling law study of uniform-state and interpolating discrete diffusion methods. We also show that Masked diffusion models can be made approximately 12% more FLOPs-efficient when trained with a simple cross-entropy objective. We find that perplexity is informative within a diffusion family but can be misleading across families, where models with worse likelihood scaling may be preferable due to faster and more practical sampling, as reflected by the speed-quality Pareto frontier. These results challenge the view that Masked diffusion is categorically the future of diffusion language modeling and that perplexity alone suffices for cross-algorithm comparison. Scaling all methods to 1.7B parameters, we show that uniform-state diffusion remains competitive on likelihood-based benchmarks and outperforms autoregressive and Masked diffusion models on GSM8K, despite worse validation perplexity. We provide the code, model checkpoints, and video tutorials on the project page: http://s-sahoo.github.io/scaling-dllms

Autoregressive (AR) language modeling is the dominant paradigm for text generation, yet its sequential token-by-token decoding makes inference memory-bound and inefficient. Existing acceleration approaches, such as speculative decoding and diffusion language models, can yield speedups under certain conditions but do not directly address high-load batch serving--the scenario most critical for industrial-scale deployment. We introduce K-Forcing, a push-forward language modeling paradigm for joint next-k-token decoding. K-Forcing distills an existing AR model into a conditional push-forward mapping--one that transforms independent uniform noise variables into a joint sample of multiple future tokens in a single forward pass. This design preserves fixed-length outputs, reuses the AR teacher backbone, and remains compatible with standard AR serving infrastructure. We train this mapping via progressive self-forcing distillation, which gradually expands the prediction window while enabling the student to closely match the sequence distribution of the AR teacher. We evaluate K-Forcing on LM1B and OpenWebText using a standard causal Transformer backbone. When aggressively configured to generate k = 4 tokens per forward pass, K-Forcing delivers approximately 2.4-3.5x speedup across different batch sizes, while incurring modest quality degradation relative to its AR teacher. As inference increasingly dominates the lifetime compute cost of modern LLMs, K-Forcing offers a promising route toward accelerating AR generation under real-world high-load deployment.

We introduce Dream 7B, the most powerful open diffusion large language model to date. Unlike autoregressive (AR) models that generate tokens sequentially, Dream 7B employs discrete diffusion modeling to refine sequences in parallel through iterative denoising. Our model consistently outperforms existing diffusion language models on general, mathematical, and coding tasks. Dream 7B demonstrates superior planning abilities and inference flexibility, including arbitrary-order generation, infilling capabilities, and tunable quality-speed trade-offs. These results are achieved through simple yet effective training techniques, including AR-based LLM initialization and context-adaptive token-level noise rescheduling. We release both Dream-Base and Dream-Instruct to facilitate further research in diffusion-based language modeling.

Autoregressive language models (ARMs) deliver strong likelihoods, but are inherently serial: they generate one token per forward pass, which limits throughput and inflates latency for long sequences. Diffusion Language Models (DLMs) parallelize across positions and thus appear promising for language generation, yet standard discrete diffusion typically needs hundreds to thousands of model evaluations to reach high quality, trading serial depth for iterative breadth. We introduce FS-DFM, Few-Step Discrete Flow-Matching. A discrete flow-matching model designed for speed without sacrificing quality. The core idea is simple: make the number of sampling steps an explicit parameter and train the model to be consistent across step budgets, so one big move lands where many small moves would. We pair this with a reliable update rule that moves probability in the right direction without overshooting, and with strong teacher guidance distilled from long-run trajectories. Together, these choices make few-step sampling stable, accurate, and easy to control. On language modeling benchmarks, FS-DFM with 8 sampling steps achieves perplexity parity with a 1,024-step discrete-flow baseline for generating 1,024 tokens using a similar-size model, delivering up to 128 times faster sampling and corresponding latency/throughput gains.

