Daily Papers

In the domain of 3D content creation, achieving optimal mesh topology through AI models has long been a pursuit for 3D artists. Previous methods, such as MeshGPT, have explored the generation of ready-to-use 3D objects via mesh auto-regressive techniques. While these methods produce visually impressive results, their reliance on token-by-token predictions in the auto-regressive process leads to several significant limitations. These include extremely slow generation speeds and an uncontrollable number of mesh faces. In this paper, we introduce MeshCraft, a novel framework for efficient and controllable mesh generation, which leverages continuous spatial diffusion to generate discrete triangle faces. Specifically, MeshCraft consists of two core components: 1) a transformer-based VAE that encodes raw meshes into continuous face-level tokens and decodes them back to the original meshes, and 2) a flow-based diffusion transformer conditioned on the number of faces, enabling the generation of high-quality 3D meshes with a predefined number of faces. By utilizing the diffusion model for the simultaneous generation of the entire mesh topology, MeshCraft achieves high-fidelity mesh generation at significantly faster speeds compared to auto-regressive methods. Specifically, MeshCraft can generate an 800-face mesh in just 3.2 seconds (35times faster than existing baselines). Extensive experiments demonstrate that MeshCraft outperforms state-of-the-art techniques in both qualitative and quantitative evaluations on ShapeNet dataset and demonstrates superior performance on Objaverse dataset. Moreover, it integrates seamlessly with existing conditional guidance strategies, showcasing its potential to relieve artists from the time-consuming manual work involved in mesh creation.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system. Specifically, we first design a codebook-based sparse encoder, which coarsens the continuous spatial domain into a sparse graph topology. Then, we employ a graph neural ordinary differential equation to model the dynamics and guide a diffusion decoder for reconstruction. SparseDiff autoregressively predicts the spatiotemporal evolution and adjust the sparse topological structure to adapt to emergent spatiotemporal patterns by adaptive re-encoding. Extensive evaluations on representative systems demonstrate that SparseDiff achieves an average prediction error reduction of 49.99\% compared to baselines, requiring only 1\% of the spatial resolution.

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

Numerous models have been developed for scanpath and saliency prediction, which are typically trained on scanpaths, which model eye movement as a sequence of discrete fixation points connected by saccades, while the rich information contained in the raw trajectories is often discarded. Moreover, most existing approaches fail to capture the variability observed among human subjects viewing the same image. They generally predict a single scanpath of fixed, pre-defined length, which conflicts with the inherent diversity and stochastic nature of real-world visual attention. To address these challenges, we propose DiffEye, a diffusion-based training framework designed to model continuous and diverse eye movement trajectories during free viewing of natural images. Our method builds on a diffusion model conditioned on visual stimuli and introduces a novel component, namely Corresponding Positional Embedding (CPE), which aligns spatial gaze information with the patch-based semantic features of the visual input. By leveraging raw eye-tracking trajectories rather than relying on scanpaths, DiffEye captures the inherent variability in human gaze behavior and generates high-quality, realistic eye movement patterns, despite being trained on a comparatively small dataset. The generated trajectories can also be converted into scanpaths and saliency maps, resulting in outputs that more accurately reflect the distribution of human visual attention. DiffEye is the first method to tackle this task on natural images using a diffusion model while fully leveraging the richness of raw eye-tracking data. Our extensive evaluation shows that DiffEye not only achieves state-of-the-art performance in scanpath generation but also enables, for the first time, the generation of continuous eye movement trajectories. Project webpage: https://diff-eye.github.io/

We present Stable Part Diffusion 4D (SP4D), a framework for generating paired RGB and kinematic part videos from monocular inputs. Unlike conventional part segmentation methods that rely on appearance-based semantic cues, SP4D learns to produce kinematic parts - structural components aligned with object articulation and consistent across views and time. SP4D adopts a dual-branch diffusion model that jointly synthesizes RGB frames and corresponding part segmentation maps. To simplify the architecture and flexibly enable different part counts, we introduce a spatial color encoding scheme that maps part masks to continuous RGB-like images. This encoding allows the segmentation branch to share the latent VAE from the RGB branch, while enabling part segmentation to be recovered via straightforward post-processing. A Bidirectional Diffusion Fusion (BiDiFuse) module enhances cross-branch consistency, supported by a contrastive part consistency loss to promote spatial and temporal alignment of part predictions. We demonstrate that the generated 2D part maps can be lifted to 3D to derive skeletal structures and harmonic skinning weights with few manual adjustments. To train and evaluate SP4D, we construct KinematicParts20K, a curated dataset of over 20K rigged objects selected and processed from Objaverse XL (Deitke et al., 2023), each paired with multi-view RGB and part video sequences. Experiments show that SP4D generalizes strongly to diverse scenarios, including real-world videos, novel generated objects, and rare articulated poses, producing kinematic-aware outputs suitable for downstream animation and motion-related tasks.

