Daily Papers

Evaluating robotics policies across thousands of environments and thousands of tasks is infeasible with existing approaches. This motivates the need for a new methodology for scalable robotics policy evaluation. In this paper, we propose dWorldEval, which uses a discrete diffusion world model as a scalable evaluation proxy for robotics policies. Specifically, dWorldEval maps all modalities - including vision, language, and robotic actions - into a unified token space, modeling them via a single transformer-based denoising network. In this paper, we propose dWorldEval, using a discrete diffusion world model as a scalable evaluation proxy for robotics policy. Specifically, it maps all modalities, including vision, language, and robotics action into a unified token space, then denoises them with a single transformer network. Building on this architecture, we employ a sparse keyframe memory to maintain spatiotemporal consistency. We also introduce a progress token that indicates the degree of task completion. At inference, the model jointly predicts future observations and progress token, allowing automatically determine success when the progress reaches 1. Extensive experiments demonstrate that dWorldEval significantly outperforms previous approaches, i.e., WorldEval, Ctrl-World, and WorldGym, on LIBERO, RoboTwin, and multiple real-robot tasks. It paves the way for a new architectural paradigm in building world simulators for robotics evaluation at scale.

Learning world models can teach an agent how the world works in an unsupervised manner. Even though it can be viewed as a special case of sequence modeling, progress for scaling world models on robotic applications such as autonomous driving has been somewhat less rapid than scaling language models with Generative Pre-trained Transformers (GPT). We identify two reasons as major bottlenecks: dealing with complex and unstructured observation space, and having a scalable generative model. Consequently, we propose a novel world modeling approach that first tokenizes sensor observations with VQVAE, then predicts the future via discrete diffusion. To efficiently decode and denoise tokens in parallel, we recast Masked Generative Image Transformer into the discrete diffusion framework with a few simple changes, resulting in notable improvement. When applied to learning world models on point cloud observations, our model reduces prior SOTA Chamfer distance by more than 65% for 1s prediction, and more than 50% for 3s prediction, across NuScenes, KITTI Odometry, and Argoverse2 datasets. Our results demonstrate that discrete diffusion on tokenized agent experience can unlock the power of GPT-like unsupervised learning for robotic agents.

Modeling cellular states and predicting their responses to perturbations are central challenges in computational biology and the development of virtual cells. Existing foundation models for single-cell transcriptomics provide powerful static representations, but they do not explicitly model the distribution of cellular states for generative simulation. Here, we introduce Lingshu-Cell, a masked discrete diffusion model that learns transcriptomic state distributions and supports conditional simulation under perturbation. By operating directly in a discrete token space that is compatible with the sparse, non-sequential nature of single-cell transcriptomic data, Lingshu-Cell captures complex transcriptome-wide expression dependencies across approximately 18,000 genes without relying on prior gene selection, such as filtering by high variability or ranking by expression level. Across diverse tissues and species, Lingshu-Cell accurately reproduces transcriptomic distributions, marker-gene expression patterns and cell-subtype proportions, demonstrating its ability to capture complex cellular heterogeneity. Moreover, by jointly embedding cell type or donor identity with perturbation, Lingshu-Cell can predict whole-transcriptome expression changes for novel combinations of identity and perturbation. It achieves leading performance on the Virtual Cell Challenge H1 genetic perturbation benchmark and in predicting cytokine-induced responses in human PBMCs. Together, these results establish Lingshu-Cell as a flexible cellular world model for in silico simulation of cell states and perturbation responses, laying the foundation for a new paradigm in biological discovery and perturbation screening.

Scaling Vision-Language-Action (VLA) models on large-scale data offers a promising path to achieving a more generalized driving intelligence. However, VLA models are limited by a ``supervision deficit'': the vast model capacity is supervised by sparse, low-dimensional actions, leaving much of their representational power underutilized. To remedy this, we propose DriveVLA-W0, a training paradigm that employs world modeling to predict future images. This task generates a dense, self-supervised signal that compels the model to learn the underlying dynamics of the driving environment. We showcase the paradigm's versatility by instantiating it for two dominant VLA archetypes: an autoregressive world model for VLAs that use discrete visual tokens, and a diffusion world model for those operating on continuous visual features. Building on the rich representations learned from world modeling, we introduce a lightweight action expert to address the inference latency for real-time deployment. Extensive experiments on the NAVSIM v1/v2 benchmark and a 680x larger in-house dataset demonstrate that DriveVLA-W0 significantly outperforms BEV and VLA baselines. Crucially, it amplifies the data scaling law, showing that performance gains accelerate as the training dataset size increases.

We introduce Emu3.5, a large-scale multimodal world model that natively predicts the next state across vision and language. Emu3.5 is pre-trained end-to-end with a unified next-token prediction objective on a corpus of vision-language interleaved data containing over 10 trillion tokens, primarily derived from sequential frames and transcripts of internet videos. The model naturally accepts interleaved vision-language inputs and generates interleaved vision-language outputs. Emu3.5 is further post-trained with large-scale reinforcement learning to enhance multimodal reasoning and generation. To improve inference efficiency, we propose Discrete Diffusion Adaptation (DiDA), which converts token-by-token decoding into bidirectional parallel prediction, accelerating per-image inference by about 20x without sacrificing performance. Emu3.5 exhibits strong native multimodal capabilities, including long-horizon vision-language generation, any-to-image (X2I) generation, and complex text-rich image generation. It also exhibits generalizable world-modeling abilities, enabling spatiotemporally consistent world exploration and open-world embodied manipulation across diverse scenarios and tasks. For comparison, Emu3.5 achieves performance comparable to Gemini 2.5 Flash Image (Nano Banana) on image generation and editing tasks and demonstrates superior results on a suite of interleaved generation tasks. We open-source Emu3.5 at https://github.com/baaivision/Emu3.5 to support community research.

World models constitute a promising approach for training reinforcement learning agents in a safe and sample-efficient manner. Recent world models predominantly operate on sequences of discrete latent variables to model environment dynamics. However, this compression into a compact discrete representation may ignore visual details that are important for reinforcement learning. Concurrently, diffusion models have become a dominant approach for image generation, challenging well-established methods modeling discrete latents. Motivated by this paradigm shift, we introduce DIAMOND (DIffusion As a Model Of eNvironment Dreams), a reinforcement learning agent trained in a diffusion world model. We analyze the key design choices that are required to make diffusion suitable for world modeling, and demonstrate how improved visual details can lead to improved agent performance. DIAMOND achieves a mean human normalized score of 1.46 on the competitive Atari 100k benchmark; a new best for agents trained entirely within a world model. To foster future research on diffusion for world modeling, we release our code, agents and playable world models at https://github.com/eloialonso/diamond.

World models represent a promising approach for training reinforcement learning agents with significantly improved sample efficiency. While most world model methods primarily rely on sequences of discrete latent variables to model environment dynamics, this compression often neglects critical visual details essential for reinforcement learning. Recent diffusion-based world models condition generation on a fixed context length of frames to predict the next observation, using separate recurrent neural networks to model rewards and termination signals. Although this architecture effectively enhances visual fidelity, the fixed context length approach inherently limits memory capacity. In this paper, we introduce EDELINE, a unified world model architecture that integrates state space models with diffusion models. Our approach outperforms existing baselines across visually challenging Atari 100k tasks, memory-demanding Crafter benchmark, and 3D first-person ViZDoom environments, demonstrating superior performance in all these diverse challenges.

We propose DOME, a diffusion-based world model that predicts future occupancy frames based on past occupancy observations. The ability of this world model to capture the evolution of the environment is crucial for planning in autonomous driving. Compared to 2D video-based world models, the occupancy world model utilizes a native 3D representation, which features easily obtainable annotations and is modality-agnostic. This flexibility has the potential to facilitate the development of more advanced world models. Existing occupancy world models either suffer from detail loss due to discrete tokenization or rely on simplistic diffusion architectures, leading to inefficiencies and difficulties in predicting future occupancy with controllability. Our DOME exhibits two key features:(1) High-Fidelity and Long-Duration Generation. We adopt a spatial-temporal diffusion transformer to predict future occupancy frames based on historical context. This architecture efficiently captures spatial-temporal information, enabling high-fidelity details and the ability to generate predictions over long durations. (2)Fine-grained Controllability. We address the challenge of controllability in predictions by introducing a trajectory resampling method, which significantly enhances the model's ability to generate controlled predictions. Extensive experiments on the widely used nuScenes dataset demonstrate that our method surpasses existing baselines in both qualitative and quantitative evaluations, establishing a new state-of-the-art performance on nuScenes. Specifically, our approach surpasses the baseline by 10.5% in mIoU and 21.2% in IoU for occupancy reconstruction and by 36.0% in mIoU and 24.6% in IoU for 4D occupancy forecasting.

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

End-to-End (E2E) solutions have emerged as a mainstream approach for autonomous driving systems, with Vision-Language-Action (VLA) models representing a new paradigm that leverages pre-trained multimodal knowledge from Vision-Language Models (VLMs) to interpret and interact with complex real-world environments. However, these methods remain constrained by the limitations of imitation learning, which struggles to inherently encode physical rules during training. Existing approaches often rely on complex rule-based post-refinement, employ reinforcement learning that remains largely limited to simulation, or utilize diffusion guidance that requires computationally expensive gradient calculations. To address these challenges, we introduce ReflectDrive, a novel learning-based framework that integrates a reflection mechanism for safe trajectory generation via discrete diffusion. We first discretize the two-dimensional driving space to construct an action codebook, enabling the use of pre-trained Diffusion Language Models for planning tasks through fine-tuning. Central to our approach is a safety-aware reflection mechanism that performs iterative self-correction without gradient computation. Our method begins with goal-conditioned trajectory generation to model multi-modal driving behaviors. Based on this, we apply local search methods to identify unsafe tokens and determine feasible solutions, which then serve as safe anchors for inpainting-based regeneration. Evaluated on the NAVSIM benchmark, ReflectDrive demonstrates significant advantages in safety-critical trajectory generation, offering a scalable and reliable solution for autonomous driving systems.