Auto-bidding plays a crucial role in facilitating online advertising by automatically providing bids for advertisers. Reinforcement learning (RL) has gained popularity for auto-bidding. However, most current RL auto-bidding methods are modeled through the Markovian Decision Process (MDP), which assumes the Markovian state transition. This assumption restricts the ability to perform in long horizon scenarios and makes the model unstable when dealing with highly random online advertising environments. To tackle this issue, this paper introduces AI-Generated Bidding (AIGB), a novel paradigm for auto-bidding through generative modeling. In this paradigm, we propose DiffBid, a conditional diffusion modeling approach for bid generation. DiffBid directly models the correlation between the return and the entire trajectory, effectively avoiding error propagation across time steps in long horizons. Additionally, DiffBid offers a versatile approach for generating trajectories that maximize given targets while adhering to specific constraints. Extensive experiments conducted on the real-world dataset and online A/B test on Alibaba advertising platform demonstrate the effectiveness of DiffBid, achieving 2.81% increase in GMV and 3.36% increase in ROI.

Autoregressive video diffusion models enable streaming generation but often degrade over long rollouts: static scene layouts drift, while mechanisms that improve spatial stability tend to suppress motion, causing natural flows such as water, fire, or smoke to stagnate. We study this stability-motion trade-off in fixed-camera long-horizon nature video generation, where the two failure modes can be more clearly separated than in moving-camera settings. We propose Steady-Forcing, a memory and training framework combining a persistent visual anchor (V-Sink), an exponential moving-average motion memory (EMA-Sink), block-relative temporal encoding, periodic cache purification, and distillation from a Wan2.1-14B teacher with motion-rewarded priors under task-focused configurations. Together, these components are designed to preserve background identity while sustaining visually plausible fluid dynamics over multi-minute autoregressive rollouts. Evaluations across seven baselines show that Steady-Forcing improves long horizon background consistency and imaging quality, while a blind user study indicates stronger perceived stability and motion continuity. The benchmark evaluation further suggest that generic VBench aggregate scores under-penalize fixed-camera artifacts as well as rewarding drift-induced optical flow as Dynamic Degree while not directly penalizing texture hardening or flow stagnation - motivating future task-specific benchmarks for static-camera nature-flow evaluation. Project page: https://minar09.github.io/steadyforcing/

In this work, we provide a systematic survey of Discrete Diffusion Language Models (dLLMs) and Discrete Diffusion Multimodal Language Models (dMLLMs). Unlike autoregressive (AR) models, dLLMs and dMLLMs adopt a multi-token, parallel decoding paradigm using full attention and a denoising-based generation strategy. This paradigm naturally enables parallel generation, fine-grained output controllability, and dynamic, response-aware perception. These capabilities are previously difficult to achieve with AR models. Recently, a growing number of industrial-scale proprietary d(M)LLMs, as well as a large number of open-source academic d(M)LLMs, have demonstrated performance comparable to their autoregressive counterparts, while achieving up to 10x acceleration in inference speed. The advancement of discrete diffusion LLMs and MLLMs has been largely driven by progress in two domains. The first is the development of autoregressive LLMs and MLLMs, which has accumulated vast amounts of data, benchmarks, and foundational infrastructure for training and inference. The second contributing domain is the evolution of the mathematical models underlying discrete diffusion. Together, these advancements have catalyzed a surge in dLLMs and dMLLMs research in early 2025. In this work, we present a comprehensive overview of the research in the dLLM and dMLLM domains. We trace the historical development of dLLMs and dMLLMs, formalize the underlying mathematical frameworks, and categorize representative models. We further analyze key techniques for training and inference, and summarize emerging applications across language, vision-language, and biological domains. We conclude by discussing future directions for research and deployment. Paper collection: https://github.com/LiQiiiii/DLLM-Survey

Vision-Language-Action (VLA) models adapt large vision-language backbones to map images and instructions to robot actions. However, prevailing VLA decoders either generate actions autoregressively in a fixed left-to-right order or attach continuous diffusion or flow matching heads outside the backbone, demanding specialized training and iterative sampling that hinder a unified, scalable architecture. We present Discrete Diffusion VLA, a single-transformer policy that models discretized action chunks with discrete diffusion and is trained with the same cross-entropy objective as the VLM backbone. The design retains diffusion's progressive refinement paradigm while remaining natively compatible with the discrete token interface of VLMs. Our method achieves an adaptive decoding order that resolves easy action elements before harder ones and uses secondary remasking to revisit uncertain predictions across refinement rounds, which improves consistency and enables robust error correction. This unified decoder preserves pretrained vision language priors, supports parallel decoding, breaks the autoregressive bottleneck, and reduces the number of function evaluations. Discrete Diffusion VLA achieves 96.3% avg. SR on LIBERO, 71.2% visual matching on SimplerEnv Fractal and 49.3% overall on SimplerEnv Bridge, improving over both autoregressive and continuous diffusion baselines. These findings indicate that discrete-diffusion action decoder supports precise action modeling and consistent training, laying groundwork for scaling VLA to larger models and datasets.

