Daily Papers

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.

Aligning diffusion models to downstream tasks often requires finetuning new models or gradient-based guidance at inference time to enable sampling from the reward-tilted posterior. In this work, we explore a simple inference-time gradient-free guidance approach, called controlled denoising (CoDe), that circumvents the need for differentiable guidance functions and model finetuning. CoDe is a blockwise sampling method applied during intermediate denoising steps, allowing for alignment with downstream rewards. Our experiments demonstrate that, despite its simplicity, CoDe offers a favorable trade-off between reward alignment, prompt instruction following, and inference cost, achieving a competitive performance against the state-of-the-art baselines. Our code is available at: https://github.com/anujinho/code.

Masked diffusion models (MDMs) are a potential alternative to autoregressive models (ARMs) for language generation, but generation quality depends critically on the generation order. Prior work either hard-codes an ordering (e.g., blockwise left-to-right) or learns an ordering policy for a pretrained MDM, which incurs extra cost and can yield suboptimal solutions due to the two-stage optimization. Motivated by this, we propose order-expressive masked diffusion model (OeMDM) for a broad class of diffusion generative processes with various generation orders, enabling the interpretation of MDM, ARM, and block diffusion in a single framework. Furthermore, building on OeMDM, we introduce learnable-order masked diffusion model (LoMDM), which jointly learns the generation ordering and diffusion backbone through a single objective from scratch, enabling the diffusion model to generate text in context-dependent ordering. Empirically, we confirm that LoMDM outperforms various discrete diffusion models across multiple language modeling benchmarks.

The recent surge of interest in comprehensive multimodal models has necessitated the unification of diverse modalities. However, the unification suffers from disparate methodologies. Continuous visual generation necessitates the full-sequence diffusion-based approach, despite its divergence from the autoregressive modeling in the text domain. We posit that autoregressive modeling, i.e., predicting the future based on past deterministic experience, remains crucial in developing both a visual generation model and a potential unified multimodal model. In this paper, we explore an interpolation between the autoregressive modeling and full-parameters diffusion to model visual information. At its core, we present ACDiT, an Autoregressive blockwise Conditional Diffusion Transformer, where the block size of diffusion, i.e., the size of autoregressive units, can be flexibly adjusted to interpolate between token-wise autoregression and full-sequence diffusion. ACDiT is easy to implement, as simple as creating a Skip-Causal Attention Mask (SCAM) during training. During inference, the process iterates between diffusion denoising and autoregressive decoding that can make full use of KV-Cache. We verify the effectiveness of ACDiT on image and video generation tasks. We also demonstrate that benefitted from autoregressive modeling, ACDiT can be seamlessly used in visual understanding tasks despite being trained on the diffusion objective. The analysis of the trade-off between autoregressive modeling and diffusion demonstrates the potential of ACDiT to be used in long-horizon visual generation tasks. These strengths make it promising as the backbone of future unified models.

Is the uniform-state diffusion framework a more powerful paradigm for discrete diffusion? Recent studies indicate that this may be the case. In combination with predictor-corrector samplers, uniform-state diffusion models (USDMs) produce samples of higher-quality than masked diffusion models (MDMs), and USDMs equal or outperform MDMs in downstream tasks, even though they exhibit greater perplexity. Two issues remain unresolved. First, existing work compares uniform and masked diffusion with un-informed correctors that re-inject noise at random positions, rather than targeting tokens most likely to be wrong. Second, prior work compares full-sequence diffusion models, so we do not know whether the same conclusion holds when tokens are generated block by block. To address these issues, we introduce BlockGen, a blockwise sequence model that we instantiate with both masked and uniform diffusion. BlockGen trains on a mixture of block sizes and its likelihood interpolates between AR and pure diffusion more finely than models with a fixed block size. BlockGen enables AR-informed predictor-corrector sampling (ARPC), which combines AR and diffusion predictions to re-generate unlikely tokens without an auxiliary verifier. Under ancestral sampling, uniform outperforms masked in the block-by-block setting, especially in the few-step regime. Under ARPC, the gap closes and reverses at high NFE. With block size 16 on GSM8K, MDMs reach slightly higher accuracy than USDMs, and we observe a similar trend in Generative Perplexity on OpenWebText. Find our code at https://github.com/jdeschena/blockgen.

When one ball strikes another, then another, video models should predict the consequences of each bounce. In controlled experiments on multi-ball hard-sphere dynamics, we find that the performance of standard bidirectional video diffusion degrades as the causal chain lengthens, even when provided more denoising steps. In a length-matched single-ball control, where ball-ball interactions are absent, the degradation largely disappears, isolating dependent-event structure rather than video length as the cause. Across intervention studies, methods that increase effective serial computation improve performance disproportionately, including autoregressive/blockwise generation and architectural depth. We identify this pattern as the seriality gap: a mismatch between tasks requiring growing serial computation and video diffusion models whose denoising loop does not provide scalable serial compute. We then prove that, for deterministic video prediction, denoising steps do not add serial computation beyond the backbone, indicating a structural obstacle for video diffusion on serial reasoning and simulation tasks.

Large Language Models (LLMs) demonstrate their reasoning ability through chain-of-thought (CoT) generation. However, LLM's autoregressive decoding may limit the ability to revisit and refine earlier tokens in a holistic manner, which can also lead to inefficient exploration for diverse solutions. In this paper, we propose LaDiR (Latent Diffusion Reasoner), a novel reasoning framework that unifies the expressiveness of continuous latent representation with the iterative refinement capabilities of latent diffusion models for an existing LLM. We first construct a structured latent reasoning space using a Variational Autoencoder (VAE) that encodes text reasoning steps into blocks of thought tokens, preserving semantic information and interpretability while offering compact but expressive representations. Subsequently, we utilize a latent diffusion model that learns to denoise a block of latent thought tokens with a blockwise bidirectional attention mask, enabling longer horizon and iterative refinement with adaptive test-time compute. This design allows efficient parallel generation of diverse reasoning trajectories, allowing the model to plan and revise the reasoning process holistically. We conduct evaluations on a suite of mathematical reasoning and planning benchmarks. Empirical results show that LaDiR consistently improves accuracy, diversity, and interpretability over existing autoregressive, diffusion-based, and latent reasoning methods, revealing a new paradigm for text reasoning with latent diffusion.

Diffusion large language models (dLLMs) have recently emerged as a promising alternative to autoregressive (AR) LLMs, offering faster inference through parallel or blockwise decoding. However, their masked language modeling formulation remains incompatible with standard token-level speculative decoding, one of the most effective acceleration techniques for AR models. In AR decoding, the causal mask preserves temporally valid token-level contexts, enabling a target model to verify multiple drafted tokens in a single forward pass. In contrast, dLLMs rely on mask tokens and bidirectional attention, causing the effective context to change across denoising steps and preventing direct token-level speculative verification. To bridge this gap, we propose a simple but effective speculative decoding algorithm for diffusion language models, named SimSD, which mainly adopts a plug-and-play masking strategy that equips dLLMs with temporally valid token-level contexts for speculative decoding. Our method explicitly introduces reference tokens from draft-model predictions and designs an attention mask that regulates their interaction with current-step tokens, allowing dLLMs to compute valid logits for drafted tokens in a single forward pass. This restores the key verification ability provided by causal masking in AR models while preserving the parallel decoding advantages of dLLMs. The proposed method is training-free and can be flexibly integrated with other acceleration techniques such as KV cache and blockwise decoding. Experiments on SDAR-family dLLMs across four benchmarks show that our method achieves up to 7.46x higher decoding throughput while maintaining and even improving average generation quality.

Diffusion Language Models (dLLMs) have emerged as promising alternatives to Auto-Regressive (AR) models. While recent efforts have validated their pre-training potential and accelerated inference speeds, the post-training landscape for dLLMs remains underdeveloped. Existing methods suffer from computational inefficiency and objective mismatches between training and inference, severely limiting performance on complex reasoning tasks such as mathematics. To address this, we introduce DiRL, an efficient post-training framework that tightly integrates FlexAttention-accelerated blockwise training with LMDeploy-optimized inference. This architecture enables a streamlined online model update loop, facilitating efficient two-stage post-training (Supervised Fine-Tuning followed by Reinforcement Learning). Building on this framework, we propose DiPO, the first unbiased Group Relative Policy Optimization (GRPO) implementation tailored for dLLMs. We validate our approach by training DiRL-8B-Instruct on high-quality math data. Our model achieves state-of-the-art math performance among dLLMs and surpasses comparable models in the Qwen2.5 series on several benchmarks.

Diffusion large language models (dLLMs) offer a promising alternative to autoregressive decoding by iteratively refining masked sequences, enabling parallel token updates and bidirectional conditioning. Their practical efficiency, however, is limited by sampling procedures that execute a fixed number of reverse denoising steps selected before decoding, spending computation on already-stable positions and sometimes committing unstable ones too early. We present LESS, a training-free, model-agnostic adaptive sampler that treats token commitment as an online stopping problem. LESS implements mutual-stability sampling through a joint stability rule that makes a masked position eligible for unmasking only when its top-1 prediction has high confidence, its top-1 token persists across recent reverse steps, and its predictive distribution is stable under top-K inter-step Jensen--Shannon divergence. We evaluate LESS on Dream-7B, LLaDA-8B, and LLaDA-1.5-8B, covering full-sequence diffusion and semi-autoregressive blockwise sampling regimes, across seven benchmarks spanning general knowledge, math, and code. LESS improves average accuracy over strong training-free adaptive samplers while using 72.1% fewer reverse steps than fixed-budget decoding. Since each reverse step requires a Transformer forward pass, these step-count reductions translate into fewer forward evaluations, lower measured wall-clock latency, and lower estimated inference compute.