Diffusion language models, especially masked discrete diffusion models, have achieved great success recently. While there are some theoretical and primary empirical results showing the advantages of latent reasoning with looped transformers or continuous chain-of-thoughts, continuous diffusion models typically underperform their discrete counterparts. In this paper, we argue that diffusion language models do not necessarily need to be in the discrete space. In particular, we prove that continuous diffusion models have stronger expressivity than discrete diffusions and looped transformers. We attribute the contradiction between the theoretical expressiveness and empirical performance to their practical trainability: while continuous diffusion provides intermediate supervision that looped transformers lack, they introduce additional difficulty decoding tokens into the discrete token space from the continuous representation space. We therefore propose Coevolutionary Continuous Discrete Diffusion (CCDD), which defines a joint multimodal diffusion process on the union of a continuous representation space and a discrete token space, leveraging a single model to simultaneously denoise in the joint space. By combining two modalities, CCDD is expressive with rich semantics in the latent space, as well as good trainability and sample quality with the help of explicit discrete tokens. We also propose effective architectures and advanced training/sampling techniques for CCDD, which reveals strong empirical performance in extensive language modeling experiments on real-world tasks.

In the post-AlphaGo era, there has been a renewed interest in search techniques such as Monte Carlo Tree Search (MCTS), particularly in their application to Large Language Models (LLMs). This renewed attention is driven by the recognition that current next-token prediction models often lack the ability for long-term planning. Is it possible to instill search-like abilities within the models to enhance their planning abilities without relying on explicit search? We propose DiffuSearch , a model that does implicit search by looking into the future world via discrete diffusion modeling. We instantiate DiffuSearch on a classical board game, Chess, where explicit search is known to be essential. Through extensive controlled experiments, we show DiffuSearch outperforms both the searchless and explicit search-enhanced policies. Specifically, DiffuSearch outperforms the one-step policy by 19.2% and the MCTS-enhanced policy by 14% on action accuracy. Furthermore, DiffuSearch demonstrates a notable 30% enhancement in puzzle-solving abilities compared to explicit search-based policies, along with a significant 540 Elo increase in game-playing strength assessment. These results indicate that implicit search via discrete diffusion is a viable alternative to explicit search over a one-step policy. All codes are publicly available at https://github.com/HKUNLP/DiffuSearch{https://github.com/HKUNLP/DiffuSearch}.

We introduce X-Streamer, an end-to-end multimodal human world modeling framework for building digital human agents capable of infinite interactions across text, speech, and video within a single unified architecture. Starting from a single portrait, X-Streamer enables real-time, open-ended video calls driven by streaming multimodal inputs. At its core is a Thinker-Actor dual-transformer architecture that unifies multimodal understanding and generation, turning a static portrait into persistent and intelligent audiovisual interactions. The Thinker module perceives and reasons over streaming user inputs, while its hidden states are translated by the Actor into synchronized multimodal streams in real time. Concretely, the Thinker leverages a pretrained large language-speech model, while the Actor employs a chunk-wise autoregressive diffusion model that cross-attends to the Thinker's hidden states to produce time-aligned multimodal responses with interleaved discrete text and audio tokens and continuous video latents. To ensure long-horizon stability, we design inter- and intra-chunk attentions with time-aligned multimodal positional embeddings for fine-grained cross-modality alignment and context retention, further reinforced by chunk-wise diffusion forcing and global identity referencing. X-Streamer runs in real time on two A100 GPUs, sustaining hours-long consistent video chat experiences from arbitrary portraits and paving the way toward unified world modeling of interactive digital humans.

Real-world image super-resolution (RWSR) is a long-standing problem as low-quality (LQ) images often have complex and unidentified degradations. Existing methods such as Generative Adversarial Networks (GANs) or continuous diffusion models present their own issues including GANs being difficult to train while continuous diffusion models requiring numerous inference steps. In this paper, we propose an Iterative Token Evaluation and Refinement (ITER) framework for RWSR, which utilizes a discrete diffusion model operating in the discrete token representation space, i.e., indexes of features extracted from a VQGAN codebook pre-trained with high-quality (HQ) images. We show that ITER is easier to train than GANs and more efficient than continuous diffusion models. Specifically, we divide RWSR into two sub-tasks, i.e., distortion removal and texture generation. Distortion removal involves simple HQ token prediction with LQ images, while texture generation uses a discrete diffusion model to iteratively refine the distortion removal output with a token refinement network. In particular, we propose to include a token evaluation network in the discrete diffusion process. It learns to evaluate which tokens are good restorations and helps to improve the iterative refinement results. Moreover, the evaluation network can first check status of the distortion removal output and then adaptively select total refinement steps needed, thereby maintaining a good balance between distortion removal and texture generation. Extensive experimental results show that ITER is easy to train and performs well within just 8 iterative steps. Our codes will be available publicly.

Vision-language-action (VLA) models aim to understand natural language instructions and visual observations and to execute corresponding actions as an embodied agent. Recent work integrates future images into the understanding-acting loop, yielding unified VLAs that jointly understand, generate, and act -- reading text and images and producing future images and actions. However, these models either rely on external experts for modality unification or treat image generation and action prediction as separate processes, limiting the benefits of direct synergy between these tasks. Our core philosophy is to optimize generation and action jointly through a synchronous denoising process, where the iterative refinement enables actions to evolve from initialization, under constant and sufficient visual guidance. We ground this philosophy in our proposed Unified Diffusion VLA and Joint Discrete Denoising Diffusion Process (JD3P), which is a joint diffusion process that integrates multiple modalities into a single denoising trajectory to serve as the key mechanism enabling understanding, generation, and acting to be intrinsically synergistic. Our model and theory are built on a unified tokenized space of all modalities and a hybrid attention mechanism. We further propose a two-stage training pipeline and several inference-time techniques that optimize performance and efficiency. Our approach achieves state-of-the-art performance on benchmarks such as CALVIN, LIBERO, and SimplerEnv with 4times faster inference than autoregressive methods, and we demonstrate its effectiveness through in-depth analysis and real-world evaluations. Our project page is available at https://irpn-eai.github.io/UD-VLA.github.io/.

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.

Vision-Language-Action (VLA) models are emerging as a next-generation paradigm for robotics. We introduce dVLA, a diffusion-based VLA that leverages a multimodal chain-of-thought to unify visual perception, language reasoning, and robotic control in a single system. dVLA jointly optimizes perception, language understanding, and action under a single diffusion objective, enabling stronger cross-modal reasoning and better generalization to novel instructions and objects. For practical deployment, we mitigate inference latency by incorporating two acceleration strategies, a prefix attention mask and KV caching, yielding up to around times speedup at test-time inference. We evaluate dVLA in both simulation and the real world: on the LIBERO benchmark, it achieves state-of-the-art performance with a 96.4% average success rate, consistently surpassing both discrete and continuous action policies; on a real Franka robot, it succeeds across a diverse task suite, including a challenging bin-picking task that requires multi-step planning, demonstrating robust real-world performance. Together, these results underscore the promise of unified diffusion frameworks for practical, high-performance VLA robotics.

The generation of Scalable Vector Graphics (SVG) assets from textual data remains a significant challenge, largely due to the scarcity of high-quality vector datasets and the limitations in scalable vector representations required for modeling intricate graphic distributions. This work introduces SVGFusion, a Text-to-SVG model capable of scaling to real-world SVG data without reliance on a text-based discrete language model or prolonged SDS optimization. The essence of SVGFusion is to learn a continuous latent space for vector graphics with a popular Text-to-Image framework. Specifically, SVGFusion consists of two modules: a Vector-Pixel Fusion Variational Autoencoder (VP-VAE) and a Vector Space Diffusion Transformer (VS-DiT). VP-VAE takes both the SVGs and corresponding rasterizations as inputs and learns a continuous latent space, whereas VS-DiT learns to generate a latent code within this space based on the text prompt. Based on VP-VAE, a novel rendering sequence modeling strategy is proposed to enable the latent space to embed the knowledge of construction logics in SVGs. This empowers the model to achieve human-like design capabilities in vector graphics, while systematically preventing occlusion in complex graphic compositions. Moreover, our SVGFusion's ability can be continuously improved by leveraging the scalability of the VS-DiT by adding more VS-DiT blocks. A large-scale SVG dataset is collected to evaluate the effectiveness of our proposed method. Extensive experimentation has confirmed the superiority of our SVGFusion over existing SVG generation methods, achieving enhanced quality and generalizability, thereby establishing a novel framework for SVG content creation. Code, model, and data will be released at: https://ximinng.github.io/SVGFusionProject/{https://ximinng.github.io/SVGFusionProject/}

Recent advancements in text-to-video (T2V) generation have been driven by two competing paradigms: autoregressive language models and diffusion models. However, each paradigm has intrinsic limitations: language models struggle with visual quality and error accumulation, while diffusion models lack semantic understanding and causal modeling. In this work, we propose LanDiff, a hybrid framework that synergizes the strengths of both paradigms through coarse-to-fine generation. Our architecture introduces three key innovations: (1) a semantic tokenizer that compresses 3D visual features into compact 1D discrete representations through efficient semantic compression, achieving a sim14,000times compression ratio; (2) a language model that generates semantic tokens with high-level semantic relationships; (3) a streaming diffusion model that refines coarse semantics into high-fidelity videos. Experiments show that LanDiff, a 5B model, achieves a score of 85.43 on the VBench T2V benchmark, surpassing the state-of-the-art open-source models Hunyuan Video (13B) and other commercial models such as Sora, Keling, and Hailuo. Furthermore, our model also achieves state-of-the-art performance in long video generation, surpassing other open-source models in this field. Our demo can be viewed at https://landiff.github.io/.