Discrete diffusion is a promising framework for modeling and generating discrete data. In this work, we present Target Concrete Score Matching (TCSM), a novel and versatile objective for training and fine-tuning discrete diffusion models. TCSM provides a general framework with broad applicability. It supports pre-training discrete diffusion models directly from data samples, and many existing discrete diffusion approaches naturally emerge as special cases of our more general TCSM framework. Furthermore, the same TCSM objective extends to post-training of discrete diffusion models, including fine-tuning using reward functions or preference data, and distillation of knowledge from pre-trained autoregressive models. These new capabilities stem from the core idea of TCSM, estimating the concrete score of the target distribution, which resides in the original (clean) data space. This allows seamless integration with reward functions and pre-trained models, which inherently only operate in the clean data space rather than the noisy intermediate spaces of diffusion processes. Our experiments on language modeling tasks demonstrate that TCSM matches or surpasses current methods. Additionally, TCSM is versatile, applicable to both pre-training and post-training scenarios, offering greater flexibility and sample efficiency.

Recent advances in diffusion models have brought remarkable visual fidelity to instruction-guided image editing. However, their global denoising process inherently entangles the edited region with the entire image context, leading to unintended spurious modifications and compromised adherence to editing instructions. In contrast, autoregressive models offer a distinct paradigm by formulating image synthesis as a sequential process over discrete visual tokens. Their causal and compositional mechanism naturally circumvents the adherence challenges of diffusion-based methods. In this paper, we present VAREdit, a visual autoregressive (VAR) framework that reframes image editing as a next-scale prediction problem. Conditioned on source image features and text instructions, VAREdit generates multi-scale target features to achieve precise edits. A core challenge in this paradigm is how to effectively condition the source image tokens. We observe that finest-scale source features cannot effectively guide the prediction of coarser target features. To bridge this gap, we introduce a Scale-Aligned Reference (SAR) module, which injects scale-matched conditioning information into the first self-attention layer. VAREdit demonstrates significant advancements in both editing adherence and efficiency. On standard benchmarks, it outperforms leading diffusion-based methods by 30\%+ higher GPT-Balance score. Moreover, it completes a 512times512 editing in 1.2 seconds, making it 2.2times faster than the similarly sized UltraEdit. The models are available at https://github.com/HiDream-ai/VAREdit.

Accurately anticipating how complex, diverse scenes will evolve requires models that represent uncertainty, simulate along extended interaction chains, and efficiently explore many plausible futures. Yet most existing approaches rely on dense video or latent-space prediction, expending substantial capacity on dense appearance rather than on the underlying sparse trajectories of points in the scene. This makes large-scale exploration of future hypotheses costly and limits performance when long-horizon, multi-modal motion is essential. We address this by formulating the prediction of open-set future scene dynamics as step-wise inference over sparse point trajectories. Our autoregressive diffusion model advances these trajectories through short, locally predictable transitions, explicitly modeling the growth of uncertainty over time. This dynamics-centric representation enables fast rollout of thousands of diverse futures from a single image, optionally guided by initial constraints on motion, while maintaining physical plausibility and long-range coherence. We further introduce OWM, a benchmark for open-set motion prediction based on diverse in-the-wild videos, to evaluate accuracy and variability of predicted trajectory distributions under real-world uncertainty. Our method matches or surpasses dense simulators in predictive accuracy while achieving orders-of-magnitude higher sampling speed, making open-set future prediction both scalable and practical. Project page: http://compvis.github.io/myriad.

The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds. We provide the code at https://github.com/Daniil-Selikhanovych/ASBM.