Diffusion large language models (dLLMs), which offer bidirectional context and flexible masked-denoising generation, are emerging as a compelling alternative to autoregressive (AR) LLMs. However, like AR LLMs, their model sizes continue to grow, motivating weight compression for deployment. Although post-training quantization (PTQ) is effective for AR LLMs, directly transferring it to dLLMs at 2-bit leads to unsatisfactory performance. To tackle these challenges, we propose Quant-dLLM, an ultra-low-bit PTQ framework tailored to dLLMs. Since masked-denoising activations in dLLMs differ from the fully visible signals assumed by standard PTQ methods, we introduce Masked Calibration Simulation (MCS) to align calibration with the timestep-dependent masking, which yields more reliable calibrations. Moreover, we propose a Data-aware Any-order Quantizer (DAQ) that learns ultra-low-bit weight representations via an optimization algorithm. It performs iterative approximation guided by our simulated calibration data. In addition, under a strict 2-bit budget, we introduce Adaptive Blockwise Mixed Precision (ABMP), a sensitivity-based precision allocation scheme that adaptively assigns bit width across channel groups. When restricted to 2-bit precision, Quant-dLLM consistently achieves higher accuracy than state-of-the-art (SOTA) AR-transfer PTQ methods on dLLMs. The code and models will be available at: https://github.com/ZTA2785/Quant-dLLM.

Training large neural networks with end-to-end backpropagation creates significant memory bottlenecks, limiting accessibility to state-of-the-art AI research. We propose DiffusionBlocks, a novel training framework that interprets neural network blocks as performing denoising operations in a continuous-time diffusion process. By partitioning the network into independently trainable blocks and optimizing noise level assignments based on equal cumulative probability mass, our approach achieves significant memory efficiency while maintaining competitive performance compared to traditional backpropagation in generative tasks. Experiments on image generation and language modeling tasks demonstrate memory reduction proportional to the number of blocks while achieving superior performance. DiffusionBlocks provides a promising pathway for democratizing access to large-scale neural network training with limited computational resources.

Autoregressive (AR) large language models (LLMs) have achieved remarkable performance across a wide range of natural language tasks, yet their inherent sequential decoding limits inference efficiency. In this work, we propose Fast-dLLM v2, a carefully designed block diffusion language model (dLLM) that efficiently adapts pretrained AR models into dLLMs for parallel text generation, requiring only approximately 1B tokens of fine-tuning. This represents a 500x reduction in training data compared to full-attention diffusion LLMs such as Dream (580B tokens), while preserving the original model's performance. Our approach introduces a novel training recipe that combines a block diffusion mechanism with a complementary attention mask, enabling blockwise bidirectional context modeling without sacrificing AR training objectives. To further accelerate decoding, we design a hierarchical caching mechanism: a block-level cache that stores historical context representations across blocks, and a sub-block cache that enables efficient parallel generation within partially decoded blocks. Coupled with our parallel decoding pipeline, Fast-dLLM v2 achieves up to 2.5x speedup over standard AR decoding without compromising generation quality. Extensive experiments across diverse benchmarks demonstrate that Fast-dLLM v2 matches or surpasses AR baselines in accuracy, while delivering state-of-the-art efficiency among dLLMs - marking a significant step toward the practical deployment of fast and accurate LLMs. Code and model will be publicly released.

Group Relative Policy Optimization (GRPO) is highly effective for post-training autoregressive (AR) language models, yet its direct application to diffusion large language models (dLLMs) often triggers reward collapse. We identify two sources of incompatibility. First, GRPO relies on importance ratios defined by sequence probabilities, which are intractable in dLLMs and must be estimated (e.g., via ELBO-based or mean-field likelihood proxies), yielding inherently noisy ratios. Second, standard GRPO's formulation is not designed for estimated ratios: its conditional clipping can be anomalously bypassed by model-agnostic estimation noise, producing gradient spikes, while its fixed group-size normalization amplifies gradient-magnitude fluctuations under high-variance ratio estimates. We show these effects form a self-reinforcing instability loop that drives policy drift and further increases ratio variance. To break this loop, we propose StableDRL, a reformulation of GRPO tailored for dLLMs that uses (i) unconditional clipping to suppress outlier-induced spikes and (ii) self-normalization to constrain updates within the convex hull of per-sample gradients. We further extend StableDRL to block-wise diffusion models via a staircase attention mechanism.

Diffusion language models (DLMs) generate text through iterative denoising, but inference requires full-sequence attention at every iteration, resulting in substantial redundant computation on masked tokens. Block-wise diffusion can reduce this cost, yet it typically relies on retraining and constrained update orders, limiting its direct applicability to pretrained DLMs. Our token-level analysis reveals pronounced structural locality in DLM inference. Decoding is driven by a small set of prefix-localized active tokens; the influence of distant undecoded context diminishes rapidly, and decoded tokens exhibit stage-wise temporal stability, enabling reuse of intermediate representations except for a brief post-decode transient. Motivated by these observations, we propose \placeholderThe source code is available at https://github.com/vhicrgit/Window-Diffusion., a window-based token pruning and caching method for inference. We maintain a local computation window that slides rightward as denoising progresses, and partition undecoded tokens into: (i) active tokens that are computed online, (ii) buffer tokens whose KV states are cached and periodically refreshed, and (iii) far-field tokens that are pruned outside the window. Computation is restricted to active and buffer tokens within the window, while far-field tokens are omitted at each stage. Experiments on LLaDA and Dream show that, under matched compute budgets, our method achieves up to 99times inference speedup while largely preserving generation performance.

Diffusion language models enable parallel token generation through block-wise decoding, but their irreversible commitments can lead to stagnation, where the reverse diffusion process fails to make further progress under a suboptimal context.We propose Reversible Diffusion Decoding (RDD), a decoding framework that introduces reversibility into block-wise diffusion generation. RDD detects stagnation as a state-dependent failure of the reverse process and enables efficient backtracking to earlier blocks without recomputation via cached model states. To avoid repeated failure trajectories, RDD applies confidence-guided re-masking to selectively reinitialize uncertain tokens while preserving reliable context.This reversible formulation allows decoding to recover from early commitment errors while maintaining the parallel efficiency of diffusion-based generation. Experiments show that RDD improves generation robustness and quality over baselines with minimal computational overhead.

Large language models (LLMs) excel at generation but dominant autoregressive (AR) decoding is inherently sequential, creating a throughput bottleneck. Diffusion Language Models (DLMs)--especially block-wise variants--enable parallel generation and intra-block bidirectional reasoning, yet training large DLMs from scratch is costly and wastes the knowledge in mature AR checkpoints. Prior "adaptation" attempts either modify logits or randomly grow attention masks to full-sequence diffusion, or simply transplant AR weights into a block-diffusion recipe, leaving a fundamental mismatch between AR causality and block-wise bidirectionality unaddressed. We reframe adaptation as a intra-paradigm path from AR to Block-Diffusion by viewing AR as Block-Diffusion with blocksize=1. Concretely, we design the pathway of adaptation as follows: we use a context-causal attention mask (causal in context, bidirectional only within the active block), an efficient parallel adaptation procedure, an auxiliary AR loss to maximize data utilization and retain pretrained knowledge, and gradual increment of the generation block size. The recipe integrates cleanly with masked block-diffusion and maintains train-inference consistency. Built on these components, NBDiff-7B (Base and Instruct) could inherit the long-context modeling and reasoning capabilities, and achieve state-of-the-art performance among the 7B-class DLMs, delivering strong gains on general-knowledge, math, and code benchmarks over strong baselines. These results demonstrate that principled AR-to-block-diffusion adaptation is an effective and compute-efficient alternative to training DLMs from scratch. Codes: https://github.com/YuchuanTian/NBDiff.

Interactive streaming music generation promises the use of generative models for live performance and co-creation that is impossible with offline models. However, SOTA models exist in the discrete-AR regime, requiring industrial levels of compute for both training and inference. In this work, we investigate whether audio diffusion models, with their wide support in the open-source community but non-streaming bidirectional nature, can be repurposed efficiently into interactive models accessible on consumer hardware. By taking a critical look at the modern pipeline for block-wise outpainting diffusion, we identify critical inefficiencies during inference that result in strictly worse computational efficiency than their discrete-AR counterparts. We propose Live Music Diffusion Models (LMDMs), a simple modification of the generative diffusion process that recovers, and then outperforms, the inference complexity of the discrete Live Music Models (LMMs) through block-wise KV Caching. Unlike LMMs, LMDMs further enable stable post-training alignment through our novel ARC-Forcing paradigm, reducing error accumulation without any explicit RL or reward models. We demonstrate the application of LMDMs in a number of creative domains, including text-conditioned generation, sketch-based music synthesis, and jamming. We finally show how LMDMs can be used as a generative instrument in a real artist-AI collaboration, utilizing LMDMs as a "generative delay" to transform musicians' improvisation live for variable timbral effects while running locally on a consumer gaming laptop.

Diffusion language models offer a promising alternative to autoregressive models due to their potential for parallel and iterative generation. However, existing approaches use a single network for both context representation and iterative denoising, forcing one model to serve both roles and limiting its capacity for either role. We propose TwoTower, a block-wise autoregressive diffusion model that decouples these roles into two towers: a frozen AR context tower that causally processes clean tokens, and a trainable diffusion denoiser tower with bidirectional block attention that refines noisy blocks via cross-attention to the context. Built on Nemotron-3-Nano-30B-A3B, an open-weight 30B hybrid Mamba-Transformer MoE model, and trained on approximately 2.1T tokens, Nemotron-TwoTower retains 98.7% of the autoregressive baseline's quality while offering 2.42X higher wall-clock generation throughput. We release the code and model weights at https://huggingface.co/collections/nvidia/nemotron-twotower.