Accurate air quality forecasting is crucial for protecting public health and guiding environmental policy, yet it remains challenging due to nonlinear spatiotemporal dynamics, wind-driven transport, and distribution shifts across regions. Physics-based models are interpretable but computationally expensive and often rely on restrictive assumptions, whereas purely data-driven models can be accurate but may lack robustness and calibrated uncertainty. To address these limitations, we propose Neural Dynamic Diffusion-Advection Fields (NeuroDDAF), a physics-informed forecasting framework that unifies neural representation learning with open-system transport modeling. NeuroDDAF integrates (i) a GRU-Graph Attention encoder to capture temporal dynamics and wind-aware spatial interactions, (ii) a Fourier-domain diffusion-advection module with learnable residuals, (iii) a wind-modulated latent Neural ODE to model continuous-time evolution under time-varying connectivity, and (iv) an evidential fusion mechanism that adaptively combines physics-guided and neural forecasts while quantifying uncertainty. Experiments on four urban datasets (Beijing, Shenzhen, Tianjin, and Ancona) across 1-3 day horizons show that NeuroDDAF consistently outperforms strong baselines, including AirPhyNet, achieving up to 9.7% reduction in RMSE and 9.4% reduction in MAE on long-term forecasts. On the Beijing dataset, NeuroDDAF attains an RMSE of 41.63 μg/m^3 for 1-day prediction and 48.88 μg/m^3 for 3-day prediction, representing the best performance among all compared methods. In addition, NeuroDDAF improves cross-city generalization and yields well-calibrated uncertainty estimates, as confirmed by ensemble variance analysis and case studies under varying wind conditions.

Masked-based autoregressive models have demonstrated promising image generation capability in continuous space. However, their potential for video generation remains under-explored. In this paper, we propose VideoMAR, a concise and efficient decoder-only autoregressive image-to-video model with continuous tokens, composing temporal frame-by-frame and spatial masked generation. We first identify temporal causality and spatial bi-directionality as the first principle of video AR models, and propose the next-frame diffusion loss for the integration of mask and video generation. Besides, the huge cost and difficulty of long sequence autoregressive modeling is a basic but crucial issue. To this end, we propose the temporal short-to-long curriculum learning and spatial progressive resolution training, and employ progressive temperature strategy at inference time to mitigate the accumulation error. Furthermore, VideoMAR replicates several unique capacities of language models to video generation. It inherently bears high efficiency due to simultaneous temporal-wise KV cache and spatial-wise parallel generation, and presents the capacity of spatial and temporal extrapolation via 3D rotary embeddings. On the VBench-I2V benchmark, VideoMAR surpasses the previous state-of-the-art (Cosmos I2V) while requiring significantly fewer parameters (9.3%), training data (0.5%), and GPU resources (0.2%).

Traditional transformer-based semantic segmentation relies on quantized embeddings. However, our analysis reveals that autoencoder accuracy on segmentation mask using quantized embeddings (e.g. VQ-VAE) is 8% lower than continuous-valued embeddings (e.g. KL-VAE). Motivated by this, we propose a continuous-valued embedding framework for semantic segmentation. By reformulating semantic mask generation as a continuous image-to-embedding diffusion process, our approach eliminates the need for discrete latent representations while preserving fine-grained spatial and semantic details. Our key contribution includes a diffusion-guided autoregressive transformer that learns a continuous semantic embedding space by modeling long-range dependencies in image features. Our framework contains a unified architecture combining a VAE encoder for continuous feature extraction, a diffusion-guided transformer for conditioned embedding generation, and a VAE decoder for semantic mask reconstruction. Our setting facilitates zero-shot domain adaptation capabilities enabled by the continuity of the embedding space. Experiments across diverse datasets (e.g., Cityscapes and domain-shifted variants) demonstrate state-of-the-art robustness to distribution shifts, including adverse weather (e.g., fog, snow) and viewpoint variations. Our model also exhibits strong noise resilience, achieving robust performance (approx 95% AP compared to baseline) under gaussian noise, moderate motion blur, and moderate brightness/contrast variations, while experiencing only a moderate impact (approx 90% AP compared to baseline) from 50% salt and pepper noise, saturation and hue shifts. Code available: https://github.com/mahmed10/CAMSS.git

In text-to-video (T2V) generation, significant attention has been directed toward its development, yet unifying discrete and continuous grounding conditions in T2V generation remains under-explored. This paper proposes a Grounded text-to-Video generation framework, termed GVDIFF. First, we inject the grounding condition into the self-attention through an uncertainty-based representation to explicitly guide the focus of the network. Second, we introduce a spatial-temporal grounding layer that connects the grounding condition with target objects and enables the model with the grounded generation capacity in the spatial-temporal domain. Third, our dynamic gate network adaptively skips the redundant grounding process to selectively extract grounding information and semantics while improving efficiency. We extensively evaluate the grounded generation capacity of GVDIFF and demonstrate its versatility in applications, including long-range video generation, sequential prompts, and object-specific editing.

This paper presents the Large Vision Diffusion Transformer (LaVin-DiT), a scalable and unified foundation model designed to tackle over 20 computer vision tasks in a generative framework. Unlike existing large vision models directly adapted from natural language processing architectures, which rely on less efficient autoregressive techniques and disrupt spatial relationships essential for vision data, LaVin-DiT introduces key innovations to optimize generative performance for vision tasks. First, to address the high dimensionality of visual data, we incorporate a spatial-temporal variational autoencoder that encodes data into a continuous latent space. Second, for generative modeling, we develop a joint diffusion transformer that progressively produces vision outputs. Third, for unified multi-task training, in-context learning is implemented. Input-target pairs serve as task context, which guides the diffusion transformer to align outputs with specific tasks within the latent space. During inference, a task-specific context set and test data as queries allow LaVin-DiT to generalize across tasks without fine-tuning. Trained on extensive vision datasets, the model is scaled from 0.1B to 3.4B parameters, demonstrating substantial scalability and state-of-the-art performance across diverse vision tasks. This work introduces a novel pathway for large vision foundation models, underscoring the promising potential of diffusion transformers. The code and models will be open-sourced.