The task of video generation requires synthesizing visually realistic and temporally coherent video frames. Existing methods primarily use asynchronous auto-regressive models or synchronous diffusion models to address this challenge. However, asynchronous auto-regressive models often suffer from inconsistencies between training and inference, leading to issues such as error accumulation, while synchronous diffusion models are limited by their reliance on rigid sequence length. To address these issues, we introduce Auto-Regressive Diffusion (AR-Diffusion), a novel model that combines the strengths of auto-regressive and diffusion models for flexible, asynchronous video generation. Specifically, our approach leverages diffusion to gradually corrupt video frames in both training and inference, reducing the discrepancy between these phases. Inspired by auto-regressive generation, we incorporate a non-decreasing constraint on the corruption timesteps of individual frames, ensuring that earlier frames remain clearer than subsequent ones. This setup, together with temporal causal attention, enables flexible generation of videos with varying lengths while preserving temporal coherence. In addition, we design two specialized timestep schedulers: the FoPP scheduler for balanced timestep sampling during training, and the AD scheduler for flexible timestep differences during inference, supporting both synchronous and asynchronous generation. Extensive experiments demonstrate the superiority of our proposed method, which achieves competitive and state-of-the-art results across four challenging benchmarks.

While diffusion models excel at generating high-quality images, prior work reports a significant performance gap between diffusion and autoregressive (AR) methods in language modeling. In this work, we show that simple masked discrete diffusion is more performant than previously thought. We apply an effective training recipe that improves the performance of masked diffusion models and derive a simplified, Rao-Blackwellized objective that results in additional improvements. Our objective has a simple form -- it is a mixture of classical masked language modeling losses -- and can be used to train encoder-only language models that admit efficient samplers, including ones that can generate arbitrary lengths of text semi-autoregressively like a traditional language model. On language modeling benchmarks, a range of masked diffusion models trained with modern engineering practices achieves a new state-of-the-art among diffusion models, and approaches AR perplexity. We release our code at: https://github.com/kuleshov-group/mdlm

Diffusion Policies have demonstrated impressive performance in robotic manipulation tasks. However, their long inference time, resulting from an extensive iterative denoising process, and the need to execute an action chunk before the next prediction to maintain consistent actions limit their applicability to latency-critical tasks or simple tasks with a short cycle time. While recent methods explored distillation or alternative policy structures to accelerate inference, these often demand additional training, which can be resource-intensive for large robotic models. In this paper, we introduce a novel approach inspired by the Real-Time Iteration (RTI) Scheme, a method from optimal control that accelerates optimization by leveraging solutions from previous time steps as initial guesses for subsequent iterations. We explore the application of this scheme in diffusion inference and propose a scaling-based method to effectively handle discrete actions, such as grasping, in robotic manipulation. The proposed scheme significantly reduces runtime computational costs without the need for distillation or policy redesign. This enables a seamless integration into many pre-trained diffusion-based models, in particular, to resource-demanding large models. We also provide theoretical conditions for the contractivity which could be useful for estimating the initial denoising step. Quantitative results from extensive simulation experiments show a substantial reduction in inference time, with comparable overall performance compared with Diffusion Policy using full-step denoising. Our project page with additional resources is available at: https://rti-dp.github.io/.

Uniform-state discrete diffusion models hold the promise of fast text generation due to their inherent ability to self-correct. However, they are typically outperformed by autoregressive models and masked diffusion models. In this work, we narrow this performance gap by leveraging a key insight: Uniform-state diffusion processes naturally emerge from an underlying Gaussian diffusion. Our method, Duo, transfers powerful techniques from Gaussian diffusion to improve both training and sampling. First, we introduce a curriculum learning strategy guided by the Gaussian process, doubling training speed by reducing variance. Models trained with curriculum learning surpass autoregressive models in zero-shot perplexity on 3 of 7 benchmarks. Second, we present Discrete Consistency Distillation, which adapts consistency distillation from the continuous to the discrete setting. This algorithm unlocks few-step generation in diffusion language models by accelerating sampling by two orders of magnitude. We provide the code and model checkpoints on the project page: http://s-sahoo.github.io/duo