Generating high-fidelity synthetic GPS trajectories is increasingly important for applications in transportation, urban planning, and what-if scenario simulation, especially as privacy concerns limit access to real-world mobility data. Existing trajectory generation models face a trade-off between efficiency and faithfulness to road network topology: continuous-space methods enable fast generation but ignore the road network, while topology-aware approaches rely on search-based autoregressive decoding that limits generation speed. We propose TrajDLM, a topology-aware trajectory generation framework based on block diffusion language models that bridges this gap. TrajDLM models trajectories as sequences of discrete road segments, combining a block diffusion backbone for efficient denoising, topology-aware embeddings from a road network encoder, and topology-constrained sampling to ensure coherent and realistic trajectories. Across three city-scale datasets, TrajDLM achieves strong performance on fine-grained local similarity metrics while being up to 2.8times faster than prior work, and demonstrates strong zero-shot transfer across domains, including unseen transportation modes. These results highlight the effectiveness of block-wise discrete diffusion as a scalable approach to accurate and efficient trajectory generation. Our code is available at https://github.com/cruiseresearchgroup/TrajDLM/

Diffusion models have demonstrated impressive image synthesis performance, yet many UNet-based models are trained at certain fixed resolutions. Their quality tends to degrade when generating images at out-of-training resolutions. We trace this issue to resolution-dependent parameter behaviors, where weights that function well at the default resolution can become adverse when spatial scales shift, weakening semantic alignment and causing structural instability in the UNet architecture. Based on this analysis, this paper introduces CR-Diff, a novel method that improves the cross-resolution visual consistency by pruning some parameters of the diffusion model. Specifically, CR-Diff has two stages. It first performs block-wise pruning to selectively eliminate adverse weights. Then, a pruned output amplification is conducted to further purify the pruned predictions. Empirically, extensive experiments suggest that CR-Diff can improve perceptual fidelity and semantic coherence across various diffusion backbones and unseen resolutions, while largely preserving the performance at default resolutions. Additionally, CR-Diff supports prompt-specific refinement, enabling quality enhancement on demand.

The success of the text-guided diffusion model has inspired the development and release of numerous powerful diffusion models within the open-source community. These models are typically fine-tuned on various expert datasets, showcasing diverse denoising capabilities. Leveraging multiple high-quality models to produce stronger generation ability is valuable, but has not been extensively studied. Existing methods primarily adopt parameter merging strategies to produce a new static model. However, they overlook the fact that the divergent denoising capabilities of the models may dynamically change across different states, such as when experiencing different prompts, initial noises, denoising steps, and spatial locations. In this paper, we propose a novel ensembling method, Adaptive Feature Aggregation (AFA), which dynamically adjusts the contributions of multiple models at the feature level according to various states (i.e., prompts, initial noises, denoising steps, and spatial locations), thereby keeping the advantages of multiple diffusion models, while suppressing their disadvantages. Specifically, we design a lightweight Spatial-Aware Block-Wise (SABW) feature aggregator that adaptive aggregates the block-wise intermediate features from multiple U-Net denoisers into a unified one. The core idea lies in dynamically producing an individual attention map for each model's features by comprehensively considering various states. It is worth noting that only SABW is trainable with about 50 million parameters, while other models are frozen. Both the quantitative and qualitative experiments demonstrate the effectiveness of our proposed Adaptive Feature Aggregation method. The code is available at https://github.com/tenvence/afa/.

Diffusion Transformers (DiTs) have demonstrated remarkable generative capabilities, particularly benefiting from Transformer architectures that enhance visual and artistic fidelity. However, their inherently sequential denoising process results in high inference latency, limiting their deployment in real-time scenarios. Existing training-free acceleration approaches typically reuse intermediate features at fixed timesteps or layers, overlooking the evolving semantic focus across denoising stages and Transformer blocks.To address this, we propose Sortblock, a training-free inference acceleration framework that dynamically caches block-wise features based on their similarity across adjacent timesteps. By ranking the evolution of residuals, Sortblock adaptively determines a recomputation ratio, selectively skipping redundant computations while preserving generation quality. Furthermore, we incorporate a lightweight linear prediction mechanism to reduce accumulated errors in skipped blocks.Extensive experiments across various tasks and DiT architectures demonstrate that Sortblock achieves over 2times inference speedup with minimal degradation in output quality, offering an effective and generalizable solution for accelerating diffusion-based generative models.

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.

Recent advancements in Diffusion Transformers (DiTs) have established them as the state-of-the-art method for video generation. However, their inherently sequential denoising process results in inevitable latency, limiting real-world applicability. Existing acceleration methods either compromise visual quality due to architectural modifications or fail to reuse intermediate features at proper granularity. Our analysis reveals that DiT blocks are the primary contributors to inference latency. Across diffusion timesteps, the feature variations of DiT blocks exhibit a U-shaped pattern with high similarity during intermediate timesteps, which suggests substantial computational redundancy. In this paper, we propose Block-Wise Caching (BWCache), a training-free method to accelerate DiT-based video generation. BWCache dynamically caches and reuses features from DiT blocks across diffusion timesteps. Furthermore, we introduce a similarity indicator that triggers feature reuse only when the differences between block features at adjacent timesteps fall below a threshold, thereby minimizing redundant computations while maintaining visual fidelity. Extensive experiments on several video diffusion models demonstrate that BWCache achieves up to 2.24times speedup with comparable visual quality.

Existing remote sensing image compression methods still explore to balance high compression efficiency with the preservation of fine details and task-relevant information. Meanwhile, high-resolution drone imagery offers valuable structural details for urban monitoring and disaster assessment, but large-area datasets can easily reach hundreds of gigabytes, creating significant challenges for storage and long-term management. In this paper, we propose a PPO-based bitrate allocation Conditional Diffusion Compression (PCDC) framework. PCDC integrates a conditional diffusion decoder with a PPO-based block-wise bitrate allocation strategy to achieve high compression ratios while maintaining strong perceptual performance. We also release a high-resolution drone image dataset with richer structural details at a consistent low altitude over residential neighborhoods in coastal urban areas. Experimental results show compression ratios of 19.3x on DIV2K and 21.2x on the drone image dataset. Moreover, downstream object detection experiments demonstrate that the reconstructed images preserve task-relevant information with negligible performance loss.

Diffusion models have become a dominant paradigm for high-quality generative modeling, while post-training is essential for adapting them to diverse downstream applications. However, post-training of large diffusion models is still challenging due to the prohibitive memory footprints and slow training speed, which existing parameter-efficient fine-tuning methods only partially address. To overcome these limitations, we propose FourTune, an efficient post-training framework for diffusion models based on an end-to-end W4A4G4 paradigm. FourTune introduces a triple-branch hybrid pipeline that augments the standard LoRA architecture with a frozen numerical stabilizer to isolate quantization-sensitive outliers, enabling stable training under native 4-bit computation. In addition, FourTune employs hardware-efficient block-wise quantization and customized fused kernels to support efficient quantized backpropagation and reduce memory bandwidth overhead. Across customization, reinforcement learning, and distillation tasks, FourTune matches the quality of full-precision fine-tuning. On FLUX.1-dev (12B), FourTune reduces memory overhead by 2.25times and increases end-to-end training throughput by 2.27times compared to BF16 LoRA.

Video Variational Autoencoder (VAE) encodes videos into a low-dimensional latent space, becoming a key component of most Latent Video Diffusion Models (LVDMs) to reduce model training costs. However, as the resolution and duration of generated videos increase, the encoding cost of Video VAEs becomes a limiting bottleneck in training LVDMs. Moreover, the block-wise inference method adopted by most LVDMs can lead to discontinuities of latent space when processing long-duration videos. The key to addressing the computational bottleneck lies in decomposing videos into distinct components and efficiently encoding the critical information. Wavelet transform can decompose videos into multiple frequency-domain components and improve the efficiency significantly, we thus propose Wavelet Flow VAE (WF-VAE), an autoencoder that leverages multi-level wavelet transform to facilitate low-frequency energy flow into latent representation. Furthermore, we introduce a method called Causal Cache, which maintains the integrity of latent space during block-wise inference. Compared to state-of-the-art video VAEs, WF-VAE demonstrates superior performance in both PSNR and LPIPS metrics, achieving 2x higher throughput and 4x lower memory consumption while maintaining competitive reconstruction quality. Our code and models are available at https://github.com/PKU-YuanGroup/WF-VAE.

State-of-the-art text-to-image diffusion models (DMs) achieve remarkable quality, yet their massive parameter scale (8-11B) poses significant challenges for inferences on resource-constrained devices. In this paper, we present HierarchicalPrune, a novel compression framework grounded in a key observation: DM blocks exhibit distinct functional hierarchies, where early blocks establish semantic structures while later blocks handle texture refinements. HierarchicalPrune synergistically combines three techniques: (1) Hierarchical Position Pruning, which identifies and removes less essential later blocks based on position hierarchy; (2) Positional Weight Preservation, which systematically protects early model portions that are essential for semantic structural integrity; and (3) Sensitivity-Guided Distillation, which adjusts knowledge-transfer intensity based on our discovery of block-wise sensitivity variations. As a result, our framework brings billion-scale diffusion models into a range more suitable for on-device inference, while preserving the quality of the output images. Specifically, when combined with INT4 weight quantisation, HierarchicalPrune achieves 77.5-80.4% memory footprint reduction (e.g., from 15.8 GB to 3.2 GB) and 27.9-38.0% latency reduction, measured on server and consumer grade GPUs, with the minimum drop of 2.6% in GenEval score and 7% in HPSv2 score compared to the original model. Last but not least, our comprehensive user study with 85 participants demonstrates that HierarchicalPrune maintains perceptual quality comparable to the original model while significantly outperforming prior works.

The objective of personalization and stylization in text-to-image is to instruct a pre-trained diffusion model to analyze new concepts introduced by users and incorporate them into expected styles. Recently, parameter-efficient fine-tuning (PEFT) approaches have been widely adopted to address this task and have greatly propelled the development of this field. Despite their popularity, existing efficient fine-tuning methods still struggle to achieve effective personalization and stylization in T2I generation. To address this issue, we propose block-wise Low-Rank Adaptation (LoRA) to perform fine-grained fine-tuning for different blocks of SD, which can generate images faithful to input prompts and target identity and also with desired style. Extensive experiments demonstrate the effectiveness of the proposed method.

Diffusion-based large language models (Diffusion LLMs) have shown promise for non-autoregressive text generation with parallel decoding capabilities. However, the practical inference speed of open-sourced Diffusion LLMs often lags behind autoregressive models due to the lack of Key-Value (KV) Cache and quality degradation when decoding multiple tokens simultaneously. To bridge this gap, we introduce a novel block-wise approximate KV Cache mechanism tailored for bidirectional diffusion models, enabling cache reuse with negligible performance drop. Additionally, we identify the root cause of generation quality degradation in parallel decoding as the disruption of token dependencies under the conditional independence assumption. To address this, we propose a confidence-aware parallel decoding strategy that selectively decodes tokens exceeding a confidence threshold, mitigating dependency violations and maintaining generation quality. Experimental results on LLaDA and Dream models across multiple LLM benchmarks demonstrate up to 27.6times throughput improvement with minimal accuracy loss, closing the performance gap with autoregressive models and paving the way for practical deployment of Diffusion LLMs.