Designing sparse attention for diffusion transformers requires reconciling two-dimensional spatial locality with GPU efficiency, a trade-off that current methods struggle to achieve. Existing approaches enforce two-dimensional spatial locality but often incur uncoalesced memory access. We present HilbertA, a 2D-aware and GPU-efficient sparse attention mechanism. HilbertA reorders image tokens along Hilbert curves to achieve a contiguous memory layout while preserving spatial neighborhoods, and employs a sliding schedule across layers to enable long-range information propagation without repeated or uncoalesced memory access. To further enhance cross-tile communication and positional awareness, HilbertA introduces a small central shared region. Implemented in Triton, HilbertA delivers comparable image quality with significant acceleration over prior methods on Flux.1-dev, demonstrating the feasibility of hardware-aligned two-dimensional sparse attention for high-resolution image generation. HilbertA delivers attention speedups of 2.3times when generating 1024times 1024 images, and up to 4.17times at 2048times 2048, while achieving image quality comparable to or surpassing baselines.

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 generating images conditionally on text, such as Dall-E 2 and Stable Diffusion, have recently made a splash far beyond the computer vision community. Here, we tackle the related problem of generating point clouds, both unconditionally, and conditionally with images. For the latter, we introduce a novel geometrically-motivated conditioning scheme based on projecting sparse image features into the point cloud and attaching them to each individual point, at every step in the denoising process. This approach improves geometric consistency and yields greater fidelity than current methods relying on unstructured, global latent codes. Additionally, we show how to apply recent continuous-time diffusion schemes. Our method performs on par or above the state of art on conditional and unconditional experiments on synthetic data, while being faster, lighter, and delivering tractable likelihoods. We show it can also scale to diverse indoors scenes.

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

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

Continuous diffusion has been the foundation of high-fidelity, controllable, and few-step generation of many data modalities such as images. However, in language modeling, prior continuous diffusion language models (DLMs) lag behind discrete counterparts due to the sparse data space and the underexplored design space. In this work, we close this gap with LangFlow, the first continuous DLM to rival discrete diffusion, by connecting embedding-space DLMs to Flow Matching via Bregman divergence, alongside three key innovations: (1) we derive a novel ODE-based NLL bound for principled evaluation of continuous flow-based language models; (2) we propose an information-uniform principle for setting the noise schedule, which motivates a learnable noise scheduler based on a Gumbel distribution; and (3) we revise prior training protocols by incorporating self-conditioning, as we find it improves both likelihood and sample quality of embedding-space DLMs with effects substantially different from discrete diffusion. Putting everything together, LangFlow rivals top discrete DLMs on both the perplexity (PPL) and the generative perplexity (Gen. PPL), reaching a PPL of 30.0 on LM1B and 24.6 on OpenWebText. It even exceeds autoregressive baselines in zero-shot transfer on 4 out of 7 benchmarks. LangFlow provides the first clear evidence that continuous diffusion is a promising paradigm for language modeling. Homepage: https://github.com/nealchen2003/LangFlow

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.

Standard discrete diffusion models treat all unobserved states identically by mapping them to an absorbing [MASK] token. This creates an 'information void' where semantic information that could be inferred from unmasked tokens is lost between denoising steps. We introduce Continuously Augmented Discrete Diffusion (CADD), a framework that augments the discrete state space with a paired diffusion in a continuous latent space. This yields graded, gradually corrupted states in which masked tokens are represented by noisy yet informative latent vectors rather than collapsed 'information voids'. At each reverse step, CADD may leverage the continuous latent as a semantic hint to guide discrete denoising. The design is clean and compatible with existing discrete diffusion training. At sampling time, the strength and choice of estimator for the continuous latent vector enables a controlled trade-off between mode-coverage (generating diverse outputs) and mode-seeking (generating contextually precise outputs) behaviors. Empirically, we demonstrate CADD improves generative quality over mask-based diffusion across text generation, image synthesis, and code modeling, with consistent gains on both qualitative and quantitative metrics against strong discrete baselines.

We introduce infty-Diff, a generative diffusion model which directly operates on infinite resolution data. By randomly sampling subsets of coordinates during training and learning to denoise the content at those coordinates, a continuous function is learned that allows sampling at arbitrary resolutions. In contrast to other recent infinite resolution generative models, our approach operates directly on the raw data, not requiring latent vector compression for context, using hypernetworks, nor relying on discrete components. As such, our approach achieves significantly higher sample quality, as evidenced by lower FID scores, as well as being able to effectively scale to higher resolutions than the training data while retaining detail.

Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce self-consistency along the full PF-ODE trajectory to steer it toward the clean data manifold, vanilla DMD relies on sparse supervision at a few predefined discrete timesteps. This restricted discrete-time formulation and mode-seeking nature of the reverse KL divergence tends to exhibit visual artifacts and over-smoothed outputs, often necessitating complex auxiliary modules -- such as GANs or reward models -- to restore visual fidelity. In this work, we introduce Continuous-Time Distribution Matching (CDM), migrating the DMD framework from discrete anchoring to continuous optimization for the first time. CDM achieves this through two continuous-time designs. First, we replace the fixed discrete schedule with a dynamic continuous schedule of random length, so that distribution matching is enforced at arbitrary points along sampling trajectories rather than only at a few fixed anchors. Second, we propose a continuous-time alignment objective that performs active off-trajectory matching on latents extrapolated via the student's velocity field, improving generalization and preserving fine visual details. Extensive experiments on different architectures, including SD3-Medium and Longcat-Image, demonstrate that CDM provides highly competitive visual fidelity for few-step image generation without relying on complex auxiliary objectives. Code is available at https://github.com/byliutao/cdm.