Scaling text-to-speech (TTS) to large-scale, multi-speaker, and in-the-wild datasets is important to capture the diversity in human speech such as speaker identities, prosodies, and styles (e.g., singing). Current large TTS systems usually quantize speech into discrete tokens and use language models to generate these tokens one by one, which suffer from unstable prosody, word skipping/repeating issue, and poor voice quality. In this paper, we develop NaturalSpeech 2, a TTS system that leverages a neural audio codec with residual vector quantizers to get the quantized latent vectors and uses a diffusion model to generate these latent vectors conditioned on text input. To enhance the zero-shot capability that is important to achieve diverse speech synthesis, we design a speech prompting mechanism to facilitate in-context learning in the diffusion model and the duration/pitch predictor. We scale NaturalSpeech 2 to large-scale datasets with 44K hours of speech and singing data and evaluate its voice quality on unseen speakers. NaturalSpeech 2 outperforms previous TTS systems by a large margin in terms of prosody/timbre similarity, robustness, and voice quality in a zero-shot setting, and performs novel zero-shot singing synthesis with only a speech prompt. Audio samples are available at https://speechresearch.github.io/naturalspeech2.

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.

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 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.

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}.

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

World models, which predict transitions based on history observation and action sequences, have shown great promise in improving data efficiency for sequential decision making. However, existing world models often require extensive domain-specific training and still produce low-fidelity, coarse predictions, limiting their applicability in complex environments. In contrast, video diffusion models trained on large, internet-scale datasets have demonstrated impressive capabilities in generating high-quality videos that capture diverse real-world dynamics. In this work, we present Vid2World, a general approach for leveraging and transferring pre-trained video diffusion models into interactive world models. To bridge the gap, Vid2World performs casualization of a pre-trained video diffusion model by crafting its architecture and training objective to enable autoregressive generation. Furthermore, it introduces a causal action guidance mechanism to enhance action controllability in the resulting interactive world model. Extensive experiments in robot manipulation and game simulation domains show that our method offers a scalable and effective approach for repurposing highly capable video diffusion models to interactive world models.

Diffusion-based world models have shown strong potential for unified world simulation, but the iterative denoising remains too costly for interactive use and long-horizon rollouts. While feature caching can accelerate inference without training, we find that policies designed for single-modal diffusion transfer poorly to world models due to two world-model-specific obstacles: token heterogeneity from multi-modal coupling and spatial variation, and non-uniform temporal dynamics where a small set of hard tokens drives error growth, making uniform skipping either unstable or overly conservative. We propose WorldCache, a caching framework tailored to diffusion world models. We introduce Curvature-guided Heterogeneous Token Prediction, which uses a physics-grounded curvature score to estimate token predictability and applies a Hermite-guided damped predictor for chaotic tokens with abrupt direction changes. We also design Chaotic-prioritized Adaptive Skipping, which accumulates a curvature-normalized, dimensionless drift signal and recomputes only when bottleneck tokens begin to drift. Experiments on diffusion world models show that WorldCache delivers up to 3.7times end-to-end speedups while maintaining 98\% rollout quality, demonstrating the vast advantages and practicality of WorldCache in resource-constrained scenarios. Our code is released in https://github.com/FofGofx/WorldCache.

World models learn to predict future states of an environment, enabling planning and mental simulation. Current approaches default to Transformer-based predictors operating in learned latent spaces. This comes at a cost: O(N^2) computation and no explicit spatial inductive bias. This paper asks a foundational question: is self-attention necessary for predictive world modeling, or can alternative computational substrates achieve comparable or superior results? I introduce FluidWorld, a proof-of-concept world model whose predictive dynamics are governed by partial differential equations (PDEs) of reaction-diffusion type. Instead of using a separate neural network predictor, the PDE integration itself produces the future state prediction. In a strictly parameter-matched three-way ablation on unconditional UCF-101 video prediction (64x64, ~800K parameters, identical encoder, decoder, losses, and data), FluidWorld is compared against both a Transformer baseline (self-attention) and a ConvLSTM baseline (convolutional recurrence). While all three models converge to comparable single-step prediction loss, FluidWorld achieves 2x lower reconstruction error, produces representations with 10-15% higher spatial structure preservation and 18-25% more effective dimensionality, and critically maintains coherent multi-step rollouts where both baselines degrade rapidly. All experiments were conducted on a single consumer-grade PC (Intel Core i5, NVIDIA RTX 4070 Ti), without any large-scale compute. These results establish that PDE-based dynamics, which natively provide O(N) spatial complexity, adaptive computation, and global spatial coherence through diffusion, are a viable and parameter-efficient alternative to both attention and convolutional recurrence for world modeling.

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 and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in world modeling. However, unlike typical generation tasks that encourage sample diversity, world models entail different sources of uncertainty and require consistent samples aligned with the ground-truth trajectory, which is a limitation we empirically observe in diffusion models. We argue that a key bottleneck in learning consistent diffusion-based world models lies in the suboptimal predictive ability, which we attribute to the entanglement of condition understanding and target denoising within shared architectures and co-training schemes. To address this, we propose Foresight Diffusion (ForeDiff), a diffusion-based world modeling framework that enhances consistency by decoupling condition understanding from target denoising. ForeDiff incorporates a separate deterministic predictive stream to process conditioning inputs independently of the denoising stream, and further leverages a pretrained predictor to extract informative representations that guide generation. Extensive experiments on robot video prediction and scientific spatiotemporal forecasting show that ForeDiff improves both predictive accuracy and sample consistency over strong baselines, offering a promising direction for diffusion-based world models.

For decades, procedural worlds have been built on procedural noise functions such as Perlin noise, which are fast and infinite, yet fundamentally limited in realism and large-scale coherence. We introduce Terrain Diffusion, an AI-era successor to Perlin noise that bridges the fidelity of diffusion models with the properties that made procedural noise indispensable: seamless infinite extent, seed-consistency, and constant-time random access. At its core is InfiniteDiffusion, a novel algorithm for infinite generation, enabling seamless, real-time synthesis of boundless landscapes. A hierarchical stack of diffusion models couples planetary context with local detail, while a compact Laplacian encoding stabilizes outputs across Earth-scale dynamic ranges. An open-source infinite-tensor framework supports constant-memory manipulation of unbounded tensors, and few-step consistency distillation enables efficient generation. Together, these components establish diffusion models as a practical foundation for procedural world generation, capable of synthesizing entire planets coherently, controllably, and without limits.

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

Recent advances in interactive video generations have demonstrated diffusion model's potential as world models by capturing complex physical dynamics and interactive behaviors. However, existing interactive world models depend on bidirectional attention and lengthy inference steps, severely limiting real-time performance. Consequently, they are hard to simulate real-world dynamics, where outcomes must update instantaneously based on historical context and current actions. To address this, we present Matrix-Game 2.0, an interactive world model generates long videos on-the-fly via few-step auto-regressive diffusion. Our framework consists of three key components: (1) A scalable data production pipeline for Unreal Engine and GTA5 environments to effectively produce massive amounts (about 1200 hours) of video data with diverse interaction annotations; (2) An action injection module that enables frame-level mouse and keyboard inputs as interactive conditions; (3) A few-step distillation based on the casual architecture for real-time and streaming video generation. Matrix Game 2.0 can generate high-quality minute-level videos across diverse scenes at an ultra-fast speed of 25 FPS. We open-source our model weights and codebase to advance research in interactive world modeling.

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 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 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.

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

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling steps. Accelerating DDMs by using larger step sizes typically introduces significant problems in generation quality, as it amplifies the impact of both the compounding decoding error due to factorized predictions and discretization error from numerical approximations, leading to a significant decrease in sampling quality. To address these challenges, we propose learnable sampler distillation (LSD), a novel approach to train fast and high-fidelity samplers for DDMs. LSD employs a distillation approach where a student sampler with a few steps learns to align its intermediate score trajectory with that of a high-quality teacher sampler with numerous steps. This alignment is achieved by optimizing learnable sampler coefficients that adaptively adjust sampling dynamics. Additionally, we further propose LSD+, which also learns time schedules that allocate steps non-uniformly. Experiments across text generation, image generation, and synthetic tasks demonstrate that our proposed approaches outperform existing samplers for DDMs, achieving substantially higher sampling quality with significantly fewer sampling steps. Our code is available at https://github.com/feiyangfu/LSD{https://github.com/feiyangfu/LSD}.