Pioneering text-to-image (T2I) diffusion models have ushered in a new era of real-world image super-resolution (Real-ISR), significantly enhancing the visual perception of reconstructed images. However, existing methods typically integrate uniform abstract textual semantics across all blocks, overlooking the distinct semantic requirements at different depths and the fine-grained, concrete semantics inherently present in the images themselves. Moreover, relying solely on a single type of guidance further disrupts the consistency of reconstruction. To address these issues, we propose MegaSR, a novel framework that mines customized block-wise semantics and expressive guidance for diffusion-based ISR. Compared to uniform textual semantics, MegaSR enables flexible adaptation to multi-granularity semantic awareness by dynamically incorporating image attributes at each block. Furthermore, we experimentally identify HED edge maps, depth maps, and segmentation maps as the most expressive guidance, and propose a multi-stage aggregation strategy to modulate them into the T2I models. Extensive experiments demonstrate the superiority of MegaSR in terms of semantic richness and structural consistency.

Recent byte-level language models (LMs) match the performance of token-level models without relying on subword vocabularies, yet their utility is limited by slow, byte-by-byte autoregressive generation. We address this bottleneck in the Byte Latent Transformer (BLT) through new training and generation techniques. First, we introduce BLT Diffusion (BLT-D), a new model and our fastest BLT variant, trained with an auxiliary block-wise diffusion objective alongside the standard next-byte prediction loss. This enables an inference procedure that generates multiple bytes in parallel per decoding step, substantially reducing the number of forward passes required to generate a sequence. Second, we propose two extensions inspired by speculative decoding that trade some of this speed for higher generation quality: BLT Self-speculation (BLT-S), in which BLT's local decoder continues generating past its normal patch boundaries to draft bytes, which are then verified with a single full-model forward pass; and BLT Diffusion+Verification (BLT-DV), which augments BLT-D with an autoregressive verification step after diffusion-based generation. All methods may achieve an estimated memory-bandwidth cost over 50% lower than BLT on generation tasks. Each approach offers its own unique advantages, together removing key barriers to the practical use of byte-level LMs.

Recent advances in block diffusion language models have demonstrated competitive performance and strong scalability on reasoning tasks. However, existing BDLMs have limited exploration under the test-time scaling setting and face more severe decoding challenges in long Chain-of-Thought reasoning, particularly in balancing the decoding speed and effectiveness. In this work, we propose a unified framework for test-time scaling in BDLMs that introduces adaptivity in both decoding and block-wise generation. At the decoding level, we propose Bounded Adaptive Confidence Decoding (BACD), a difficulty-aware sampling strategy that dynamically adjusts denoising based on model confidence, accelerating inference while controlling error accumulation. Beyond step-wise adaptivity, we introduce Think Coarse, Critic Fine (TCCF), a test-time scaling paradigm that allocates large block sizes to exploratory reasoning and smaller block sizes to refinement, achieving an effective efficiency-effectiveness balance. To enable efficient and effective decoding with a large block size, we adopt Progressive Block Size Extension, which mitigates performance degradation when scaling block sizes. Extensive experiments show that applying BACD and TCCF to TDAR-8B yields significant improvements over strong baselines such as TraDo-8B (2.26x speedup, +11.2 points on AIME24). These results mark an important step toward unlocking the potential of BDLMs for test-time scaling in complex reasoning tasks.

Generating long-form content, such as minute-long videos and extended texts, is increasingly important for modern generative models. Block diffusion improves inference efficiency via KV caching and block-wise causal inference and has been widely adopted in diffusion language models and video generation. However, in long-context settings, block diffusion still incurs substantial overhead from repeatedly computing attention over a growing KV cache. We identify an underexplored property of block diffusion: cross-step redundancy of attention within a block. Our analysis shows that attention outputs from tokens outside the current block remain largely stable across diffusion steps, while block-internal attention varies significantly. Based on this observation, we propose FlashBlock, a cached block-external attention mechanism that reuses stable attention output, reducing attention computation and KV cache access without modifying the diffusion process. Moreover, FlashBlock is orthogonal to sparse attention and can be combined as a complementary residual reuse strategy, substantially improving model accuracy under aggressive sparsification. Experiments on diffusion language models and video generation demonstrate up to 1.44times higher token throughput and up to 1.6times reduction in attention time, with negligible impact on generation quality. Project page: https://caesarhhh.github.io/FlashBlock/.

Diffusion Language Models (DLMs) offer a promising parallel generation paradigm but suffer from slow inference due to numerous refinement steps and the inability to use standard KV caching. We introduce CDLM (Consistency Diffusion Language Models), a training-based acceleration method that simultaneously tackles both bottlenecks. CDLM integrates consistency modeling to drastically reduce the number of required sampling steps by enabling multi-token finalization. Furthermore, we enforce a block-wise causal attention mask during fine-tuning, making the model fully compatible with KV caching. Experiments show CDLM achieves 3.6x-14.5x lower latency while maintaining competitive accuracy on math and coding tasks. The full training and evaluation code is available at https://github.com/SqueezeAILab/CDLM.

Masked diffusion language models (MDLMs) have recently emerged as a promising alternative to autoregressive (AR) language models, offering properties such as parallel decoding, flexible generation orders, and the potential for fewer inference steps. Despite these advantages, decoding strategies and reinforcement learning (RL) algorithms tailored for MDLMs remain underexplored. A naive approach is to directly transfer techniques well-established for AR models to MDLMs. However, this raises an immediate question: Is such a naive transfer truly optimal? For example, 1) Block-wise and semi-AR decoding strategies are not employed during the training of MDLMs, so why do they outperform full diffusion-style decoding during inference? 2) Applying RL algorithms designed for AR models directly to MDLMs exhibits a training-inference inconsistency, since MDLM decoding are non-causal (parallel). This results in inconsistencies between the rollout trajectory and the optimization trajectory. To address these challenges, we propose EOS Early Rejection (EOSER) and Ascending Step-Size (ASS) decoding scheduler, which unlock the potential of MDLMs to perform full diffusion-style decoding, achieving competitive performance with fewer decoding steps. Additionally, we introduce Consistency Trajectory Group Relative Policy Optimization (CJ-GRPO) for taming MDLMs, which emphasizes the consistency between rollout trajectory and optimization trajectory, and reduces the optimization errors caused by skip-step optimization. We conduct extensive experiments on reasoning tasks, such as mathematical and planning benchmarks, using LLaDA-8B-Instruct. The results demonstrate that the proposed EOSER and ASS mechanisms, together with CJ-GRPO, hold significant promise for effectively and efficiently taming MDLMs. Code: https://github.com/yjyddq/EOSER-ASS-RL.

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to purely autoregressive language models because they can decode multiple tokens in parallel. However, state-of-the-art block-wise dLLMs rely on a "remasking" mechanism that decodes only the most confident tokens and discards the rest, effectively wasting computation. We demonstrate that recycling computation from the discarded tokens is beneficial, as these tokens retain contextual information useful for subsequent decoding iterations. In light of this, we propose Residual Context Diffusion (RCD), a module that converts these discarded token representations into contextual residuals and injects them back for the next denoising step. RCD uses a decoupled two-stage training pipeline to bypass the memory bottlenecks associated with backpropagation. We validate our method on both long CoT reasoning (SDAR) and short CoT instruction following (LLaDA) models. We demonstrate that a standard dLLM can be efficiently converted to the RCD paradigm with merely ~1 billion tokens. RCD consistently improves frontier dLLMs by 5-10 points in accuracy with minimal extra computation overhead across a wide range of benchmarks. Notably, on the most challenging AIME tasks, RCD nearly doubles baseline accuracy and attains up to 4-5x fewer denoising steps at equivalent accuracy levels.

Diffusion language models (dLMs) have emerged as a promising paradigm that enables parallel, non-autoregressive generation, but their learning efficiency lags behind that of autoregressive (AR) language models when trained from scratch. To this end, we study AR-to-dLM conversion to transform pretrained AR models into efficient dLMs that excel in speed while preserving AR models' task accuracy. We achieve this by identifying limitations in the attention patterns and objectives of existing AR-to-dLM methods and then proposing principles and methodologies for more effective AR-to-dLM conversion. Specifically, we first systematically compare different attention patterns and find that maintaining pretrained AR weight distributions is critical for effective AR-to-dLM conversion. As such, we introduce a continuous pretraining scheme with a block-wise attention pattern, which remains causal across blocks while enabling bidirectional modeling within each block. We find that this approach can better preserve pretrained AR models' weight distributions than fully bidirectional modeling, in addition to its known benefit of enabling KV caching, and leads to a win-win in accuracy and efficiency. Second, to mitigate the training-test gap in mask token distributions (uniform vs. highly left-to-right), we propose a position-dependent token masking strategy that assigns higher masking probabilities to later tokens during training to better mimic test-time behavior. Leveraging this framework, we conduct extensive studies of dLMs' attention patterns, training dynamics, and other design choices, providing actionable insights into scalable AR-to-dLM conversion. These studies lead to the Efficient-DLM family, which outperforms state-of-the-art AR models and dLMs, e.g., our Efficient-DLM 8B achieves +5.4%/+2.7% higher accuracy with 4.5x/2.7x higher throughput compared to Dream 7B and Qwen3 4B, respectively.

Creating graphic layouts is a fundamental step in graphic designs. In this work, we present a novel generative model named LayoutDiffusion for automatic layout generation. As layout is typically represented as a sequence of discrete tokens, LayoutDiffusion models layout generation as a discrete denoising diffusion process. It learns to reverse a mild forward process, in which layouts become increasingly chaotic with the growth of forward steps and layouts in the neighboring steps do not differ too much. Designing such a mild forward process is however very challenging as layout has both categorical attributes and ordinal attributes. To tackle the challenge, we summarize three critical factors for achieving a mild forward process for the layout, i.e., legality, coordinate proximity and type disruption. Based on the factors, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule. Experiments on RICO and PubLayNet datasets show that LayoutDiffusion outperforms state-of-the-art approaches significantly. Moreover, it enables two conditional layout generation tasks in a plug-and-play manner without re-training and achieves better performance than existing methods.