Continuous physical fields represent a large fraction of data under scientific investigation. Their multiscale structures are central to discovery, yet useful coordinates are not known in advance. Standard self-supervised methods define context and targets in fixed image coordinates, posing a predictive task misaligned with fields organized across a continuous scale hierarchy. We introduce ScaleAware-JEPA, a framework that constructs dense, label-free latent coordinates for continuous scalar fields. Constrained Diffusion Decomposition (CDD) separates each field into pixel-registered scale components and provides the scale coordinates that define the masking geometry. The resulting JEPA objective predicts hidden structure with a context footprint tied to the diffusion scale of each component rather than to an arbitrary patch size. Across MHD turbulence, interstellar molecular gas and urban nighttime-light structure, the learned geometry maps back to coherent morphology, forming dense structural atlases without labels or predefined segmentation rules. By tying latent prediction to the scale hierarchy of a field, ScaleAware-JEPA constructs latent coordinates through which complex physical patterns can be inspected before their relevant structures have been prescribed. Code is available at https://github.com/gxli/SA-JEPA.

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

Diffusion models (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.

Text-to-image synthesis has progressed to the point where models can generate visually compelling images from natural language prompts. Yet, existing methods often fail to reconcile high-level semantic fidelity with explicit spatial control, particularly in scenes involving multiple objects, nuanced relations, or complex layouts. To bridge this gap, we propose a Hierarchical Cross-Modal Alignment (HCMA) framework for grounded text-to-image generation. HCMA integrates two alignment modules into each diffusion sampling step: a global module that continuously aligns latent representations with textual descriptions to ensure scene-level coherence, and a local module that employs bounding-box layouts to anchor objects at specified locations, enabling fine-grained spatial control. Extensive experiments on the MS-COCO 2014 validation set show that HCMA surpasses state-of-the-art baselines, achieving a 0.69 improvement in Frechet Inception Distance (FID) and a 0.0295 gain in CLIP Score. These results demonstrate HCMA's effectiveness in faithfully capturing intricate textual semantics while adhering to user-defined spatial constraints, offering a robust solution for semantically grounded image generation. Our code is available at https://github.com/hwang-cs-ime/HCMA.

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 that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have some limitations in modeling discrete data, e.g., languages. For example, the generally used Gaussian noise can not handle the discrete corruption well, and the objectives in continuous spaces fail to be stable for textual data in the diffusion process especially when the dimension is high. To alleviate these issues, we introduce a novel diffusion model for language modeling, Masked-Diffuse LM, with lower training cost and better performances, inspired by linguistic features in languages. Specifically, we design a linguistic-informed forward process which adds corruptions to the text through strategically soft-masking to better noise the textual data. Also, we directly predict the categorical distribution with cross-entropy loss function in every diffusion step to connect the continuous space and discrete space in a more efficient and straightforward way. Through experiments on 5 controlled generation tasks, we demonstrate that our Masked-Diffuse LM can achieve better generation quality than the state-of-the-art diffusion models with better efficiency.

Denoising diffusion models have emerged as the go-to framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution (OOD) tasks, which remains an under-explored challenge. Realistic reconstructions inconsistent with the measured data can be generated, hallucinating image features that are uniquely present in the training dataset. To simultaneously enforce data-consistency and leverage data-driven priors, we introduce a novel sampling framework called Steerable Conditional Diffusion. This framework adapts the denoising network specifically to the available measured data. Utilising our proposed method, we achieve substantial enhancements in OOD performance across diverse imaging modalities, advancing the robust deployment of denoising diffusion models in real-world applications.

Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism of particle's motion in expanding medium has only been investigated in the framework of continuous-time random walk. To focus on more diffusion processes and physical observables, we build the Langevin picture of anomalous diffusion in expanding medium, and conduct detailed analyses in the framework of Langevin equation. With the help of a subordinator, both subdiffusion process and superdiffusion process in expanding medium are discussed. We find that the expanding medium with different changing rate (exponential form and power-law form) leads to quite different diffusion phenomena. The particle's intrinsic diffusion behavior also plays an important role. Our detailed theoretical analyses and simulations present a panoramic view of investigating anomalous diffusion in expanding medium under the framework of Langevin equation.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Using image models naively for solving inverse video problems often suffers from flickering, texture-sticking, and temporal inconsistency in generated videos. To tackle these problems, in this paper, we view frames as continuous functions in the 2D space, and videos as a sequence of continuous warping transformations between different frames. This perspective allows us to train function space diffusion models only on images and utilize them to solve temporally correlated inverse problems. The function space diffusion models need to be equivariant with respect to the underlying spatial transformations. To ensure temporal consistency, we introduce a simple post-hoc test-time guidance towards (self)-equivariant solutions. Our method allows us to deploy state-of-the-art latent diffusion models such as Stable Diffusion XL to solve video inverse problems. We demonstrate the effectiveness of our method for video inpainting and 8times video super-resolution, outperforming existing techniques based on noise transformations. We provide generated video results: https://giannisdaras.github.io/warped_diffusion.github.io/.