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 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 have significantly improved the performance of image editing. Existing methods realize various approaches to achieve high-quality image editing, including but not limited to text control, dragging operation, and mask-and-inpainting. Among these, instruction-based editing stands out for its convenience and effectiveness in following human instructions across diverse scenarios. However, it still focuses on simple editing operations like adding, replacing, or deleting, and falls short of understanding aspects of world dynamics that convey the realistic dynamic nature in the physical world. Therefore, this work, EditWorld, introduces a new editing task, namely world-instructed image editing, which defines and categorizes the instructions grounded by various world scenarios. We curate a new image editing dataset with world instructions using a set of large pretrained models (e.g., GPT-3.5, Video-LLava and SDXL). To enable sufficient simulation of world dynamics for image editing, our EditWorld trains model in the curated dataset, and improves instruction-following ability with designed post-edit strategy. Extensive experiments demonstrate our method significantly outperforms existing editing methods in this new task. Our dataset and code will be available at https://github.com/YangLing0818/EditWorld

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

This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to develop a family of reparameterized discrete diffusion models. The derived generic framework is highly flexible, offers a fresh perspective of the generation process in discrete diffusion models, and features more effective training and decoding techniques. We conduct extensive experiments to evaluate the text generation capability of our model, demonstrating significant improvements over existing diffusion models.

The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schrödinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent advances in discrete diffusion and flow models have sparked growing interest in applying SB methods to discrete domains, there is still no reliable way to evaluate how well these methods actually solve the underlying problem. We address this challenge by introducing a benchmark for SB on discrete spaces. Our construction yields pairs of probability distributions with analytically known SB solutions, enabling rigorous evaluation. As a byproduct of building this benchmark, we obtain two new SB algorithms, DLightSB and DLightSB-M, and additionally extend prior related work to construct the α-CSBM algorithm. We demonstrate the utility of our benchmark by evaluating both existing and new solvers in high-dimensional discrete settings. This work provides the first step toward proper evaluation of SB methods on discrete spaces, paving the way for more reproducible future studies.

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

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

An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the multidimensional torus is analyzed. The equations describe the dynamics of population species with repulsive or attractive interactions. The numerical scheme is based on a generalized Scharfetter-Gummel discretization of the nonlocal flux term. For merely integrable kernel functions, the scheme preserves the positivity, total mass, and entropy structure. The existence of a discrete solution and its convergence to a solution to the continuous problem, as the mesh size tends to zero, are shown. A key difficulty is the degeneracy of the generalized Bernoulli function in the Scharfetter-Gummel approximation. This issue is overcome by proving a uniform estimate for the discrete Fisher information, which requires both the Boltzmann and Rao entropy inequalities. Numerical simulations illustrate the features of the scheme in one and two space dimensions.

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4.70 FID in 10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10 dataset, and a 4sim 16times speedup compared with previous state-of-the-art training-free samplers on various datasets.

Modern LLM pre-training consumes vast amounts of compute and training data, making the scaling behavior, or scaling laws, of different models a key distinguishing factor. Discrete diffusion language models (DLMs) have been proposed as an alternative to autoregressive language models (ALMs). However, their scaling behavior has not yet been fully explored, with prior work suggesting that they require more data and compute to match the performance of ALMs. We study the scaling behavior of DLMs on different noise types by smoothly interpolating between masked and uniform diffusion while paying close attention to crucial hyperparameters such as batch size and learning rate. Our experiments reveal that the scaling behavior of DLMs strongly depends on the noise type and is considerably different from ALMs. While all noise types converge to similar loss values in compute-bound scaling, we find that uniform diffusion requires more parameters and less data for compute-efficient training compared to masked diffusion, making them a promising candidate in data-bound settings. We scale our uniform diffusion model up to 10B parameters trained for 10^{22} FLOPs, confirming the predicted scaling behavior and making it the largest publicly known uniform diffusion model to date.

A world model is an AI system that simulates how an environment evolves under actions, enabling planning through imagined futures rather than reactive perception. Current world models, however, suffer from visual conflation: the mistaken assumption that high-fidelity video generation implies an understanding of physical and causal dynamics. We show that while modern models excel at predicting pixels, they frequently violate invariant constraints, fail under intervention, and break down in safety-critical decision-making. This survey argues that visual realism is an unreliable proxy for world understanding. Instead, effective world models must encode causal structure, respect domain-specific constraints, and remain stable over long horizons. We propose a reframing of world models as actionable simulators rather than visual engines, emphasizing structured 4D interfaces, constraint-aware dynamics, and closed-loop evaluation. Using medical decision-making as an epistemic stress test, where trial-and-error is impossible and errors are irreversible, we demonstrate that a world model's value is determined not by how realistic its rollouts appear, but by its ability to support counterfactual reasoning, intervention planning, and robust long-horizon foresight.

A world model provides an agent with a representation of its environment, enabling it to predict the causal consequences of its actions. Current world models typically cannot directly and explicitly imitate the actual environment in front of a robot, often resulting in unrealistic behaviors and hallucinations that make them unsuitable for real-world robotics applications. To overcome those challenges, we propose to rethink robot world models as learnable digital twins. We introduce DreMa, a new approach for constructing digital twins automatically using learned explicit representations of the real world and its dynamics, bridging the gap between traditional digital twins and world models. DreMa replicates the observed world and its structure by integrating Gaussian Splatting and physics simulators, allowing robots to imagine novel configurations of objects and to predict the future consequences of robot actions thanks to its compositionality. We leverage this capability to generate new data for imitation learning by applying equivariant transformations to a small set of demonstrations. Our evaluations across various settings demonstrate significant improvements in accuracy and robustness by incrementing actions and object distributions, reducing the data needed to learn a policy and improving the generalization of the agents. As a highlight, we show that a real Franka Emika Panda robot, powered by DreMa's imagination, can successfully learn novel physical tasks from just a single example per task variation (one-shot policy learning). Our project page can be found in: https://dreamtomanipulate.github.io/.

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.

Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the tendency of a node to select neighbors with a probability depending on physical distance. Here, we introduce a class of random spatial networks (RSNs) which generalizes many existing random network models but adds spatial structure. In these networks, nodes are placed randomly in space and joined in edges with a probability depending on their distance and their individual expected degrees, in a manner that crucially remains analytically tractable. We use this network class to propose a new generalization of small-world networks, where the average shortest path lengths in the graph are small, as in classical Watts-Strogatz small-world networks, but with close spatial proximity of nodes that are neighbors in the network playing the role of large clustering. Small-world effects are demonstrated on these spatial small-world networks without clustering. We are able to derive partial integro-differential equations governing susceptible-infectious-recovered disease spreading through an RSN, and we demonstrate the existence of traveling wave solutions. If the distance kernel governing edge placement decays slower than exponential, the population-scale dynamics are dominated by long-range hops followed by local spread of traveling waves. This provides a theoretical modeling framework for recent observations of how epidemics like Ebola evolve in modern connected societies, with long-range connections seeding new focal points from which the epidemic locally spreads in a wavelike manner.

Discrete diffusion models are promising alternatives to autoregressive approaches for text generation, yet their decoding methods remain under-studied. Standard decoding methods for autoregressive models, such as beam search, do not directly apply to iterative denoising, and existing diffusion decoding techniques provide limited control over in-batch diversity. To bridge this gap, we introduce a generalized beam-search framework for discrete diffusion that generates candidates in parallel and supports modular beam-selection objectives. As a diversity-focused instantiation, we propose D5P4, which formulates the selection step as MAP inference over a Determinantal Point Process. Leveraging a scalable greedy solver, D5P4 maintains multi-GPU compatibility and enables an explicit trade-off between model probability and target diversity with near-zero compute overhead. Experiments on free-form generation and question answering demonstrate that D5P4 improves diversity over strong baselines while maintaining competitive generation quality.

While recent multimodal large language models (MLLMs) have made impressive strides, they predominantly employ a conventional autoregressive architecture as their backbone, leaving significant room to explore effective and efficient alternatives in architectural design. Concurrently, recent studies have successfully applied discrete diffusion models to various domains, such as visual understanding and image generation, revealing their considerable potential as a promising backbone for multimodal systems. Drawing inspiration from these pioneering research, we introduce Omni-Diffusion, the first any-to-any multimodal language model built entirely on mask-based discrete diffusion models, which unifies understanding and generation across text, speech, and images. Omni-Diffusion employs a unified mask-based discrete diffusion model to directly capture the joint distribution over discrete multimodal tokens. This approach supports not only bimodal tasks but also more complex scenarios involving multiple modalities. On a diverse set of benchmarks, our method outperforms or performs on par with existing multimodal systems that process two or more modalities, highlighting the significant promise of diffusion models in powering the next generation of multimodal foundation models. Project webpage: https://omni-diffusion.github.io.

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 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.

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

Navigation is a fundamental skill of agents with visual-motor capabilities. We introduce a Navigation World Model (NWM), a controllable video generation model that predicts future visual observations based on past observations and navigation actions. To capture complex environment dynamics, NWM employs a Conditional Diffusion Transformer (CDiT), trained on a diverse collection of egocentric videos of both human and robotic agents, and scaled up to 1 billion parameters. In familiar environments, NWM can plan navigation trajectories by simulating them and evaluating whether they achieve the desired goal. Unlike supervised navigation policies with fixed behavior, NWM can dynamically incorporate constraints during planning. Experiments demonstrate its effectiveness in planning trajectories from scratch or by ranking trajectories sampled from an external policy. Furthermore, NWM leverages its learned visual priors to imagine trajectories in unfamiliar environments from a single input image, making it a flexible and powerful tool for next-generation navigation systems.