Block-wise discrete diffusion offers an attractive balance between parallel generation and causal dependency modeling, making it a promising backbone for vision-language modeling. However, its practical adoption has been limited by high training cost, slow convergence, and instability, which have so far kept it behind strong autoregressive (AR) baselines. We present SDAR-VL, the first systematic application of block-wise discrete diffusion to large-scale vision-language understanding (VLU), together with an integrated framework for efficient and stable training. This framework unifies three components: (1) Asynchronous Block-wise Noise Scheduling to diversify supervision within each batch; (2) Effective Mask Ratio Scaling for unbiased loss normalization under stochastic masking; and (3) a Progressive Beta Noise Curriculum that increases effective mask coverage while preserving corruption diversity. Experiments on 21 single-image, multi-image, and video benchmarks show that SDAR-VL consistently improves training efficiency, convergence stability, and task performance over conventional block diffusion. On this evaluation suite, SDAR-VL sets a new state of the art among diffusion-based vision-language models and, under matched settings, matches or surpasses strong AR baselines such as LLaVA-OneVision as well as the global diffusion baseline LLaDA-V, establishing block-wise diffusion as a practical backbone for VLU.

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.

Reinforcement learning (RL) has been effective for post-training autoregressive (AR) language models, but extending these methods to diffusion language models (DLMs) is challenging due to intractable sequence-level likelihoods. Existing approaches therefore rely on surrogate likelihoods or heuristic approximations, which can introduce bias and obscure the sequential structure of denoising. We formulate diffusion-based sequence generation as a finite-horizon Markov decision process over the denoising trajectory and derive an exact, unbiased policy gradient that decomposes over denoising steps and is expressed in terms of intermediate advantages, without requiring explicit evaluation of the sequence likelihood. To obtain a practical and compute-efficient estimator, we (i) select denoising steps for policy updates via an entropy-guided approximation bound, and (ii) estimate intermediate advantages using a one-step denoising reward naturally provided by the diffusion model, avoiding costly multi-step rollouts. Experiments on coding and logical reasoning benchmarks demonstrate state-of-the-art results, with strong competitive performance on mathematical reasoning, outperforming existing RL post-training approaches for DLMs. Code is available at https://github.com/vishnutez/egspo-dllm-rl.

The rapid progress of large multimodal models has inspired efforts toward unified frameworks that couple understanding and generation. While such paradigms have shown remarkable success in 2D, extending them to 3D remains largely underexplored. Existing attempts to unify 3D tasks under a single autoregressive (AR) paradigm lead to significant performance degradation due to forced signal quantization and prohibitive training cost. Our key insight is that the essential challenge lies not in enforcing a unified autoregressive paradigm, but in enabling effective information interaction between generation and understanding while minimally compromising their inherent capabilities and leveraging pretrained models to reduce training cost. Guided by this perspective, we present the first unified framework for 3D understanding and generation that combines autoregression with diffusion. Specifically, we adopt an autoregressive next-token prediction paradigm for 3D understanding, and a continuous diffusion paradigm for 3D generation. A lightweight transformer bridges the feature space of large language models and the conditional space of 3D diffusion models, enabling effective cross-modal information exchange while preserving the priors learned by standalone models. Extensive experiments demonstrate that our framework achieves state-of-the-art performance across diverse 3D understanding and generation benchmarks, while also excelling in 3D editing tasks. These results highlight the potential of unified AR+diffusion models as a promising direction for building more general-purpose 3D intelligence.

In this work, we propose Mutual Forcing, a framework for fast autoregressive audio-video generation with long-horizon audio-video synchronization. Our approach addresses two key challenges: joint audio-video modeling and fast autoregressive generation. To ease joint audio-video optimization, we adopt a two-stage training strategy: we first train uni-modal generators and then couple them into a unified audio-video model for joint training on paired data. For streaming generation, we ask whether a native fast causal audio-video model can be trained directly, instead of following existing streaming distillation pipelines that typically train a bidirectional model first and then convert it into a causal generator through multiple distillation stages. Our answer is Mutual Forcing, which builds directly on native autoregressive model and integrates few-step and multi-step generation within a single weight-shared model, enabling self-distillation and improved training-inference consistency. The multi-step mode improves the few-step mode via self-distillation, while the few-step mode generates historical context during training to improve training-inference consistency; because the two modes share parameters, these two effects reinforce each other within a single model. Compared with prior approaches such as Self-Forcing, Mutual Forcing removes the need for an additional bidirectional teacher model, supports more flexible training sequence lengths, reduces training overhead, and allows the model to improve directly from real paired data rather than a fixed teacher. Experiments show that Mutual Forcing matches or surpasses strong baselines that require around 50 sampling steps while using only 4 to 8 steps, demonstrating substantial advantages in both efficiency and quality. The project page is available at https://mutualforcing.github.io.