We present a novel task called online video editing, which is designed to edit streaming frames while maintaining temporal consistency. Unlike existing offline video editing assuming all frames are pre-established and accessible, online video editing is tailored to real-life applications such as live streaming and online chat, requiring (1) fast continual step inference, (2) long-term temporal modeling, and (3) zero-shot video editing capability. To solve these issues, we propose Streaming Video Diffusion (SVDiff), which incorporates the compact spatial-aware temporal recurrence into off-the-shelf Stable Diffusion and is trained with the segment-level scheme on large-scale long videos. This simple yet effective setup allows us to obtain a single model that is capable of executing a broad range of videos and editing each streaming frame with temporal coherence. Our experiments indicate that our model can edit long, high-quality videos with remarkable results, achieving a real-time inference speed of 15.2 FPS at a resolution of 512x512.

This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or epidemics. After reviewing the assumptions and mean-field type approximations involved in the construction of chemical rate equations for uniform reactant densities, we first discuss spatial clustering in birth-death systems, where non-linearities are introduced through either density-limiting pair reactions, or equivalently via local imposition of finite carrying capacities. The competition of offspring production, death, and non-linear inhibition induces a population extinction threshold, which represents a non-equilibrium phase transition that separates active from absorbing states. This continuous transition is characterized by the universal scaling exponents of critical directed percolation clusters. Next we focus on the emergence of depletion zones in single-species annihilation processes and spatial population segregation with the associated reaction fronts in two-species pair annihilation. These strong (anti-)correlation effects are dynamically generated by the underlying stochastic kinetics. Finally, we address noise-induced and fluctuation-stabilized spatio-temporal patterns in basic predator-prey systems, exemplified by spreading activity fronts in the two-species Lotka-Volterra model as well as spiral structures in the May-Leonard variant of cyclically competing three-species systems akin to rock-paper-scissors games.

Recently, diffusion models have achieved great success in mono-channel audio generation. However, when it comes to stereo audio generation, the soundscapes often have a complex scene of multiple objects and directions. Controlling stereo audio with spatial contexts remains challenging due to high data costs and unstable generative models. To the best of our knowledge, this work represents the first attempt to address these issues. We first construct a large-scale, simulation-based, and GPT-assisted dataset, BEWO-1M, with abundant soundscapes and descriptions even including moving and multiple sources. Beyond text modality, we have also acquired a set of images and rationally paired stereo audios through retrieval to advance multimodal generation. Existing audio generation models tend to generate rather random and indistinct spatial audio. To provide accurate guidance for Latent Diffusion Models, we introduce the SpatialSonic model utilizing spatial-aware encoders and azimuth state matrices to reveal reasonable spatial guidance. By leveraging spatial guidance, our model not only achieves the objective of generating immersive and controllable spatial audio from text but also extends to other modalities as the pioneer attempt. Finally, under fair settings, we conduct subjective and objective evaluations on simulated and real-world data to compare our approach with prevailing methods. The results demonstrate the effectiveness of our method, highlighting its capability to generate spatial audio that adheres to physical rules.

The availability of large-scale multimodal datasets and advancements in diffusion models have significantly accelerated progress in 4D content generation. Most prior approaches rely on multiple image or video diffusion models, utilizing score distillation sampling for optimization or generating pseudo novel views for direct supervision. However, these methods are hindered by slow optimization speeds and multi-view inconsistency issues. Spatial and temporal consistency in 4D geometry has been extensively explored respectively in 3D-aware diffusion models and traditional monocular video diffusion models. Building on this foundation, we propose a strategy to migrate the temporal consistency in video diffusion models to the spatial-temporal consistency required for 4D generation. Specifically, we present a novel framework, Diffusion4D, for efficient and scalable 4D content generation. Leveraging a meticulously curated dynamic 3D dataset, we develop a 4D-aware video diffusion model capable of synthesizing orbital views of dynamic 3D assets. To control the dynamic strength of these assets, we introduce a 3D-to-4D motion magnitude metric as guidance. Additionally, we propose a novel motion magnitude reconstruction loss and 3D-aware classifier-free guidance to refine the learning and generation of motion dynamics. After obtaining orbital views of the 4D asset, we perform explicit 4D construction with Gaussian splatting in a coarse-to-fine manner. The synthesized multi-view consistent 4D image set enables us to swiftly generate high-fidelity and diverse 4D assets within just several minutes. Extensive experiments demonstrate that our method surpasses prior state-of-the-art techniques in terms of generation efficiency and 4D geometry consistency across various prompt modalities.

Diffusion models have emerged as a promising approach for text generation, with recent works falling into two main categories: discrete and continuous diffusion models. Discrete diffusion models apply token corruption independently using categorical distributions, allowing for different diffusion progress across tokens but lacking fine-grained control. Continuous diffusion models map tokens to continuous spaces and apply fine-grained noise, but the diffusion progress is uniform across tokens, limiting their ability to capture semantic nuances. To address these limitations, we propose \underline{N}on-simultan\underline{e}ous C\underline{o}ntinuous \underline{Diff}usion Models (NeoDiff), a novel diffusion model that integrates the strengths of both discrete and continuous approaches. NeoDiff introduces a Poisson diffusion process for the forward process, enabling a flexible and fine-grained noising paradigm, and employs a time predictor for the reverse process to adaptively modulate the denoising progress based on token semantics. Furthermore, NeoDiff utilizes an optimized schedule for inference to ensure more precise noise control and improved performance. Our approach unifies the theories of discrete and continuous diffusion models, offering a more principled and effective framework for text generation. Experimental results on several text generation tasks demonstrate NeoDiff's superior performance compared to baselines of non-autoregressive continuous and discrete diffusion models, iterative-based methods and autoregressive diffusion-based methods. These results highlight NeoDiff's potential as a powerful tool for generating high-quality text and advancing the field of diffusion-based text generation.