In recent years, diffusion based methods have emerged as a powerful paradigm for generative modeling. Although discrete diffusion for natural language processing has been explored to a lesser extent, it shows promise for tasks requiring iterative denoising of token based data. In standard approaches to text generation, transformers dominate, but their reliance on self attention often incurs high computational costs. This paper introduces a fully diffusion driven discrete text generation model built without any transformer or large convolution modules. Instead, the model integrates structured state space dynamics in the time domain with a novel Complex Fourier Multi Layer Perceptron module that operates in the frequency domain. The forward noising process randomly samples the vocabulary to replace tokens with a controlled probability, while the learned reverse model systematically reverts corrupted sequences toward their original states. By composing local state space updates with global Fourier based mixing, the approach effectively captures both short and long range dependencies.

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

A World Model is a generative model used to simulate an environment. World Models have proven capable of learning spatial and temporal representations of Reinforcement Learning environments. In some cases, a World Model offers an agent the opportunity to learn entirely inside of its own dream environment. In this work we explore improving the generalization capabilities from dream environments to real environments (Dream2Real). We present a general approach to improve a controller's ability to transfer from a neural network dream environment to reality at little additional cost. These improvements are gained by drawing on inspiration from Domain Randomization, where the basic idea is to randomize as much of a simulator as possible without fundamentally changing the task at hand. Generally, Domain Randomization assumes access to a pre-built simulator with configurable parameters but oftentimes this is not available. By training the World Model using dropout, the dream environment is capable of creating a nearly infinite number of different dream environments. Previous use cases of dropout either do not use dropout at inference time or averages the predictions generated by multiple sampled masks (Monte-Carlo Dropout). Dropout's Dream Land leverages each unique mask to create a diverse set of dream environments. Our experimental results show that Dropout's Dream Land is an effective technique to bridge the reality gap between dream environments and reality. Furthermore, we additionally perform an extensive set of ablation studies.

Diffusion models have achieved state-of-the-art performance across multiple domains, with recent advancements extending their applicability to discrete data. However, aligning discrete diffusion models with task-specific preferences remains challenging, particularly in scenarios where explicit reward functions are unavailable. In this work, we introduce Discrete Diffusion DPO (D3PO), the first adaptation of Direct Preference Optimization (DPO) to discrete diffusion models formulated as continuous-time Markov chains. Our approach derives a novel loss function that directly fine-tunes the generative process using preference data while preserving fidelity to a reference distribution. We validate D3PO on a structured binary sequence generation task, demonstrating that the method effectively aligns model outputs with preferences while maintaining structural validity. Our results highlight that D3PO enables controlled fine-tuning without requiring explicit reward models, making it a practical alternative to reinforcement learning-based approaches. Future research will explore extending D3PO to more complex generative tasks, including language modeling and protein sequence generation, as well as investigating alternative noise schedules, such as uniform noising, to enhance flexibility across different applications.

Digital Surface Models (DSM) offer a wealth of height information for understanding the Earth's surface as well as monitoring the existence or change in natural and man-made structures. Classical height estimation requires multi-view geospatial imagery or LiDAR point clouds which can be expensive to acquire. Single-view height estimation using neural network based models shows promise however it can struggle with reconstructing high resolution features. The latest advancements in diffusion models for high resolution image synthesis and editing have yet to be utilized for remote sensing imagery, particularly height estimation. Our approach involves training a generative diffusion model to learn the joint distribution of optical and DSM images across both domains as a Markov chain. This is accomplished by minimizing a denoising score matching objective while being conditioned on the source image to generate realistic high resolution 3D surfaces. In this paper we experiment with conditional denoising diffusion probabilistic models (DDPM) for height estimation from a single remotely sensed image and show promising results on the Vaihingen benchmark dataset.

The concept of world models has garnered significant attention due to advancements in multimodal large language models such as GPT-4 and video generation models such as Sora, which are central to the pursuit of artificial general intelligence. This survey offers a comprehensive review of the literature on world models. Generally, world models are regarded as tools for either understanding the present state of the world or predicting its future dynamics. This review presents a systematic categorization of world models, emphasizing two primary functions: (1) constructing internal representations to understand the mechanisms of the world, and (2) predicting future states to simulate and guide decision-making. Initially, we examine the current progress in these two categories. We then explore the application of world models in key domains, including generative games, autonomous driving, robotics, and social simulacra, with a focus on how each domain utilizes these aspects. Finally, we outline key challenges and provide insights into potential future research directions. We summarize the representative papers along with their code repositories in https://github.com/tsinghua-fib-lab/World-Model.

Robotic manipulation policies are commonly initialized through imitation learning, but their performance is limited by the scarcity and narrow coverage of expert data. Reinforcement learning can refine polices to alleviate this limitation, yet real-robot training is costly and unsafe, while training in simulators suffers from the sim-to-real gap. Recent advances in generative models have demonstrated remarkable capabilities in real-world simulation, with diffusion models in particular excelling at generation. This raises the question of how diffusion model-based world models can be combined to enhance pre-trained policies in robotic manipulation. In this work, we propose World4RL, a framework that employs diffusion-based world models as high-fidelity simulators to refine pre-trained policies entirely in imagined environments for robotic manipulation. Unlike prior works that primarily employ world models for planning, our framework enables direct end-to-end policy optimization. World4RL is designed around two principles: pre-training a diffusion world model that captures diverse dynamics on multi-task datasets and refining policies entirely within a frozen world model to avoid online real-world interactions. We further design a two-hot action encoding scheme tailored for robotic manipulation and adopt diffusion backbones to improve modeling fidelity. Extensive simulation and real-world experiments demonstrate that World4RL provides high-fidelity environment modeling and enables consistent policy refinement, yielding significantly higher success rates compared to imitation learning and other baselines. More visualization results are available at https://world4rl.github.io/.

World Model, the supposed algorithmic surrogate of the real-world environment which biological agents experience with and act upon, has been an emerging topic in recent years because of the rising needs to develop virtual agents with artificial (general) intelligence. There has been much debate on what a world model really is, how to build it, how to use it, and how to evaluate it. In this essay, starting from the imagination in the famed Sci-Fi classic Dune, and drawing inspiration from the concept of "hypothetical thinking" in psychology literature, we offer critiques of several schools of thoughts on world modeling, and argue the primary goal of a world model to be simulating all actionable possibilities of the real world for purposeful reasoning and acting. Building on the critiques, we propose a new architecture for a general-purpose world model, based on hierarchical, multi-level, and mixed continuous/discrete representations, and a generative and self-supervision learning framework, with an outlook of a Physical, Agentic, and Nested (PAN) AGI system enabled by such a model.

Recent studies have demonstrated the strong empirical performance of diffusion models on discrete sequences across domains from natural language to biological sequence generation. For example, in the protein inverse folding task, conditional diffusion models have achieved impressive results in generating natural-like sequences that fold back into the original structure. However, practical design tasks often require not only modeling a conditional distribution but also optimizing specific task objectives. For instance, we may prefer protein sequences with high stability. To address this, we consider the scenario where we have pre-trained discrete diffusion models that can generate natural-like sequences, as well as reward models that map sequences to task objectives. We then formulate the reward maximization problem within discrete diffusion models, analogous to reinforcement learning (RL), while minimizing the KL divergence against pretrained diffusion models to preserve naturalness. To solve this RL problem, we propose a novel algorithm, DRAKES, that enables direct backpropagation of rewards through entire trajectories generated by diffusion models, by making the originally non-differentiable trajectories differentiable using the Gumbel-Softmax trick. Our theoretical analysis indicates that our approach can generate sequences that are both natural-like and yield high rewards. While similar tasks have been recently explored in diffusion models for continuous domains, our work addresses unique algorithmic and theoretical challenges specific to discrete diffusion models, which arise from their foundation in continuous-time Markov chains rather than Brownian motion. Finally, we demonstrate the effectiveness of DRAKES in generating DNA and protein sequences that optimize enhancer activity and protein stability, respectively, important tasks for gene therapies and protein-based therapeutics.

A world model enables an intelligent agent to imagine, predict, and reason about how the world evolves in response to its actions, and accordingly to plan and strategize. While recent video generation models produce realistic visual sequences, they typically operate in the prompt-to-full-video manner without causal control, interactivity, or long-horizon consistency required for purposeful reasoning. Existing world modeling efforts, on the other hand, often focus on restricted domains (e.g., physical, game, or 3D-scene dynamics) with limited depth and controllability, and struggle to generalize across diverse environments and interaction formats. In this work, we introduce PAN, a general, interactable, and long-horizon world model that predicts future world states through high-quality video simulation conditioned on history and natural language actions. PAN employs the Generative Latent Prediction (GLP) architecture that combines an autoregressive latent dynamics backbone based on a large language model (LLM), which grounds simulation in extensive text-based knowledge and enables conditioning on language-specified actions, with a video diffusion decoder that reconstructs perceptually detailed and temporally coherent visual observations, to achieve a unification between latent space reasoning (imagination) and realizable world dynamics (reality). Trained on large-scale video-action pairs spanning diverse domains, PAN supports open-domain, action-conditioned simulation with coherent, long-term dynamics. Extensive experiments show that PAN achieves strong performance in action-conditioned world simulation, long-horizon forecasting, and simulative reasoning compared to other video generators and world models, taking a step towards general world models that enable predictive simulation of future world states for reasoning and acting.