In this work, we propose Causal Autoregressive Diffusion (CARD), a novel framework that unifies the training efficiency of ARMs with the high-throughput inference of diffusion models. CARD reformulates the diffusion process within a strictly causal attention mask, enabling dense, per-token supervision in a single forward pass. To address the optimization instability of causal diffusion, we introduce a soft-tailed masking schema to preserve local context and a context-aware reweighting mechanism derived from signal-to-noise principles. This design enables dynamic parallel decoding, where the model leverages KV-caching to adaptively generate variable-length token sequences based on confidence. Empirically, CARD outperforms existing discrete diffusion baselines while reducing training latency by 3 times compared to block diffusion methods. Our results demonstrate that CARD achieves ARM-level data efficiency while unlocking the latency benefits of parallel generation, establishing a robust paradigm for next-generation efficient LLMs.

In generative models, two paradigms have gained attraction in various applications: next-set prediction-based Masked Generative Models and next-noise prediction-based Non-Autoregressive Models, e.g., Diffusion Models. In this work, we propose using discrete-state models to connect them and explore their scalability in the vision domain. First, we conduct a step-by-step analysis in a unified design space across two types of models including timestep-independence, noise schedule, temperature, guidance strength, etc in a scalable manner. Second, we re-cast typical discriminative tasks, e.g., image segmentation, as an unmasking process from [MASK]tokens on a discrete-state model. This enables us to perform various sampling processes, including flexible conditional sampling by only training once to model the joint distribution. All aforementioned explorations lead to our framework named Discrete Interpolants, which enables us to achieve state-of-the-art or competitive performance compared to previous discrete-state based methods in various benchmarks, like ImageNet256, MS COCO, and video dataset FaceForensics. In summary, by leveraging [MASK] in discrete-state models, we can bridge Masked Generative and Non-autoregressive Diffusion models, as well as generative and discriminative tasks.

Uniform Discrete Diffusion Model (UDM) has recently emerged as a promising paradigm for discrete generative modeling; however, its integration with reinforcement learning remains largely unexplored. We observe that naively applying GRPO to UDM leads to training instability and marginal performance gains. To address this, we propose \Ours, the first framework to integrate UDM with RL. Our method is guided by two key insights: (i) treating the final clean sample as the action provides more accurate and stable optimization signals; and (ii) reconstructing trajectories via the diffusion forward process better aligns probability paths with the pretraining distribution. Additionally, we introduce two strategies, Reduced-Step and CFG-Free, to further improve training efficiency. \Ours significantly improves base model performance across multiple T2I tasks. Notably, GenEval accuracy improves from 69% to 96% and PickScore increases from 20.46 to 23.81, achieving state-of-the-art performance in both continuous and discrete settings. On the OCR benchmark, accuracy rises from 8% to 57%, further validating the generalization ability of our method. Code is available at https://github.com/Yovecent/UDM-GRPO{https://github.com/Yovecent/UDM-GRPO}.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

Recent advances in motion diffusion models have substantially improved the realism of human motion synthesis. However, existing approaches either rely on full-sequence diffusion models with bidirectional generation, which limits temporal causality and real-time applicability, or autoregressive models that suffer from instability and cumulative errors. In this work, we present Causal Motion Diffusion Models (CMDM), a unified framework for autoregressive motion generation based on a causal diffusion transformer that operates in a semantically aligned latent space. CMDM builds upon a Motion-Language-Aligned Causal VAE (MAC-VAE), which encodes motion sequences into temporally causal latent representations. On top of this latent representation, an autoregressive diffusion transformer is trained using causal diffusion forcing to perform temporally ordered denoising across motion frames. To achieve fast inference, we introduce a frame-wise sampling schedule with causal uncertainty, where each subsequent frame is predicted from partially denoised previous frames. The resulting framework supports high-quality text-to-motion generation, streaming synthesis, and long-horizon motion generation at interactive rates. Experiments on HumanML3D and SnapMoGen demonstrate that CMDM outperforms existing diffusion and autoregressive models in both semantic fidelity and temporal smoothness, while substantially reducing inference latency.