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.

Diffusion-based language models (DLLMs) offer non-sequential, block-wise generation and richer data reuse compared to autoregressive (AR) models, but existing code DLLMs still lag behind strong AR baselines under comparable budgets. We revisit this setting in a controlled study and introduce Stable-DiffCoder, a block diffusion code model that reuses the Seed-Coder architecture, data, and training pipeline. To enable efficient knowledge learning and stable training, we incorporate a block diffusion continual pretraining (CPT) stage enhanced by a tailored warmup and block-wise clipped noise schedule. Under the same data and architecture, Stable-DiffCoder overall outperforms its AR counterpart on a broad suite of code benchmarks. Moreover, relying only on the CPT and supervised fine-tuning stages, Stable-DiffCoder achieves stronger performance than a wide range of \~8B ARs and DLLMs, demonstrating that diffusion-based training can improve code modeling quality beyond AR training alone. Moreover, diffusion-based any-order modeling improves structured code modeling for editing and reasoning, and through data augmentation, benefits low-resource coding languages.

Diffusion Large Language Models (dLLMs) have emerged as a promising paradigm for parallel token generation, with block-wise variants garnering significant research interest. Despite their potential, existing dLLMs typically suffer from a rigid accuracy-parallelism trade-off: increasing the number of tokens per forward (TPF) via aggressive parallel decoding often leads to performance degradation and increased generation instability. We identify that this limitation stems from the model's inability to navigate high-parallelism regimes where approximation errors and local corruptions accumulate, ultimately undermining the reliability of parallel generation. To address this, we propose LightningRL, a post-training framework designed to directly optimize the speed-quality Pareto frontier of pre-trained dLLMs. Instead of forcing uniform parallelization, our approach leverages reinforcement learning to identify and reinforce high-parallelism trajectories that maintain generation accuracy. Built upon the Group Relative Policy Optimization (GRPO) framework, LightningRL introduces several enhancements tailored for dLLMs: (1) stabilized training via per-reward decoupled normalization; (2) token-level negative log-likelihood (NLL) regularization on correct trajectories to anchor model performance; and (3) a dynamic sampling strategy with TPF-aware filtering to enhance training efficiency. Experimental results across mathematical and coding benchmarks demonstrate that LightningRL consistently advances the Pareto frontier, achieving competitive task accuracy while significantly increasing parallelism, reaching an average TPF of 7.32 (with a peak of 11.10 on the MBPP dataset). Our code is available at https://github.com/SJTU-DENG-Lab/LightningRL.

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.

Diffusion Policy has demonstrated strong visuomotor modeling capabilities, but its high computational cost renders it impractical for real-time robotic control. Despite huge redundancy across repetitive denoising steps, existing diffusion acceleration techniques fail to generalize to Diffusion Policy due to fundamental architectural and data divergences. In this paper, we propose Block-wise Adaptive Caching(BAC), a method to accelerate Diffusion Policy by caching intermediate action features. BAC achieves lossless action generation acceleration by adaptively updating and reusing cached features at the block level, based on a key observation that feature similarities vary non-uniformly across timesteps and locks. To operationalize this insight, we first propose the Adaptive Caching Scheduler, designed to identify optimal update timesteps by maximizing the global feature similarities between cached and skipped features. However, applying this scheduler for each block leads to signiffcant error surges due to the inter-block propagation of caching errors, particularly within Feed-Forward Network (FFN) blocks. To mitigate this issue, we develop the Bubbling Union Algorithm, which truncates these errors by updating the upstream blocks with signiffcant caching errors before downstream FFNs. As a training-free plugin, BAC is readily integrable with existing transformer-based Diffusion Policy and vision-language-action models. Extensive experiments on multiple robotic benchmarks demonstrate that BAC achieves up to 3x inference speedup for free.

Recent advances in vision-language-action (VLA) models have shown promise in integrating image generation with action prediction to improve generalization and reasoning in robot manipulation. However, existing methods are limited to challenging image-based forecasting, which suffers from redundant information and lacks comprehensive and critical world knowledge, including dynamic, spatial and semantic information. To address these limitations, we propose DreamVLA, a novel VLA framework that integrates comprehensive world knowledge forecasting to enable inverse dynamics modeling, thereby establishing a perception-prediction-action loop for manipulation tasks. Specifically, DreamVLA introduces a dynamic-region-guided world knowledge prediction, integrated with the spatial and semantic cues, which provide compact yet comprehensive representations for action planning. This design aligns with how humans interact with the world by first forming abstract multimodal reasoning chains before acting. To mitigate interference among the dynamic, spatial and semantic information during training, we adopt a block-wise structured attention mechanism that masks their mutual attention, preventing information leakage and keeping each representation clean and disentangled. Moreover, to model the conditional distribution over future actions, we employ a diffusion-based transformer that disentangles action representations from shared latent features. Extensive experiments on both real-world and simulation environments demonstrate that DreamVLA achieves 76.7% success rate on real robot tasks and 4.44 average length on the CALVIN ABC-D benchmarks.

Diffusion Transformers (DiTs) set the state of the art in visual generation, yet their quadratic self-attention cost fundamentally limits scaling to long token sequences. Recent Top-K sparse attention approaches reduce the computation of DiTs by compressing tokens into block-wise representation and selecting a small set of relevant key blocks, but still suffer from (i) quadratic selection cost on compressed tokens and (ii) increasing K required to maintain model quality as sequences grow. We identify that their inefficiency is due to the single-level design, as a single coarse level is insufficient to represent the global structure. In this paper, we introduce Log-linear Sparse Attention (LLSA), a trainable sparse attention mechanism for extremely long token sequences that reduces both selection and attention costs from quadratic to log-linear complexity by utilizing a hierarchical structure. LLSA performs hierarchical Top-K selection, progressively adopting sparse Top-K selection with the indices found at the previous level, and introduces a Hierarchical KV Enrichment mechanism that preserves global context while using fewer tokens of different granularity during attention computation. To support efficient training, we develop a high-performance GPU implementation that uses only sparse indices for both the forward and backward passes, eliminating the need for dense attention masks. We evaluate LLSA on high-resolution pixel-space image generation without using patchification and VAE encoding. LLSA accelerates attention inference by 28.27x and DiT training by 6.09x on 256x256 pixel token sequences, while maintaining generation quality. The results demonstrate that LLSA offers a promising direction for training long-sequence DiTs efficiently. Code is available at: https://github.com/SingleZombie/LLSA

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

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/

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

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.

We present a method for generating video sequences with coherent motion between a pair of input key frames. We adapt a pretrained large-scale image-to-video diffusion model (originally trained to generate videos moving forward in time from a single input image) for key frame interpolation, i.e., to produce a video in between two input frames. We accomplish this adaptation through a lightweight fine-tuning technique that produces a version of the model that instead predicts videos moving backwards in time from a single input image. This model (along with the original forward-moving model) is subsequently used in a dual-directional diffusion sampling process that combines the overlapping model estimates starting from each of the two keyframes. Our experiments show that our method outperforms both existing diffusion-based methods and traditional frame interpolation techniques.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

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.

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

Diffusion models have quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive and unsuitable for real-time sequential inverse problems such as ultrasound imaging. Considering the strong temporal structure across sequences of frames, we propose a novel approach that models the transition dynamics to improve the efficiency of sequential diffusion posterior sampling in conditional image synthesis. Through modeling sequence data using a video vision transformer (ViViT) transition model based on previous diffusion outputs, we can initialize the reverse diffusion trajectory at a lower noise scale, greatly reducing the number of iterations required for convergence. We demonstrate the effectiveness of our approach on a real-world dataset of high frame rate cardiac ultrasound images and show that it achieves the same performance as a full diffusion trajectory while accelerating inference 25times, enabling real-time posterior sampling. Furthermore, we show that the addition of a transition model improves the PSNR up to 8\% in cases with severe motion. Our method opens up new possibilities for real-time applications of diffusion models in imaging and other domains requiring real-time inference.

Block Diffusion Language Models (BD-LMs) improve diffusion-based text generation with KV caching and flexible-length generation. A natural next step is to extend them from Single-Block Diffusion (SingleBD) to Multi-Block Diffusion (MultiBD), where a running-set of consecutive blocks is decoded concurrently for inter-block parallelism. However, existing BD-LMs are mostly trained under teacher forcing, where the model observes only one noisy block conditioned on a clean prefix. While the recent diffusion forcing strategy introduces visibility among multiple noisy blocks, its training states still differ from MultiBD inference, where decoding operates on a bounded running-set with heterogeneous slot-wise noise patterns. To bridge this gap, we propose Multi-Block Diffusion Language Models (MBD-LMs), obtained by post-training BD-LMs with Multi-block Teacher Forcing (MultiTF). MultiTF integrates teacher forcing and diffusion forcing by training on bounded noise-groups conditioned on clean prefixes, with randomized noise-schedulers that better match MultiBD inference states. To make MultiBD practically executable, we further introduce an optimized decoding algorithm based on the Block Buffer mechanism that preserves prefix-cache reuse, keeps input shapes static, and translates increased decoding parallelism into wall-clock acceleration. Empirically, MBD-LLaDA2-Mini increases average Tokens Per Forward pass (TPF) from 3.47 to 6.19 and improves average accuracy from 79.95% to 81.03%; when combined with DMax, MBD-LLaDA2-Mini-DMax reaches an average TPF of 9.34 with only a 1.02% accuracy drop on math and code benchmarks.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we uncover a vexing propensity of diffusion models: they frequently exhibit the infinite Lipschitz near the zero point of timesteps. This poses a threat to the stability and accuracy of the diffusion process, which relies on integral operations. We provide a comprehensive evaluation of the issue from both theoretical and empirical perspectives. To address this challenge, we propose a novel approach, dubbed E-TSDM, which eliminates the Lipschitz singularity of the diffusion model near zero. Remarkably, our technique yields a substantial improvement in performance, e.g., on the high-resolution FFHQ dataset (256times256). Moreover, as a byproduct of our method, we manage to achieve a dramatic reduction in the Frechet Inception Distance of other acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. We conduct extensive experiments on diverse datasets to validate our theory and method. Our work not only advances the understanding of the general diffusion process, but also provides insights for the design of diffusion models.