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

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

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of x_T as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime z=(x_t,t) that indexes the family of denoising distributions p(x_0 | x_t) across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry.

Continuous-space video generation has advanced rapidly, while discrete approaches lag behind due to error accumulation and long-context inconsistency. In this work, we revisit discrete generative modeling and present Uniform discRete diffuSion with metric pAth (URSA), a simple yet powerful framework that bridges the gap with continuous approaches for the scalable video generation. At its core, URSA formulates the video generation task as an iterative global refinement of discrete spatiotemporal tokens. It integrates two key designs: a Linearized Metric Path and a Resolution-dependent Timestep Shifting mechanism. These designs enable URSA to scale efficiently to high-resolution image synthesis and long-duration video generation, while requiring significantly fewer inference steps. Additionally, we introduce an asynchronous temporal fine-tuning strategy that unifies versatile tasks within a single model, including interpolation and image-to-video generation. Extensive experiments on challenging video and image generation benchmarks demonstrate that URSA consistently outperforms existing discrete methods and achieves performance comparable to state-of-the-art continuous diffusion methods. Code and models are available at https://github.com/baaivision/URSA

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

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.

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

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.

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. Functional diffusion is very versatile as images, videos, audio, 3D shapes, deformations, \etc, can be handled by the same framework with minimal changes. In addition, functional diffusion is especially suited for irregular data or data defined in non-standard domains. In our work, we derive the necessary foundations for functional diffusion and propose a first implementation based on the transformer architecture. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.

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

Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing resources for explaining diffusion either require an advanced theoretical foundation or focus on their neural network architectures rather than their rich geometric properties. We introduce Diffusion Explorer, an interactive tool to explain the geometric properties of diffusion models. Users can train 2D diffusion models in the browser and observe the temporal dynamics of their sampling process. Diffusion Explorer leverages interactive animation, which has been shown to be a powerful tool for making engaging visualizations of dynamic systems, making it well suited to explaining diffusion models which represent stochastic processes that evolve over time. Diffusion Explorer is open source and a live demo is available at alechelbling.com/Diffusion-Explorer.

Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have presented diffusion as an alternative to autoregressive language generation. We instead view diffusion as a complementary method that can augment the generative capabilities of existing pre-trained language models. We demonstrate that continuous diffusion models can be learned in the latent space of a pre-trained encoder-decoder model, enabling us to sample continuous latent representations that can be decoded into natural language with the pre-trained decoder. We show that our latent diffusion models are more effective at sampling novel text from data distributions than a strong autoregressive baseline and also enable controllable generation.

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and space. Central to our approach is a combination of continuous-time neural networks with two novel neural architectures, i.e., Jump and Attentive Continuous-time Normalizing Flows. This approach allows us to learn complex distributions for both the spatial and temporal domain and to condition non-trivially on the observed event history. We validate our models on data sets from a wide variety of contexts such as seismology, epidemiology, urban mobility, and neuroscience.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

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.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

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

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.

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems involve non-Euclidean distributions, such as hyperspherical manifolds, where class-specific patterns are governed by angular geometry within hypercones. When modeled in Euclidean space, these angular subtleties are lost, leading to suboptimal generative performance. To address this limitation, we introduce HyperSphereDiff to align hyperspherical structures with directional noise, preserving class geometry and effectively capturing angular uncertainty. We demonstrate both theoretically and empirically that this approach aligns the generative process with the intrinsic geometry of hyperspherical data, resulting in more accurate and geometry-aware generative models. We evaluate our framework on four object datasets and two face datasets, showing that incorporating angular uncertainty better preserves the underlying hyperspherical manifold. Resources are available at: {https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/}

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

We propose a unified, few-step generative modeling framework based on cumulative flow maps for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and cumulative parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction instantiation. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

Despite recent advancements in image generation, diffusion models still remain largely underexplored in Earth Observation. In this paper we show that state-of-the-art pretrained diffusion models can be conditioned on cartographic data to generate realistic satellite images. We provide two large datasets of paired OpenStreetMap images and satellite views over the region of Mainland Scotland and the Central Belt. We train a ControlNet model and qualitatively evaluate the results, demonstrating that both image quality and map fidelity are possible. Finally, we provide some insights on the opportunities and challenges of applying these models for remote sensing. Our model weights and code for creating the dataset are publicly available at https://github.com/miquel-espinosa/map-sat.