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

World Models have emerged as a powerful paradigm for learning compact, predictive representations of environment dynamics, enabling agents to reason, plan, and generalize beyond direct experience. Despite recent interest in World Models, most available implementations remain publication-specific, severely limiting their reusability, increasing the risk of bugs, and reducing evaluation standardization. To mitigate these issues, we introduce stable-worldmodel (SWM), a modular, tested, and documented world-model research ecosystem that provides efficient data-collection tools, standardized environments, planning algorithms, and baseline implementations. In addition, each environment in SWM enables controllable factors of variation, including visual and physical properties, to support robustness and continual learning research. Finally, we demonstrate the utility of SWM by using it to study zero-shot robustness in DINO-WM.

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.

World models are emerging as a transformative paradigm in artificial intelligence, enabling agents to construct internal representations of their environments for predictive reasoning, planning, and decision-making. By learning latent dynamics, world models provide a sample-efficient framework that is especially valuable in data-constrained or safety-critical scenarios. In this paper, we present a comprehensive overview of world models, highlighting their architecture, training paradigms, and applications across prediction, generation, planning, and causal reasoning. We compare and distinguish world models from related concepts such as digital twins, the metaverse, and foundation models, clarifying their unique role as embedded cognitive engines for autonomous agents. We further propose Wireless Dreamer, a novel world model-based reinforcement learning framework tailored for wireless edge intelligence optimization, particularly in low-altitude wireless networks (LAWNs). Through a weather-aware UAV trajectory planning case study, we demonstrate the effectiveness of our framework in improving learning efficiency and decision quality.

Recent approaches have demonstrated the promise of using diffusion models to generate interactive and explorable worlds. However, most of these methods face critical challenges such as excessively large parameter sizes, reliance on lengthy inference steps, and rapidly growing historical context, which severely limit real-time performance and lack text-controlled generation capabilities. To address these challenges, we propose \method, a novel framework designed to generate realistic, interactive, and continuous worlds from a single image or text prompt. \method achieves this through a carefully designed framework that supports keyboard-based exploration of the generated worlds. The framework comprises three core components: (1) a long-video generation framework integrating unified context compression with linear attention; (2) a real-time streaming acceleration strategy powered by bidirectional attention distillation and an enhanced text embedding scheme; (3) a text-controlled method for generating world events. We have provided the codebase in the supplementary material.

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

This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding or removing edges and changing the categories. A graph transformer network is trained to revert this process, simplifying the problem of distribution learning over graphs into a sequence of node and edge classification tasks. We further improve sample quality by introducing a Markovian noise model that preserves the marginal distribution of node and edge types during diffusion, and by incorporating auxiliary graph-theoretic features. A procedure for conditioning the generation on graph-level features is also proposed. DiGress achieves state-of-the-art performance on molecular and non-molecular datasets, with up to 3x validity improvement on a planar graph dataset. It is also the first model to scale to the large GuacaMol dataset containing 1.3M drug-like molecules without the use of molecule-specific representations.

Building world models that accurately and comprehensively represent the real world is the utmost aspiration for conditional image generative models as it would enable their use as world simulators. For these models to be successful world models, they should not only excel at image quality and prompt-image consistency but also ensure high representation diversity. However, current research in generative models mostly focuses on creative applications that are predominantly concerned with human preferences of image quality and aesthetics. We note that generative models have inference time mechanisms - or knobs - that allow the control of generation consistency, quality, and diversity. In this paper, we use state-of-the-art text-to-image and image-and-text-to-image models and their knobs to draw consistency-diversity-realism Pareto fronts that provide a holistic view on consistency-diversity-realism multi-objective. Our experiments suggest that realism and consistency can both be improved simultaneously; however there exists a clear tradeoff between realism/consistency and diversity. By looking at Pareto optimal points, we note that earlier models are better at representation diversity and worse in consistency/realism, and more recent models excel in consistency/realism while decreasing significantly the representation diversity. By computing Pareto fronts on a geodiverse dataset, we find that the first version of latent diffusion models tends to perform better than more recent models in all axes of evaluation, and there exist pronounced consistency-diversity-realism disparities between geographical regions. Overall, our analysis clearly shows that there is no best model and the choice of model should be determined by the downstream application. With this analysis, we invite the research community to consider Pareto fronts as an analytical tool to measure progress towards world models.

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the topological properties of graphs since learning to denoise the noisy samples does not explicitly learn the graph structures to be generated. To tackle this limitation, we propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process. Specifically, we design the generative process as a mixture of endpoint-conditioned diffusion processes which is driven toward the predicted graph that results in rapid convergence. We further introduce a simple parameterization of the mixture process and develop an objective for learning the final graph structure, which enables maximum likelihood training. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features. Our code is available at https://github.com/harryjo97/GruM.

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.

We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and the coagulation-fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite-dimensional truncation of the infinite-dimensional ODE. For these solutions we prove that, in the class of models we call isolated both the total number of particles and the total mass are conserved, whereas in those models we can non-isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations we obtain uniqueness of solutions to the initial value problems.

World models aim to endow AI systems with the ability to represent, generate, and interact with dynamic environments in a coherent and temporally consistent manner. While recent video generation models have demonstrated impressive visual quality, they remain limited in real-time interaction, long-horizon consistency, and persistent memory of dynamic scenes, hindering their evolution into practical world models. In this report, we present TeleWorld, a real-time multimodal 4D world modeling framework that unifies video generation, dynamic scene reconstruction, and long-term world memory within a closed-loop system. TeleWorld introduces a novel generation-reconstruction-guidance paradigm, where generated video streams are continuously reconstructed into a dynamic 4D spatio-temporal representation, which in turn guides subsequent generation to maintain spatial, temporal, and physical consistency. To support long-horizon generation with low latency, we employ an autoregressive diffusion-based video model enhanced with Macro-from-Micro Planning (MMPL)--a hierarchical planning method that reduces error accumulation from frame-level to segment-level-alongside efficient Distribution Matching Distillation (DMD), enabling real-time synthesis under practical computational budgets. Our approach achieves seamless integration of dynamic object modeling and static scene representation within a unified 4D framework, advancing world models toward practical, interactive, and computationally accessible systems. Extensive experiments demonstrate that TeleWorld achieves strong performance in both static and dynamic world understanding, long-term consistency, and real-time generation efficiency, positioning it as a practical step toward interactive, memory-enabled world models for multimodal generation and embodied intelligence.

Discrete diffusion models have achieved success in tasks like image generation and masked language modeling but face limitations in controlled content editing. We introduce DICE (Discrete Inversion for Controllable Editing), the first approach to enable precise inversion for discrete diffusion models, including multinomial diffusion and masked generative models. By recording noise sequences and masking patterns during the reverse diffusion process, DICE enables accurate reconstruction and flexible editing of discrete data without the need for predefined masks or attention manipulation. We demonstrate the effectiveness of DICE across both image and text domains, evaluating it on models such as VQ-Diffusion, Paella, and RoBERTa. Our results show that DICE preserves high data fidelity while enhancing editing capabilities, offering new opportunities for fine-grained content manipulation in discrete spaces. For project webpage, see https://hexiaoxiao-cs.github.io/DICE/.

With growing attention to tabular data these days, the attempt to apply a synthetic table to various tasks has been expanded toward various scenarios. Owing to the recent advances in generative modeling, fake data generated by tabular data synthesis models become sophisticated and realistic. However, there still exists a difficulty in modeling discrete variables (columns) of tabular data. In this work, we propose to process continuous and discrete variables separately (but being conditioned on each other) by two diffusion models. The two diffusion models are co-evolved during training by reading conditions from each other. In order to further bind the diffusion models, moreover, we introduce a contrastive learning method with a negative sampling method. In our experiments with 11 real-world tabular datasets and 8 baseline methods, we prove the efficacy of the proposed method, called CoDi.

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

Diffusion Probabilistic Models (DPMs) are generative models showing competitive performance in various domains, including image synthesis and 3D point cloud generation. Sampling from pre-trained DPMs involves multiple neural function evaluations (NFEs) to transform Gaussian noise samples into images, resulting in higher computational costs compared to single-step generative models such as GANs or VAEs. Therefore, reducing the number of NFEs while preserving generation quality is crucial. To address this, we propose LD3, a lightweight framework designed to learn the optimal time discretization for sampling. LD3 can be combined with various samplers and consistently improves generation quality without having to retrain resource-intensive neural networks. We demonstrate analytically and empirically that LD3 improves sampling efficiency with much less computational overhead. We evaluate our method with extensive experiments on 7 pre-trained models, covering unconditional and conditional sampling in both pixel-space and latent-space DPMs. We achieve FIDs of 2.38 (10 NFE), and 2.27 (10 NFE) on unconditional CIFAR10 and AFHQv2 in 5-10 minutes of training. LD3 offers an efficient approach to sampling from pre-trained diffusion models. Code is available at https://github.com/vinhsuhi/LD3.

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 33.2% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

Video diffusion models (VDMs) have advanced significantly in recent years, enabling the generation of highly realistic videos and drawing the attention of the community in their potential as world simulators. However, despite their capabilities, VDMs often fail to produce physically plausible videos due to an inherent lack of understanding of physics, resulting in incorrect dynamics and event sequences. To address this limitation, we propose a novel two-stage image-to-video generation framework that explicitly incorporates physics. In the first stage, we employ a Vision Language Model (VLM) as a coarse-grained motion planner, integrating chain-of-thought and physics-aware reasoning to predict a rough motion trajectories/changes that approximate real-world physical dynamics while ensuring the inter-frame consistency. In the second stage, we use the predicted motion trajectories/changes to guide the video generation of a VDM. As the predicted motion trajectories/changes are rough, noise is added during inference to provide freedom to the VDM in generating motion with more fine details. Extensive experimental results demonstrate that our framework can produce physically plausible motion, and comparative evaluations highlight the notable superiority of our approach over existing methods. More video results are available on our Project Page: https://madaoer.github.io/projects/physically_plausible_video_generation.