Diffusion models have emerged as a powerful paradigm for modern generative modeling, demonstrating strong potential for large language models (LLMs). Unlike conventional autoregressive (AR) models that generate tokens sequentially, diffusion models enable parallel token sampling, leading to faster generation and eliminating left-to-right generation constraints. Despite their empirical success, the theoretical understanding of diffusion model approaches remains underdeveloped. In this work, we develop convergence guarantees for diffusion language models from an information-theoretic perspective. Our analysis demonstrates that the sampling error, measured by the Kullback-Leibler (KL) divergence, decays inversely with the number of iterations T and scales linearly with the mutual information between tokens in the target text sequence. In particular, we establish matching upper and lower bounds, up to some constant factor, to demonstrate the tightness of our convergence analysis. These results offer novel theoretical insights into the practical effectiveness of diffusion language models.

Despite a growing interest in diffusion-based language models, existing work has not shown that these models can attain nontrivial likelihoods on standard language modeling benchmarks. In this work, we take the first steps towards closing the likelihood gap between autoregressive and diffusion-based language models, with the goal of building and releasing a diffusion model which outperforms a small but widely-known autoregressive model. We pursue this goal through algorithmic improvements, scaling laws, and increased compute. On the algorithmic front, we introduce several methodological improvements for the maximum-likelihood training of diffusion language models. We then study scaling laws for our diffusion models and find compute-optimal training regimes which differ substantially from autoregressive models. Using our methods and scaling analysis, we train and release Plaid 1B, a large diffusion language model which outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent samples in unconditional and zero-shot control settings.

Modeling long-range dependencies in time series generation poses a fundamental trade-off between representational capacity and computational efficiency. Traditional temporal diffusion models suffer from local entanglement and the O(L^2) cost of attention mechanisms. We address these limitations by introducing PaCoDi (Parallel Complex Diffusion), a spectral-native architecture that decouples generative modeling in the frequency domain. PaCoDi fundamentally alters the problem topology: the Fourier Transform acts as a diagonalizing operator, converting locally coupled temporal signals into globally decorrelated spectral components. Theoretically, we prove the Quadrature Forward Diffusion and Conditional Reverse Factorization theorem, demonstrating that the complex diffusion process can be split into independent real and imaginary branches. We bridge the gap between this decoupled theory and data reality using a Mean Field Theory (MFT) approximation reinforced by an interactive correction mechanism. Furthermore, we generalize this discrete DDPM to continuous-time Frequency SDEs, rigorously deriving the Spectral Wiener Process describe the differential spectral Brownian motion limit. Crucially, PaCoDi exploits the Hermitian Symmetry of real-valued signals to compress the sequence length by half, achieving a 50% reduction in attention FLOPs without information loss. We further derive a rigorous Heteroscedastic Loss to handle the non-isotropic noise distribution on the compressed manifold. Extensive experiments show that PaCoDi outperforms existing baselines in both generation quality and inference speed, offering a theoretically grounded and computationally efficient solution for time series modeling.

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard Gaussian noise with super-imposed Poisson jumps representing a finite activity Levy process. The generative process is shown to be governed by a generalized score function that depends on the jump amplitude distribution and can be estimated by minimizing a simple MSE loss as in conventional Gaussian models. Both probability flow ODE and SDE formulations are derived using basic technical effort. A detailed implementation for a pure jump process with Laplace distributed amplitudes yields a generalized score function in closed analytical form and is shown to outperform the equivalent Gaussian model in specific parameter regimes.