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

Compositional diffusion models offer a promising route to long-horizon planning by denoising multiple overlapping sub-trajectories while ensuring that together they constitute a global solution. However, enforcing local behavior over long chains is often insufficient for a coherent global structure to emerge. Recent works tackle this limitation through intrinsic search, which explores multiple paths during the denoising process. While intrinsic search improves global coherence, it comes at the cost of repeated evaluations of an already compute-heavy model. In this work, we argue that extrinsic search, performed outside the denoising process, offers a more effective mode of exploration for long-horizon planning while naturally enabling the use of classical algorithms to solve unseen combinatorial tasks at test time. Our eXtrinsic search-guided Diffuser (XDiffuser) first computes a plan over a state-space graph -- serving as a lightweight local connectivity oracle for the diffusion model. The plan is then used to guide denoising for a single trajectory, effectively offloading the burden of exploration. XDiffuser outperforms diffusion-based baselines on long-horizon tasks, with particularly large gains in the low-quality data regime and on unseen tasks beyond goal-reaching, including multi-agent coordination and TSP-style reasoning. Project website: https://yanivhass.github.io/XDiffuser-site/

Controllable layout generation refers to the process of creating a plausible visual arrangement of elements within a graphic design (e.g., document and web designs) with constraints representing design intentions. Although recent diffusion-based models have achieved state-of-the-art FID scores, they tend to exhibit more pronounced misalignment compared to earlier transformer-based models. In this work, we propose the LAyout Constraint diffusion modEl (LACE), a unified model to handle a broad range of layout generation tasks, such as arranging elements with specified attributes and refining or completing a coarse layout design. The model is based on continuous diffusion models. Compared with existing methods that use discrete diffusion models, continuous state-space design can enable the incorporation of differentiable aesthetic constraint functions in training. For conditional generation, we introduce conditions via masked input. Extensive experiment results show that LACE produces high-quality layouts and outperforms existing state-of-the-art baselines.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

Current controllable diffusion models typically rely on fixed architectures that modify intermediate activations to inject guidance conditioned on a new modality. This approach uses a static conditioning strategy for a dynamic, multi-stage denoising process, limiting the model's ability to adapt its response as the generation evolves from coarse structure to fine detail. We introduce TC-LoRA (Temporally Modulated Conditional LoRA), a new paradigm that enables dynamic, context-aware control by conditioning the model's weights directly. Our framework uses a hypernetwork to generate LoRA adapters on-the-fly, tailoring weight modifications for the frozen backbone at each diffusion step based on time and the user's condition. This mechanism enables the model to learn and execute an explicit, adaptive strategy for applying conditional guidance throughout the entire generation process. Through experiments on various data domains, we demonstrate that this dynamic, parametric control significantly enhances generative fidelity and adherence to spatial conditions compared to static, activation-based methods. TC-LoRA establishes an alternative approach in which the model's conditioning strategy is modified through a deeper functional adaptation of its weights, allowing control to align with the dynamic demands of the task and generative stage.

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.

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.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Continual learning aims to acquire tasks sequentially without catastrophic forgetting, yet standard strategies face a core tradeoff: regularization-based methods (e.g., EWC) can overconstrain updates when task optima are weakly overlapping, while replay-based methods can retain performance but drift due to imperfect replay. We study a hybrid perspective: trust region continual learning that combines generative replay with a Fisher-metric trust region constraint. We show that, under local approximations, the resulting update admits a MAML-style interpretation with a single implicit inner step: replay supplies an old-task gradient signal (query-like), while the Fisher-weighted penalty provides an efficient offline curvature shaping (support-like). This yields an emergent meta-learning property in continual learning: the model becomes an initialization that rapidly re-converges to prior task optima after each task transition, without explicitly optimizing a bilevel objective. Empirically, on task-incremental diffusion image generation and continual diffusion-policy control, trust region continual learning achieves the best final performance and retention, and consistently recovers early-task performance faster than EWC, replay, and continual meta-learning baselines.

Recent advancements in diffusion models have significantly improved the realism and generalizability of character-driven animation, enabling the synthesis of high-quality motion from just a single RGB image and a set of driving poses. Nevertheless, generating temporally coherent long-form content remains challenging. Existing approaches are constrained by computational and memory limitations, as they are typically trained on short video segments, thus performing effectively only over limited frame lengths and hindering their potential for extended coherent generation. To address these constraints, we propose TalkingPose, a novel diffusion-based framework specifically designed for producing long-form, temporally consistent human upper-body animations. TalkingPose leverages driving frames to precisely capture expressive facial and hand movements, transferring these seamlessly to a target actor through a stable diffusion backbone. To ensure continuous motion and enhance temporal coherence, we introduce a feedback-driven mechanism built upon image-based diffusion models. Notably, this mechanism does not incur additional computational costs or require secondary training stages, enabling the generation of animations with unlimited duration. Additionally, we introduce a comprehensive, large-scale dataset to serve as a new benchmark for human upper-body animation.

Diffusion models are a new class of generative models, and have dramatically promoted image generation with unprecedented quality and diversity. Existing diffusion models mainly try to reconstruct input image from a corrupted one with a pixel-wise or feature-wise constraint along spatial axes. However, such point-based reconstruction may fail to make each predicted pixel/feature fully preserve its neighborhood context, impairing diffusion-based image synthesis. As a powerful source of automatic supervisory signal, context has been well studied for learning representations. Inspired by this, we for the first time propose ConPreDiff to improve diffusion-based image synthesis with context prediction. We explicitly reinforce each point to predict its neighborhood context (i.e., multi-stride features/tokens/pixels) with a context decoder at the end of diffusion denoising blocks in training stage, and remove the decoder for inference. In this way, each point can better reconstruct itself by preserving its semantic connections with neighborhood context. This new paradigm of ConPreDiff can generalize to arbitrary discrete and continuous diffusion backbones without introducing extra parameters in sampling procedure. Extensive experiments are conducted on unconditional image generation, text-to-image generation and image inpainting tasks. Our ConPreDiff consistently outperforms previous methods and achieves a new SOTA text-to-image generation results on MS-COCO, with a zero-shot FID score of 6.21.