Discrete diffusion models have recently gained significant attention due to their ability to process complex discrete structures for language modeling. However, fine-tuning these models with policy gradient methods, as is commonly done in Reinforcement Learning from Human Feedback (RLHF), remains a challenging task. We propose an efficient, broadly applicable, and theoretically justified policy gradient algorithm, called Score Entropy Policy Optimization (SEPO), for fine-tuning discrete diffusion models over non-differentiable rewards. Our numerical experiments across several discrete generative tasks demonstrate the scalability and efficiency of our method. Our code is available at https://github.com/ozekri/SEPO.

Diffusion models have demonstrated exceptional visual quality in video generation, making them promising for autonomous driving world modeling. However, existing video diffusion-based world models struggle with flexible-length, long-horizon predictions and integrating trajectory planning. This is because conventional video diffusion models rely on global joint distribution modeling of fixed-length frame sequences rather than sequentially constructing localized distributions at each timestep. In this work, we propose Epona, an autoregressive diffusion world model that enables localized spatiotemporal distribution modeling through two key innovations: 1) Decoupled spatiotemporal factorization that separates temporal dynamics modeling from fine-grained future world generation, and 2) Modular trajectory and video prediction that seamlessly integrate motion planning with visual modeling in an end-to-end framework. Our architecture enables high-resolution, long-duration generation while introducing a novel chain-of-forward training strategy to address error accumulation in autoregressive loops. Experimental results demonstrate state-of-the-art performance with 7.4\% FVD improvement and minutes longer prediction duration compared to prior works. The learned world model further serves as a real-time motion planner, outperforming strong end-to-end planners on NAVSIM benchmarks. Code will be publicly available at https://github.com/Kevin-thu/Epona/{https://github.com/Kevin-thu/Epona/}.

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

As online shopping is growing, the ability for buyers to virtually visualize products in their settings-a phenomenon we define as "Virtual Try-All"-has become crucial. Recent diffusion models inherently contain a world model, rendering them suitable for this task within an inpainting context. However, traditional image-conditioned diffusion models often fail to capture the fine-grained details of products. In contrast, personalization-driven models such as DreamPaint are good at preserving the item's details but they are not optimized for real-time applications. We present "Diffuse to Choose," a novel diffusion-based image-conditioned inpainting model that efficiently balances fast inference with the retention of high-fidelity details in a given reference item while ensuring accurate semantic manipulations in the given scene content. Our approach is based on incorporating fine-grained features from the reference image directly into the latent feature maps of the main diffusion model, alongside with a perceptual loss to further preserve the reference item's details. We conduct extensive testing on both in-house and publicly available datasets, and show that Diffuse to Choose is superior to existing zero-shot diffusion inpainting methods as well as few-shot diffusion personalization algorithms like DreamPaint.

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium thermodynamics, we view points in point clouds as particles in a thermodynamic system in contact with a heat bath, which diffuse from the original distribution to a noise distribution. Point cloud generation thus amounts to learning the reverse diffusion process that transforms the noise distribution to the distribution of a desired shape. Specifically, we propose to model the reverse diffusion process for point clouds as a Markov chain conditioned on certain shape latent. We derive the variational bound in closed form for training and provide implementations of the model. Experimental results demonstrate that our model achieves competitive performance in point cloud generation and auto-encoding. The code is available at https://github.com/luost26/diffusion-point-cloud.

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.

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.

We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models, to obtain new samples from a distribution given samples from a discrete space. GGM deploys a discrete Markov chain called the heat bath dynamics (or the Glauber dynamics) to denoise a sequence of noisy tokens to a sample from a joint distribution of discrete tokens. Our novel conceptual framework provides an exact reduction of the task of learning the denoising Markov chain to solving a class of binary classification tasks. More specifically, the model learns to classify a given token in a noisy sequence as signal or noise. In contrast, prior works on discrete diffusion models either solve regression problems to learn importance ratios, or minimize loss functions given by variational approximations. We apply GGM to language modeling and image generation, where images are discretized using image tokenizers like VQGANs. We show that it outperforms existing discrete diffusion models in language generation, and demonstrates strong performance for image generation without using dataset-specific image tokenizers. We also show that our model is capable of performing well in zero-shot control settings like text and image infilling.

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

Generation-driven world models create immersive virtual environments but suffer slow inference due to the iterative nature of diffusion models. While recent advances have improved diffusion model efficiency, directly applying these techniques to world models introduces limitations such as quality degradation. In this paper, we present HERO, a training-free hierarchical acceleration framework tailored for efficient world models. Owing to the multi-modal nature of world models, we identify a feature coupling phenomenon, wherein shallow layers exhibit high temporal variability, while deeper layers yield more stable feature representations. Motivated by this, HERO adopts hierarchical strategies to accelerate inference: (i) In shallow layers, a patch-wise refresh mechanism efficiently selects tokens for recomputation. With patch-wise sampling and frequency-aware tracking, it avoids extra metric computation and remain compatible with FlashAttention. (ii) In deeper layers, a linear extrapolation scheme directly estimates intermediate features. This completely bypasses the computations in attention modules and feed-forward networks. Our experiments show that HERO achieves a 1.73times speedup with minimal quality degradation, significantly outperforming existing diffusion acceleration methods.

Recent advances in generative AI have unveiled significant potential for the creation of 3D content. However, current methods either apply a pre-trained 2D diffusion model with the time-consuming score distillation sampling (SDS), or a direct 3D diffusion model trained on limited 3D data losing generation diversity. In this work, we approach the problem by employing a multi-view 2.5D diffusion fine-tuned from a pre-trained 2D diffusion model. The multi-view 2.5D diffusion directly models the structural distribution of 3D data, while still maintaining the strong generalization ability of the original 2D diffusion model, filling the gap between 2D diffusion-based and direct 3D diffusion-based methods for 3D content generation. During inference, multi-view normal maps are generated using the 2.5D diffusion, and a novel differentiable rasterization scheme is introduced to fuse the almost consistent multi-view normal maps into a consistent 3D model. We further design a normal-conditioned multi-view image generation module for fast appearance generation given the 3D geometry. Our method is a one-pass diffusion process and does not require any SDS optimization as post-processing. We demonstrate through extensive experiments that, our direct 2.5D generation with the specially-designed fusion scheme can achieve diverse, mode-seeking-free, and high-fidelity 3D content generation in only 10 seconds. Project page: https://nju-3dv.github.io/projects/direct25.

Most multi-agent systems rely exclusively on autoregressive language models (ARMs) that are based on sequential generation. Although effective for fluent text, ARMs limit global reasoning and plan revision. On the other hand, Discrete Diffusion Language Models (DDLMs) enable non-sequential, globally revisable generation and have shown strong planning capabilities, but their limited text fluency hinders direct collaboration with ARMs. We introduce Latent-DARM, a latent-space communication framework bridging DDLM (planners) and ARM (executors), maximizing collaborative benefits. Across mathematical, scientific, and commonsense reasoning benchmarks, Latent-DARM outperforms text-based interfaces on average, improving accuracy from 27.0% to 36.0% on DART-5 and from 0.0% to 14.0% on AIME2024. Latent-DARM approaches the results of state-of-the-art reasoning models while using less than 2.2% of its token budget. This work advances multi-agent collaboration among agents with heterogeneous models.

Recent advances in video generation have spurred the development of world models capable of simulating 3D-consistent environments and interactions with static objects. However, a significant limitation remains in their ability to model dynamic, reactive agents that can intelligently influence and interact with the world. To address this gap, we introduce COMBAT, a real-time, action-controlled world model trained on the complex 1v1 fighting game Tekken 3. Our work demonstrates that diffusion models can successfully simulate a dynamic opponent that reacts to player actions, learning its behavior implicitly. Our approach utilizes a 1.2 billion parameter Diffusion Transformer, conditioned on latent representations from a deep compression autoencoder. We employ state-of-the-art techniques, including causal distillation and diffusion forcing, to achieve real-time inference. Crucially, we observe the emergence of sophisticated agent behavior by training the model solely on single-player inputs, without any explicit supervision for the opponent's policy. Unlike traditional imitation learning methods, which require complete action labels, COMBAT learns effectively from partially observed data to generate responsive behaviors for a controllable Player 1. We present an extensive study and introduce novel evaluation methods to benchmark this emergent agent behavior, establishing a strong foundation for training interactive agents within diffusion-based world models.

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.

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 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.

This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or diffusion models, for generative artificial intelligence. We provide a detailed basic mathematical framework for DDPMs and explain the main ideas behind training and generation procedures. In this overview article we also review selected extensions and improvements of the basic framework from the literature such as improved DDPMs, denoising diffusion implicit models, classifier-free diffusion guidance models, and latent diffusion models.