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.

Discrete diffusion models have steadily improved in quality relative to autoregressive (AR) models. However, these models are normally constrained to fixed-length generation and do not support key-value (KV) caching. Block diffusion partially bridges diffusion and AR by generating token blocks left-to-right, but its fixed-size sequential blocks limit decoding flexibility and parallelism. Here, we present a new class of language models, set diffusion, comprised of (i) a likelihood parameterization that factorizes over flexible-position, flexible-length token sets and (ii) a set-causal diffusion architecture that supports KV cache updates after every inference step. By factorizing over token sets instead of fixed-size blocks, tokens can be decoded in arbitrarily-ordered sets, including sliding-window sets, enabling faster inference and support for any-order decoding. Set diffusion achieves better speed-quality tradeoffs on mathematical reasoning, summarization, and unconditional generation compared to prior diffusion language models while offering stronger infilling performance than block diffusion. We provide the code, along with the model weights and blog post on the project page: https://m-arriola.com/setdlms/

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language generation, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC

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.

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method "boosts" current diffusion-based SR models without any additional training.

We introduce Discrete Voxel Diffusion (DVD), a discrete diffusion framework to generate, assess, and edit sparse voxels for SLat (Structured LATent) based 3D generative pipelines. Although discrete diffusion has not generally displaced continuous diffusion in image-like generation, we show that it can be an effective first-stage prior for sparse voxel scaffolds. By treating voxel occupancy as a native discrete variable, DVD avoids continuous-to-discrete thresholding and provides a simple framework for voxel generation, uncertainty estimation, and editing. Beyond quality gains, DVD provides more interpretable generation dynamics through explicit categorical modeling. Furthermore, we leverage the predictive entropy as a robust uncertainty metric to identify ambiguous voxel regions and complicated samples, facilitating tasks such as data filtering and quality assessment. Finally, we propose a lightweight fine-tuning strategy using block-structured perturbation patterns. This approach empowers the model to inpaint and edit voxels within a single sampling round, requiring negligible auxiliary computation and no additional model evaluations. Code is available at https://github.com/TeCai/DVD.

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.

Diffusion models excel in high-quality generation but suffer from slow inference due to iterative sampling. While recent methods have successfully transformed diffusion models into one-step generators, they neglect model size reduction, limiting their applicability in compute-constrained scenarios. This paper aims to develop small, efficient one-step diffusion models based on the powerful rectified flow framework, by exploring joint compression of inference steps and model size. The rectified flow framework trains one-step generative models using two operations, reflow and distillation. Compared with the original framework, squeezing the model size brings two new challenges: (1) the initialization mismatch between large teachers and small students during reflow; (2) the underperformance of naive distillation on small student models. To overcome these issues, we propose Annealing Reflow and Flow-Guided Distillation, which together comprise our SlimFlow framework. With our novel framework, we train a one-step diffusion model with an FID of 5.02 and 15.7M parameters, outperforming the previous state-of-the-art one-step diffusion model (FID=6.47, 19.4M parameters) on CIFAR10. On ImageNet 64times64 and FFHQ 64times64, our method yields small one-step diffusion models that are comparable to larger models, showcasing the effectiveness of our method in creating compact, efficient one-step diffusion models.

Diffusion models are emerging expressive generative models, in which a large number of time steps (inference steps) are required for a single image generation. To accelerate such tedious process, reducing steps uniformly is considered as an undisputed principle of diffusion models. We consider that such a uniform assumption is not the optimal solution in practice; i.e., we can find different optimal time steps for different models. Therefore, we propose to search the optimal time steps sequence and compressed model architecture in a unified framework to achieve effective image generation for diffusion models without any further training. Specifically, we first design a unified search space that consists of all possible time steps and various architectures. Then, a two stage evolutionary algorithm is introduced to find the optimal solution in the designed search space. To further accelerate the search process, we employ FID score between generated and real samples to estimate the performance of the sampled examples. As a result, the proposed method is (i).training-free, obtaining the optimal time steps and model architecture without any training process; (ii). orthogonal to most advanced diffusion samplers and can be integrated to gain better sample quality. (iii). generalized, where the searched time steps and architectures can be directly applied on different diffusion models with the same guidance scale. Experimental results show that our method achieves excellent performance by using only a few time steps, e.g. 17.86 FID score on ImageNet 64 times 64 with only four steps, compared to 138.66 with DDIM. The code is available at https://github.com/lilijiangg/AutoDiffusion.

Diffusion models have recently revolutionized the field of image synthesis due to their ability to generate photorealistic images. However, one of the major drawbacks of diffusion models is that the image generation process is costly. A large image-to-image network has to be applied many times to iteratively refine an image from random noise. While many recent works propose techniques to reduce the number of required steps, they generally treat the underlying denoising network as a black box. In this work, we investigate the behavior of the layers within the network and find that 1) the layers' output changes smoothly over time, 2) the layers show distinct patterns of change, and 3) the change from step to step is often very small. We hypothesize that many layer computations in the denoising network are redundant. Leveraging this, we introduce block caching, in which we reuse outputs from layer blocks of previous steps to speed up inference. Furthermore, we propose a technique to automatically determine caching schedules based on each block's changes over timesteps. In our experiments, we show through FID, human evaluation and qualitative analysis that Block Caching allows to generate images with higher visual quality at the same computational cost. We demonstrate this for different state-of-the-art models (LDM and EMU) and solvers (DDIM and DPM).

Discrete denoising diffusion models (DDMs) have recently emerged as a compelling alternative to autoregressive (AR) modeling for discrete data, offering parallel generation and iterative global refinement capabilities. Unlike continuous diffusion, where the state space is fixed, DDMs are fundamentally shaped by how the discrete state space is constructed: the tokenization scheme, the vocabulary topology, and domain-specific structural alphabets. This work introduces a unified conceptual framework that views discrete diffusion models through the construction of the underlying discrete state space. Within this framework, existing formulations, including transition-matrix, masking/absorbing-state, and score/ratio-based approaches, emerge as different instantiations of a common design space. The framework further exposes common design trade-offs across training objectives, inference algorithms, scaling behavior, systems optimization, and evaluation protocols, suggesting several promising directions for future research.

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset.

Diffusion models (DMs) have established themselves as the state-of-the-art generative modeling approach in the visual domain and beyond. A crucial drawback of DMs is their slow sampling speed, relying on many sequential function evaluations through large neural networks. Sampling from DMs can be seen as solving a differential equation through a discretized set of noise levels known as the sampling schedule. While past works primarily focused on deriving efficient solvers, little attention has been given to finding optimal sampling schedules, and the entire literature relies on hand-crafted heuristics. In this work, for the first time, we propose a general and principled approach to optimizing the sampling schedules of DMs for high-quality outputs, called Align Your Steps. We leverage methods from stochastic calculus and find optimal schedules specific to different solvers, trained DMs and datasets. We evaluate our novel approach on several image, video as well as 2D toy data synthesis benchmarks, using a variety of different samplers, and observe that our optimized schedules outperform previous hand-crafted schedules in almost all experiments. Our method demonstrates the untapped potential of sampling schedule optimization, especially in the few-step synthesis regime.

Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is no need to maintain a high dimensionality in the evolution process, especially in the early generation phase. To this end, we make a theoretical generalization of the forward diffusion process via signal decomposition. Concretely, we manage to decompose an image into multiple orthogonal components and control the attenuation of each component when perturbing the image. That way, along with the noise strength increasing, we are able to diminish those inconsequential components and thus use a lower-dimensional signal to represent the source, barely losing information. Such a reformulation allows to vary dimensions in both training and inference of diffusion models. Extensive experiments on a range of datasets suggest that our approach substantially reduces the computational cost and achieves on-par or even better synthesis performance compared to baseline methods. We also show that our strategy facilitates high-resolution image synthesis and improves FID of diffusion model trained on FFHQ at 1024times1024 resolution from 52.40 to 10.46. Code and models will be made publicly available.

Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D methods do not fully exploit the 3D distribution prior. To address this, we propose a novel approach using two perpendicular pre-trained 2D diffusion models to solve the 3D inverse problem. By modeling the 3D data distribution as a product of 2D distributions sliced in different directions, our method effectively addresses the curse of dimensionality. Our experimental results demonstrate that our method is highly effective for 3D medical image reconstruction tasks, including MRI Z-axis super-resolution, compressed sensing MRI, and sparse-view CT. Our method can generate high-quality voxel volumes suitable for medical applications.

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.

Diffusion models have emerged as powerful generative models capable of producing high-quality contents such as images, videos, and audio, demonstrating their potential to revolutionize digital content creation. However, these capabilities come at the cost of their significant computational resources and lengthy generation time, underscoring the critical need to develop efficient techniques for practical deployment. In this survey, we provide a systematic and comprehensive review of research on efficient diffusion models. We organize the literature in a taxonomy consisting of three main categories, covering distinct yet interconnected efficient diffusion model topics from algorithm-level, system-level, and framework perspective, respectively. We have also created a GitHub repository where we organize the papers featured in this survey at https://github.com/AIoT-MLSys-Lab/Efficient-Diffusion-Model-Survey. We hope our survey can serve as a valuable resource to help researchers and practitioners gain a systematic understanding of efficient diffusion model research and inspire them to contribute to this important and exciting field.

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.

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 probabilistic models (DPMs) have exhibited excellent performance for high-fidelity image generation while suffering from inefficient sampling. Recent works accelerate the sampling procedure by proposing fast ODE solvers that leverage the specific ODE form of DPMs. However, they highly rely on specific parameterization during inference (such as noise/data prediction), which might not be the optimal choice. In this work, we propose a novel formulation towards the optimal parameterization during sampling that minimizes the first-order discretization error of the ODE solution. Based on such formulation, we propose DPM-Solver-v3, a new fast ODE solver for DPMs by introducing several coefficients efficiently computed on the pretrained model, which we call empirical model statistics. We further incorporate multistep methods and a predictor-corrector framework, and propose some techniques for improving sample quality at small numbers of function evaluations (NFE) or large guidance scales. Experiments show that DPM-Solver-v3 achieves consistently better or comparable performance in both unconditional and conditional sampling with both pixel-space and latent-space DPMs, especially in 5sim10 NFEs. We achieve FIDs of 12.21 (5 NFE), 2.51 (10 NFE) on unconditional CIFAR10, and MSE of 0.55 (5 NFE, 7.5 guidance scale) on Stable Diffusion, bringing a speed-up of 15\%sim30\% compared to previous state-of-the-art training-free methods. Code is available at https://github.com/thu-ml/DPM-Solver-v3.