Diffusion models have recently been shown to be relevant for high-quality speech generation. Most work has been focused on generating spectrograms, and as such, they further require a subsequent model to convert the spectrogram to a waveform (i.e., a vocoder). This work proposes a diffusion probabilistic end-to-end model for generating a raw speech waveform. The proposed model is autoregressive, generating overlapping frames sequentially, where each frame is conditioned on a portion of the previously generated one. Hence, our model can effectively synthesize an unlimited speech duration while preserving high-fidelity synthesis and temporal coherence. We implemented the proposed model for unconditional and conditional speech generation, where the latter can be driven by an input sequence of phonemes, amplitudes, and pitch values. Working on the waveform directly has some empirical advantages. Specifically, it allows the creation of local acoustic behaviors, like vocal fry, which makes the overall waveform sounds more natural. Furthermore, the proposed diffusion model is stochastic and not deterministic; therefore, each inference generates a slightly different waveform variation, enabling abundance of valid realizations. Experiments show that the proposed model generates speech with superior quality compared with other state-of-the-art neural speech generation systems.

An increasing number of autoregressive models, such as MAR, FlowAR, xAR, and Harmon adopt diffusion sampling to improve the quality of image generation. However, this strategy leads to low inference efficiency, because it usually takes 50 to 100 steps for diffusion to sample a token. This paper explores how to effectively address this issue. Our key motivation is that as more tokens are generated during the autoregressive process, subsequent tokens follow more constrained distributions and are easier to sample. To intuitively explain, if a model has generated part of a dog, the remaining tokens must complete the dog and thus are more constrained. Empirical evidence supports our motivation: at later generation stages, the next tokens can be well predicted by a multilayer perceptron, exhibit low variance, and follow closer-to-straight-line denoising paths from noise to tokens. Based on our finding, we introduce diffusion step annealing (DiSA), a training-free method which gradually uses fewer diffusion steps as more tokens are generated, e.g., using 50 steps at the beginning and gradually decreasing to 5 steps at later stages. Because DiSA is derived from our finding specific to diffusion in autoregressive models, it is complementary to existing acceleration methods designed for diffusion alone. DiSA can be implemented in only a few lines of code on existing models, and albeit simple, achieves 5-10times faster inference for MAR and Harmon and 1.4-2.5times for FlowAR and xAR, while maintaining the generation quality.

We present Bit Diffusion: a simple and generic approach for generating discrete data with continuous state and continuous time diffusion models. The main idea behind our approach is to first represent the discrete data as binary bits, and then train a continuous diffusion model to model these bits as real numbers which we call analog bits. To generate samples, the model first generates the analog bits, which are then thresholded to obtain the bits that represent the discrete variables. We further propose two simple techniques, namely Self-Conditioning and Asymmetric Time Intervals, which lead to a significant improvement in sample quality. Despite its simplicity, the proposed approach can achieve strong performance in both discrete image generation and image captioning tasks. For discrete image generation, we significantly improve previous state-of-the-art on both CIFAR-10 (which has 3K discrete 8-bit tokens) and ImageNet-64x64 (which has 12K discrete 8-bit tokens), outperforming the best autoregressive model in both sample quality (measured by FID) and efficiency. For image captioning on MS-COCO dataset, our approach achieves competitive results compared to autoregressive models.

Recent advances in autoregressive (AR) models have demonstrated their potential to rival diffusion models in image synthesis. However, for complex spatially-conditioned generation, current AR approaches rely on fine-tuning the pre-trained model, leading to significant training costs. In this paper, we propose the Efficient Control Model (ECM), a plug-and-play framework featuring a lightweight control module that introduces control signals via a distributed architecture. This architecture consists of context-aware attention layers that refine conditional features using real-time generated tokens, and a shared gated feed-forward network (FFN) designed to maximize the utilization of its limited capacity and ensure coherent control feature learning. Furthermore, recognizing the critical role of early-stage generation in determining semantic structure, we introduce an early-centric sampling strategy that prioritizes learning early control sequences. This approach reduces computational cost by lowering the number of training tokens per iteration, while a complementary temperature scheduling during inference compensates for the resulting insufficient training of late-stage tokens. Extensive experiments on scale-based AR models validate that our method achieves high-fidelity and diverse control over image generation, surpassing existing baselines while significantly improving both training and inference efficiency.