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

World models (WMs) are intended to serve as internal simulators of the real world that enable agents to understand, anticipate, and act upon complex environments. Existing WM benchmarks remain narrowly focused on next-state prediction and visual fidelity, overlooking the richer simulation capabilities required for intelligent behavior. To address this gap, we introduce WR-Arena, a comprehensive benchmark for evaluating WMs along three fundamental dimensions of next world simulation: (i) Action Simulation Fidelity, the ability to interpret and follow semantically meaningful, multi-step instructions and generate diverse counterfactual rollouts; (ii) Long-horizon Forecast, the ability to sustain accurate, coherent, and physically plausible simulations across extended interactions; and (iii) Simulative Reasoning and Planning, the ability to support goal-directed reasoning by simulating, comparing, and selecting among alternative futures in both structured and open-ended environments. We build a task taxonomy and curate diverse datasets designed to probe these capabilities, moving beyond single-turn and perceptual evaluations. Through extensive experiments with state-of-the-art WMs, our results expose a substantial gap between current models and human-level hypothetical reasoning, and establish WR-Arena as both a diagnostic tool and a guideline for advancing next-generation world models capable of robust understanding, forecasting, and purposeful action. The code is available at https://github.com/MBZUAI-IFM/WR-Arena.

The landscape of video generation is shifting, from a focus on generating visually appealing clips to building virtual environments that support interaction and maintain physical plausibility. These developments point toward the emergence of video foundation models that function not only as visual generators but also as implicit world models, models that simulate the physical dynamics, agent-environment interactions, and task planning that govern real or imagined worlds. This survey provides a systematic overview of this evolution, conceptualizing modern video foundation models as the combination of two core components: an implicit world model and a video renderer. The world model encodes structured knowledge about the world, including physical laws, interaction dynamics, and agent behavior. It serves as a latent simulation engine that enables coherent visual reasoning, long-term temporal consistency, and goal-driven planning. The video renderer transforms this latent simulation into realistic visual observations, effectively producing videos as a "window" into the simulated world. We trace the progression of video generation through four generations, in which the core capabilities advance step by step, ultimately culminating in a world model, built upon a video generation model, that embodies intrinsic physical plausibility, real-time multimodal interaction, and planning capabilities spanning multiple spatiotemporal scales. For each generation, we define its core characteristics, highlight representative works, and examine their application domains such as robotics, autonomous driving, and interactive gaming. Finally, we discuss open challenges and design principles for next-generation world models, including the role of agent intelligence in shaping and evaluating these systems. An up-to-date list of related works is maintained at this link.

Discrete diffusion models are gaining traction in the visual generative area for their efficiency and compatibility. However, the pioneered attempts still fall behind the continuous counterparts, which we attribute to the noise (absorbing state) design and sampling heuristics. In this study, we propose the rehashing noise framework for discrete diffusion transformer, termed ReDDiT, to extend absorbing states and improve expressive capacity of discrete diffusion models. ReDDiT enriches the potential paths that latent variables can traverse during training with randomized multi-index corruption. The derived rehash sampler, which reverses the randomized absorbing paths, guarantees the diversity and low discrepancy of the generation process. These reformulations lead to more consistent and competitive generation quality, mitigating the need for heavily tuned randomness. Experiments show that ReDDiT significantly outperforms the baseline (reducing gFID from 6.18 to 1.61) and is on par with the continuous counterparts with higher efficiency.

We present Seed Diffusion Preview, a large-scale language model based on discrete-state diffusion, offering remarkably fast inference speed. Thanks to non-sequential, parallel generation, discrete diffusion models provide a notable speedup to mitigate the inherent latency of token-by-token decoding, as demonstrated recently (e.g., Mercury Coder, Gemini Diffusion). Seed Diffusion Preview achieves an inference speed of 2,146 token/s over H20 GPUs while maintaining competitive performance across a sweep of standard code evaluation benchmarks, significantly faster than contemporary Mercury and Gemini Diffusion, establishing new state of the art on the speed-quality Pareto frontier for code models.

This paper presents WorldPlay, a streaming video diffusion model that enables real-time, interactive world modeling with long-term geometric consistency, resolving the trade-off between speed and memory that limits current methods. WorldPlay draws power from three key innovations. 1) We use a Dual Action Representation to enable robust action control in response to the user's keyboard and mouse inputs. 2) To enforce long-term consistency, our Reconstituted Context Memory dynamically rebuilds context from past frames and uses temporal reframing to keep geometrically important but long-past frames accessible, effectively alleviating memory attenuation. 3) We also propose Context Forcing, a novel distillation method designed for memory-aware model. Aligning memory context between the teacher and student preserves the student's capacity to use long-range information, enabling real-time speeds while preventing error drift. Taken together, WorldPlay generates long-horizon streaming 720p video at 24 FPS with superior consistency, comparing favorably with existing techniques and showing strong generalization across diverse scenes. Project page and online demo can be found: https://3d-models.hunyuan.tencent.com/world/ and https://3d.hunyuan.tencent.com/sceneTo3D.

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.

In recent times, the generation of 3D assets from text prompts has shown impressive results. Both 2D and 3D diffusion models can generate decent 3D objects based on prompts. 3D diffusion models have good 3D consistency, but their quality and generalization are limited as trainable 3D data is expensive and hard to obtain. 2D diffusion models enjoy strong abilities of generalization and fine generation, but the 3D consistency is hard to guarantee. This paper attempts to bridge the power from the two types of diffusion models via the recent explicit and efficient 3D Gaussian splatting representation. A fast 3D generation framework, named as \name, is proposed, where the 3D diffusion model provides point cloud priors for initialization and the 2D diffusion model enriches the geometry and appearance. Operations of noisy point growing and color perturbation are introduced to enhance the initialized Gaussians. Our \name can generate a high-quality 3D instance within 25 minutes on one GPU, much faster than previous methods, while the generated instances can be directly rendered in real time. Demos and code are available at https://taoranyi.com/gaussiandreamer/.

Discrete diffusion models have emerged as a promising direction for vision-language tasks, offering bidirectional context modeling and theoretical parallelization. However, their practical application is severely hindered by a train-inference discrepancy, which leads to catastrophic error cascades: initial token errors during parallel decoding pollute the generation context, triggering a chain reaction of compounding errors and leading to syntactic errors and semantic hallucinations. To address this fundamental challenge, we reframe the generation process from passive denoising to active refining. We introduce ReDiff, a refining-enhanced diffusion framework that teaches the model to identify and correct its own errors. Our approach features a two-stage training process: first, we instill a foundational revision capability by training the model to revise synthetic errors; second, we implement a novel online self-correction loop where the model is explicitly trained to revise its own flawed drafts by learning from an expert's corrections. This mistake-driven learning endows the model with the crucial ability to revisit and refine its already generated output, effectively breaking the error cascade. Extensive experiments demonstrate that ReDiff significantly improves the coherence and factual accuracy of generated content, enabling stable and efficient parallel generation far superior to traditional denoising methods. Our codes and models are available at https://rediff-hku.github.io/.

Recent progress in 3D reconstruction has made it easy to create realistic digital twins from everyday environments. However, current digital twins remain largely static and are limited to navigation and view synthesis without embodied interactivity. To bridge this gap, we introduce Dexterous World Model (DWM), a scene-action-conditioned video diffusion framework that models how dexterous human actions induce dynamic changes in static 3D scenes. Given a static 3D scene rendering and an egocentric hand motion sequence, DWM generates temporally coherent videos depicting plausible human-scene interactions. Our approach conditions video generation on (1) static scene renderings following a specified camera trajectory to ensure spatial consistency, and (2) egocentric hand mesh renderings that encode both geometry and motion cues to model action-conditioned dynamics directly. To train DWM, we construct a hybrid interaction video dataset. Synthetic egocentric interactions provide fully aligned supervision for joint locomotion and manipulation learning, while fixed-camera real-world videos contribute diverse and realistic object dynamics. Experiments demonstrate that DWM enables realistic and physically plausible interactions, such as grasping, opening, and moving objects, while maintaining camera and scene consistency. This framework represents a first step toward video diffusion-based interactive digital twins and enables embodied simulation from egocentric actions.

Model-based reinforcement learning agents utilizing transformers have shown improved sample efficiency due to their ability to model extended context, resulting in more accurate world models. However, for complex reasoning and planning tasks, these methods primarily rely on continuous representations. This complicates modeling of discrete properties of the real world such as disjoint object classes between which interpolation is not plausible. In this work, we introduce discrete abstract representations for transformer-based learning (DART), a sample-efficient method utilizing discrete representations for modeling both the world and learning behavior. We incorporate a transformer-decoder for auto-regressive world modeling and a transformer-encoder for learning behavior by attending to task-relevant cues in the discrete representation of the world model. For handling partial observability, we aggregate information from past time steps as memory tokens. DART outperforms previous state-of-the-art methods that do not use look-ahead search on the Atari 100k sample efficiency benchmark with a median human-normalized score of 0.790 and beats humans in 9 out of 26 games. We release our code at https://pranaval.github.io/DART/.

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.

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

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

Diffusion models have emerged as powerful generative models in the text-to-image domain. This paper studies their application as observation-to-action models for imitating human behaviour in sequential environments. Human behaviour is stochastic and multimodal, with structured correlations between action dimensions. Meanwhile, standard modelling choices in behaviour cloning are limited in their expressiveness and may introduce bias into the cloned policy. We begin by pointing out the limitations of these choices. We then propose that diffusion models are an excellent fit for imitating human behaviour, since they learn an expressive distribution over the joint action space. We introduce several innovations to make diffusion models suitable for sequential environments; designing suitable architectures, investigating the role of guidance, and developing reliable sampling strategies. Experimentally, diffusion models closely match human demonstrations in a simulated robotic control task and a modern 3D gaming environment.