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.

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.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Latent diffusion models have become the popular choice for scaling up diffusion models for high resolution image synthesis. Compared to pixel-space models that are trained end-to-end, latent models are perceived to be more efficient and to produce higher image quality at high resolution. Here we challenge these notions, and show that pixel-space models can in fact be very competitive to latent approaches both in quality and efficiency, achieving 1.5 FID on ImageNet512 and new SOTA results on ImageNet128 and ImageNet256. We present a simple recipe for scaling end-to-end pixel-space diffusion models to high resolutions. 1: Use the sigmoid loss (Kingma & Gao, 2023) with our prescribed hyper-parameters. 2: Use our simplified memory-efficient architecture with fewer skip-connections. 3: Scale the model to favor processing the image at high resolution with fewer parameters, rather than using more parameters but at a lower resolution. When combining these three steps with recently proposed tricks like guidance intervals, we obtain a family of pixel-space diffusion models we call Simple Diffusion v2 (SiD2).

Recently, diffusion models have achieved significant advances in vision, text, and robotics. However, they still face slow generation speeds due to sequential denoising processes. To address this, a parallel sampling method based on Picard iteration was introduced, effectively reducing sequential steps while ensuring exact convergence to the original output. Nonetheless, Picard iteration does not guarantee faster convergence, which can still result in slow generation in practice. In this work, we propose a new parallelization scheme, the Picard Consistency Model (PCM), which significantly reduces the number of generation steps in Picard iteration. Inspired by the consistency model, PCM is directly trained to predict the fixed-point solution, or the final output, at any stage of the convergence trajectory. Additionally, we introduce a new concept called model switching, which addresses PCM's limitations and ensures exact convergence. Extensive experiments demonstrate that PCM achieves up to a 2.71x speedup over sequential sampling and a 1.77x speedup over Picard iteration across various tasks, including image generation and robotic control.

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior sampling methods proposed for solving common BIPs rely on heuristic approximations to the generative process. To exploit the generative capability of DMs and avoid the usage of such approximations, we propose an ensemble-based algorithm that performs posterior sampling without the use of heuristic approximations. Our algorithm is motivated by existing works that combine DM-based methods with the sequential Monte Carlo (SMC) method. By examining how the prior evolves through the diffusion process encoded by the pre-trained score function, we derive a modified partial differential equation (PDE) governing the evolution of the corresponding posterior distribution. This PDE includes a modified diffusion term and a reweighting term, which can be simulated via stochastic weighted particle methods. Theoretically, we prove that the error between the true posterior distribution can be bounded in terms of the training error of the pre-trained score function and the number of particles in the ensemble. Empirically, we validate our algorithm on several inverse problems in imaging to show that our method gives more accurate reconstructions compared to existing DM-based methods.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Diffusion models achieved great success in image synthesis, but still face challenges in high-resolution generation. Through the lens of discrete cosine transformation, we find the main reason is that the same noise level on a higher resolution results in a higher Signal-to-Noise Ratio in the frequency domain. In this work, we present Relay Diffusion Model (RDM), which transfers a low-resolution image or noise into an equivalent high-resolution one for diffusion model via blurring diffusion and block noise. Therefore, the diffusion process can continue seamlessly in any new resolution or model without restarting from pure noise or low-resolution conditioning. RDM achieves state-of-the-art FID on CelebA-HQ and sFID on ImageNet 256times256, surpassing previous works such as ADM, LDM and DiT by a large margin. All the codes and checkpoints are open-sourced at https://github.com/THUDM/RelayDiffusion.

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples that are highly diverse and representative of the underlying distribution. However, one of the main limitations of diffusion models is the complexity of sample generation, since a large number of inference timesteps is required to faithfully capture the data distribution. In this paper, we present MMD-DDM, a novel method for fast sampling of diffusion models. Our approach is based on the idea of using the Maximum Mean Discrepancy (MMD) to finetune the learned distribution with a given budget of timesteps. This allows the finetuned model to significantly improve the speed-quality trade-off, by substantially increasing fidelity in inference regimes with few steps or, equivalently, by reducing the required number of steps to reach a target fidelity, thus paving the way for a more practical adoption of diffusion models in a wide range of applications. We evaluate our approach on unconditional image generation with extensive experiments across the CIFAR-10, CelebA, ImageNet and LSUN-Church datasets. Our findings show that the proposed method is able to produce high-quality samples in a fraction of the time required by widely-used diffusion models, and outperforms state-of-the-art techniques for accelerated sampling. Code is available at: https://github.com/diegovalsesia/MMD-DDM.

Diffusion models are a powerful class of generative models which simulate stochastic differential equations (SDEs) to generate data from noise. While diffusion models have achieved remarkable progress, they have limitations in unpaired image-to-image (I2I) translation tasks due to the Gaussian prior assumption. Schr\"{o}dinger Bridge (SB), which learns an SDE to translate between two arbitrary distributions, have risen as an attractive solution to this problem. Yet, to our best knowledge, none of SB models so far have been successful at unpaired translation between high-resolution images. In this work, we propose Unpaired Neural Schr\"{o}dinger Bridge (UNSB), which expresses the SB problem as a sequence of adversarial learning problems. This allows us to incorporate advanced discriminators and regularization to learn a SB between unpaired data. We show that UNSB is scalable and successfully solves various unpaired I2I translation tasks. Code: https://github.com/cyclomon/UNSB

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) models, offering sub-linear generation latency and bidirectional capabilities that are particularly appealing for code generation and editing. Achieving sub-linear latency in discrete DLMs requires predicting multiple tokens in parallel. However, standard DLMs sample tokens independently from conditional marginal distributions, failing to capture the joint dependencies among concurrently generated tokens. As a result, they often lead to syntactic inconsistencies and break multi-token structures. In this work, we introduce CoDiLA (Coherent Diffusion with Local Autoregression), a method that reconciles parallel sampling with local dependency modeling. Rather than forcing the DLM to resolve fine-grained syntax, CoDiLA delegates local decoding to a small, auxiliary AR model operating on the diffusion latents. This design allows for parallel block generation while ensuring sequential validity within each block and maintaining core DLM capabilities, including bidirectional modeling across blocks. We demonstrate that using a highly compact auxiliary AR model (e.g., 0.6B parameters) effectively eliminates coherence artifacts, establishing a new Pareto frontier for accuracy and speed in code generation benchmarks.

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey & Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at https://github.com/mandt-lab/PSLD.

Generating minute-long videos is a critical step toward developing world models, providing a foundation for realistic extended scenes and advanced AI simulators. The emerging semi-autoregressive (block diffusion) paradigm integrates the strengths of diffusion and autoregressive models, enabling arbitrary-length video generation and improving inference efficiency through KV caching and parallel sampling. However, it yet faces two enduring challenges: (i) KV-cache-induced long-horizon error accumulation, and (ii) the lack of fine-grained long-video benchmarks and coherence-aware metrics. To overcome these limitations, we propose BlockVid, a novel block diffusion framework equipped with semantic-aware sparse KV cache, an effective training strategy called Block Forcing, and dedicated chunk-wise noise scheduling and shuffling to reduce error propagation and enhance temporal consistency. We further introduce LV-Bench, a fine-grained benchmark for minute-long videos, complete with new metrics evaluating long-range coherence. Extensive experiments on VBench and LV-Bench demonstrate that BlockVid consistently outperforms existing methods in generating high-quality, coherent minute-long videos. In particular, it achieves a 22.2% improvement on VDE Subject and a 19.4% improvement on VDE Clarity in LV-Bench over the state of the art approaches. Project website: https://ziplab.co/BlockVid. Inferix (Code): https://github.com/alibaba-damo-academy/Inferix.

We introduce Diffusion World Model (DWM), a conditional diffusion model capable of predicting multistep future states and rewards concurrently. As opposed to traditional one-step dynamics models, DWM offers long-horizon predictions in a single forward pass, eliminating the need for recursive quires. We integrate DWM into model-based value estimation, where the short-term return is simulated by future trajectories sampled from DWM. In the context of offline reinforcement learning, DWM can be viewed as a conservative value regularization through generative modeling. Alternatively, it can be seen as a data source that enables offline Q-learning with synthetic data. Our experiments on the D4RL dataset confirm the robustness of DWM to long-horizon simulation. In terms of absolute performance, DWM significantly surpasses one-step dynamics models with a 44% performance gain, and achieves state-of-the-art performance.

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In this work, we use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose parallel decoding method that generates images with only one model forward pass. We propose diffusion model sampling with neural operator (DSNO) that maps the initial condition, i.e., Gaussian distribution, to the continuous-time solution trajectory of the reverse diffusion process. To model the temporal correlations along the trajectory, we introduce temporal convolution layers that are parameterized in the Fourier space into the given diffusion model backbone. We show our method achieves state-of-the-art FID of 4.12 for CIFAR-10 and 8.35 for ImageNet-64 in the one-model-evaluation setting.

Diffusion models have shown remarkable results in generating 2D images and small-scale 3D objects. However, their application to the synthesis of large-scale 3D scenes has been rarely explored. This is mainly due to the inherent complexity and bulky size of 3D scenery data, particularly outdoor scenes, and the limited availability of comprehensive real-world datasets, which makes training a stable scene diffusion model challenging. In this work, we explore how to effectively generate large-scale 3D scenes using the coarse-to-fine paradigm. We introduce a framework, the Pyramid Discrete Diffusion model (PDD), which employs scale-varied diffusion models to progressively generate high-quality outdoor scenes. Experimental results of PDD demonstrate our successful exploration in generating 3D scenes both unconditionally and conditionally. We further showcase the data compatibility of the PDD model, due to its multi-scale architecture: a PDD model trained on one dataset can be easily fine-tuned with another dataset. Code is available at https://github.com/yuhengliu02/pyramid-discrete-diffusion.

By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a guiding mechanism to control the image generation process without retraining. However, since these models typically operate directly in pixel space, optimization of powerful DMs often consumes hundreds of GPU days and inference is expensive due to sequential evaluations. To enable DM training on limited computational resources while retaining their quality and flexibility, we apply them in the latent space of powerful pretrained autoencoders. In contrast to previous work, training diffusion models on such a representation allows for the first time to reach a near-optimal point between complexity reduction and detail preservation, greatly boosting visual fidelity. By introducing cross-attention layers into the model architecture, we turn diffusion models into powerful and flexible generators for general conditioning inputs such as text or bounding boxes and high-resolution synthesis becomes possible in a convolutional manner. Our latent diffusion models (LDMs) achieve a new state of the art for image inpainting and highly competitive performance on various tasks, including unconditional image generation, semantic scene synthesis, and super-resolution, while significantly reducing computational requirements compared to pixel-based DMs. Code is available at https://github.com/CompVis/latent-diffusion .

We introduce the Joint Video-Image Diffusion model (JVID), a novel approach to generating high-quality and temporally coherent videos. We achieve this by integrating two diffusion models: a Latent Image Diffusion Model (LIDM) trained on images and a Latent Video Diffusion Model (LVDM) trained on video data. Our method combines these models in the reverse diffusion process, where the LIDM enhances image quality and the LVDM ensures temporal consistency. This unique combination allows us to effectively handle the complex spatio-temporal dynamics in video generation. Our results demonstrate quantitative and qualitative improvements in producing realistic and coherent videos.

Discrete diffusion models enable parallel token sampling for faster inference than autoregressive approaches. However, prior diffusion models use a decoder-only architecture, which requires sampling algorithms that invoke the full network at every denoising step and incur high computational cost. Our key insight is that discrete diffusion models perform two types of computation: 1) representing clean tokens and 2) denoising corrupted tokens, which enables us to use separate modules for each task. We propose an encoder-decoder architecture to accelerate discrete diffusion inference, which relies on an encoder to represent clean tokens and a lightweight decoder to iteratively refine a noised sequence. We also show that this architecture enables faster training of block diffusion models, which partition sequences into blocks for better quality and are commonly used in diffusion language model inference. We introduce a framework for Efficient Encoder-Decoder Diffusion (E2D2), consisting of an architecture with specialized training and sampling algorithms, and we show that E2D2 achieves superior trade-offs between generation quality and inference throughput on summarization, translation, and mathematical reasoning tasks. We provide the code, model weights, and blog post on the project page: https://m-arriola.com/e2d2

The Diffusion model, a prevalent framework for image generation, encounters significant challenges in terms of broad applicability due to its extended inference times and substantial memory requirements. Efficient Post-training Quantization (PTQ) is pivotal for addressing these issues in traditional models. Different from traditional models, diffusion models heavily depend on the time-step t to achieve satisfactory multi-round denoising. Usually, t from the finite set {1, ldots, T} is encoded to a temporal feature by a few modules totally irrespective of the sampling data. However, existing PTQ methods do not optimize these modules separately. They adopt inappropriate reconstruction targets and complex calibration methods, resulting in a severe disturbance of the temporal feature and denoising trajectory, as well as a low compression efficiency. To solve these, we propose a Temporal Feature Maintenance Quantization (TFMQ) framework building upon a Temporal Information Block which is just related to the time-step t and unrelated to the sampling data. Powered by the pioneering block design, we devise temporal information aware reconstruction (TIAR) and finite set calibration (FSC) to align the full-precision temporal features in a limited time. Equipped with the framework, we can maintain the most temporal information and ensure the end-to-end generation quality. Extensive experiments on various datasets and diffusion models prove our state-of-the-art results. Remarkably, our quantization approach, for the first time, achieves model performance nearly on par with the full-precision model under 4-bit weight quantization. Additionally, our method incurs almost no extra computational cost and accelerates quantization time by 2.0 times on LSUN-Bedrooms 256 times 256 compared to previous works.

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

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.

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite their effectiveness, this design struggles to capture distinct signal characteristics across timesteps simultaneously and incurs substantial inference costs due to the iterative evaluation of the entire model. To address these limitations, we propose Blockwise Flow Matching (BFM), a novel framework that partitions the generative trajectory into multiple temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise design enables each block to specialize effectively in its designated interval, improving inference efficiency and sample quality. To further enhance generation fidelity, we introduce a Semantic Feature Guidance module that explicitly conditions velocity blocks on semantically rich features aligned with pretrained representations. Additionally, we propose a lightweight Feature Residual Approximation strategy that preserves semantic quality while significantly reducing inference cost. Extensive experiments on ImageNet 256x256 demonstrate that BFM establishes a substantially improved Pareto frontier over existing Flow Matching methods, achieving 2.1x to 4.9x accelerations in inference complexity at comparable generation performance. Code is available at https://github.com/mlvlab/BFM.

A diffusion model learns to predict a vector field of gradients. We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and repurposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION dataset.

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.

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.

Diffusion models have achieved remarkable performance in generative modeling, yet their theoretical foundations are often intricate, and the gap between mathematical formulations in papers and practical open-source implementations can be difficult to bridge. Existing tutorials primarily focus on deriving equations, offering limited guidance on how diffusion models actually operate in code. To address this, we present a concise implementation of approximately 300 lines that explains diffusion models from a code-execution perspective. Our minimal example preserves the essential components -- including forward diffusion, reverse sampling, the noise-prediction network, and the training loop -- while removing unnecessary engineering details. This technical report aims to provide researchers with a clear, implementation-first understanding of how diffusion models work in practice and how code and theory correspond. Our code and pre-trained models are available at: https://github.com/disanda/GM/tree/main/DDPM-DDIM-ClassifierFree.

Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training quantization for high-performance inference. Recent works propose low-bitwidth (e.g., 8-bit or 4-bit) quantization for diffusion models, however 4-bit integer quantization typically results in low-quality images. We observe that on several widely used hardware platforms, there is little or no difference in compute capability between floating-point and integer arithmetic operations of the same bitwidth (e.g., 8-bit or 4-bit). Therefore, we propose an effective floating-point quantization method for diffusion models that provides better image quality compared to integer quantization methods. We employ a floating-point quantization method that was effective for other processing tasks, specifically computer vision and natural language tasks, and tailor it for diffusion models by integrating weight rounding learning during the mapping of the full-precision values to the quantized values in the quantization process. We comprehensively study integer and floating-point quantization methods in state-of-the-art diffusion models. Our floating-point quantization method not only generates higher-quality images than that of integer quantization methods, but also shows no noticeable degradation compared to full-precision models (32-bit floating-point), when both weights and activations are quantized to 8-bit floating-point values, while has minimal degradation with 4-bit weights and 8-bit activations.

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

Diffusion models achieve strong generative performance but often rely on large datasets that may include sensitive content. This challenge is compounded by the models' tendency to memorize training data, raising privacy concerns. SFBD (Lu et al., 2025) addresses this by training on corrupted data and using limited clean samples to capture local structure and improve convergence. However, its iterative denoising and fine-tuning loop requires manual coordination, making it burdensome to implement. We reinterpret SFBD as an alternating projection algorithm and introduce a continuous variant, SFBD flow, that removes the need for alternating steps. We further show its connection to consistency constraint-based methods, and demonstrate that its practical instantiation, Online SFBD, consistently outperforms strong baselines across benchmarks.

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network weights is approximated by a denoising diffusion model. The diffusion model we employ focuses on modifying a single layer of the base model and is conditioned on the input, activations, and output of this layer. Since the diffusion model is stochastic in nature, multiple initializations generate different networks, forming an ensemble, which leads to further improvements. Our experiments demonstrate the wide applicability of the method for image classification, 3D reconstruction, tabular data, speech separation, and natural language processing. Our code is available at https://github.com/ShaharLutatiPersonal/OCD

Diffusion models create data from noise by inverting the forward paths of data towards noise and have emerged as a powerful generative modeling technique for high-dimensional, perceptual data such as images and videos. Rectified flow is a recent generative model formulation that connects data and noise in a straight line. Despite its better theoretical properties and conceptual simplicity, it is not yet decisively established as standard practice. In this work, we improve existing noise sampling techniques for training rectified flow models by biasing them towards perceptually relevant scales. Through a large-scale study, we demonstrate the superior performance of this approach compared to established diffusion formulations for high-resolution text-to-image synthesis. Additionally, we present a novel transformer-based architecture for text-to-image generation that uses separate weights for the two modalities and enables a bidirectional flow of information between image and text tokens, improving text comprehension, typography, and human preference ratings. We demonstrate that this architecture follows predictable scaling trends and correlates lower validation loss to improved text-to-image synthesis as measured by various metrics and human evaluations. Our largest models outperform state-of-the-art models, and we will make our experimental data, code, and model weights publicly available.

Diffusion Probabilistic Methods are employed for state-of-the-art image generation. In this work, we present a method for extending such models for performing image segmentation. The method learns end-to-end, without relying on a pre-trained backbone. The information in the input image and in the current estimation of the segmentation map is merged by summing the output of two encoders. Additional encoding layers and a decoder are then used to iteratively refine the segmentation map, using a diffusion model. Since the diffusion model is probabilistic, it is applied multiple times, and the results are merged into a final segmentation map. The new method produces state-of-the-art results on the Cityscapes validation set, the Vaihingen building segmentation benchmark, and the MoNuSeg dataset.

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

We present SwD, a scale-wise distillation framework for diffusion models (DMs), which effectively employs next-scale prediction ideas for diffusion-based few-step generators. In more detail, SwD is inspired by the recent insights relating diffusion processes to the implicit spectral autoregression. We suppose that DMs can initiate generation at lower data resolutions and gradually upscale the samples at each denoising step without loss in performance while significantly reducing computational costs. SwD naturally integrates this idea into existing diffusion distillation methods based on distribution matching. Also, we enrich the family of distribution matching approaches by introducing a novel patch loss enforcing finer-grained similarity to the target distribution. When applied to state-of-the-art text-to-image diffusion models, SwD approaches the inference times of two full resolution steps and significantly outperforms the counterparts under the same computation budget, as evidenced by automated metrics and human preference studies.

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models. We present empirical evidence supporting the effectiveness of our method.