Generative models have the potential to accelerate key steps in the discovery of novel molecular therapeutics and materials. Diffusion models have recently emerged as a powerful approach, excelling at unconditional sample generation and, with data-driven guidance, conditional generation within their training domain. Reliably sampling from high-value regions beyond the training data, however, remains an open challenge -- with current methods predominantly focusing on modifying the diffusion process itself. In this paper, we develop context-guided diffusion (CGD), a simple plug-and-play method that leverages unlabeled data and smoothness constraints to improve the out-of-distribution generalization of guided diffusion models. We demonstrate that this approach leads to substantial performance gains across various settings, including continuous, discrete, and graph-structured diffusion processes with applications across drug discovery, materials science, and protein design.

Diffusion models (DMs) excel in photo-realistic image synthesis, but their adaptation to LiDAR scene generation poses a substantial hurdle. This is primarily because DMs operating in the point space struggle to preserve the curve-like patterns and 3D geometry of LiDAR scenes, which consumes much of their representation power. In this paper, we propose LiDAR Diffusion Models (LiDMs) to generate LiDAR-realistic scenes from a latent space tailored to capture the realism of LiDAR scenes by incorporating geometric priors into the learning pipeline. Our method targets three major desiderata: pattern realism, geometry realism, and object realism. Specifically, we introduce curve-wise compression to simulate real-world LiDAR patterns, point-wise coordinate supervision to learn scene geometry, and patch-wise encoding for a full 3D object context. With these three core designs, our method achieves competitive performance on unconditional LiDAR generation in 64-beam scenario and state of the art on conditional LiDAR generation, while maintaining high efficiency compared to point-based DMs (up to 107times faster). Furthermore, by compressing LiDAR scenes into a latent space, we enable the controllability of DMs with various conditions such as semantic maps, camera views, and text prompts.

Multi-view image generation holds significant application value in computer vision, particularly in domains like 3D reconstruction, virtual reality, and augmented reality. Most existing methods, which rely on extending single images, face notable computational challenges in maintaining cross-view consistency and generating high-resolution outputs. To address these issues, we propose the Geometry-guided Multi-View Diffusion Model, which incorporates mechanisms for extracting multi-view geometric information and adjusting the intensity of geometric features to generate images that are both consistent across views and rich in detail. Specifically, we design a multi-view geometry information extraction module that leverages depth maps, normal maps, and foreground segmentation masks to construct a shared geometric structure, ensuring shape and structural consistency across different views. To enhance consistency and detail restoration during generation, we develop a decoupled geometry-enhanced attention mechanism that strengthens feature focus on key geometric details, thereby improving overall image quality and detail preservation. Furthermore, we apply an adaptive learning strategy that fine-tunes the model to better capture spatial relationships and visual coherence between the generated views, ensuring realistic results. Our model also incorporates an iterative refinement process that progressively improves the output quality through multiple stages of image generation. Finally, a dynamic geometry information intensity adjustment mechanism is proposed to adaptively regulate the influence of geometric data, optimizing overall quality while ensuring the naturalness of generated images. More details can be found on the project page: https://sobeymil.github.io/GeoMVD.com.

Current controls over diffusion models (e.g., through text or ControlNet) for image generation fall short in recognizing abstract, continuous attributes like illumination direction or non-rigid shape change. In this paper, we present an approach for allowing users of text-to-image models to have fine-grained control of several attributes in an image. We do this by engineering special sets of input tokens that can be transformed in a continuous manner -- we call them Continuous 3D Words. These attributes can, for example, be represented as sliders and applied jointly with text prompts for fine-grained control over image generation. Given only a single mesh and a rendering engine, we show that our approach can be adopted to provide continuous user control over several 3D-aware attributes, including time-of-day illumination, bird wing orientation, dollyzoom effect, and object poses. Our method is capable of conditioning image creation with multiple Continuous 3D Words and text descriptions simultaneously while adding no overhead to the generative process. Project Page: https://ttchengab.github.io/continuous_3d_words

Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the intrinsic mutual interference among image regions contradicts the need for practical downstream application scenarios where the preservation of low-level pixel information from given conditioning is desired (e.g., customization tasks like personalized generation and inpainting based on a user-provided single image). In this work, we investigate the diffusion (physics) in diffusion (machine learning) properties and propose our Cyclic One-Way Diffusion (COW) method to control the direction of diffusion phenomenon given a pre-trained frozen diffusion model for versatile customization application scenarios, where the low-level pixel information from the conditioning needs to be preserved. Notably, unlike most current methods that incorporate additional conditions by fine-tuning the base text-to-image diffusion model or learning auxiliary networks, our method provides a novel perspective to understand the task needs and is applicable to a wider range of customization scenarios in a learning-free manner. Extensive experiment results show that our proposed COW can achieve more flexible customization based on strict visual conditions in different application settings. Project page: https://wangruoyu02.github.io/cow.github.io/.

We introduce a single-view reconstruction technique of volumetric fields in which multiple light scattering effects are omnipresent, such as in clouds. We model the unknown distribution of volumetric fields using an unconditional diffusion model trained on a novel benchmark dataset comprising 1,000 synthetically simulated volumetric density fields. The neural diffusion model is trained on the latent codes of a novel, diffusion-friendly, monoplanar representation. The generative model is used to incorporate a tailored parametric diffusion posterior sampling technique into different reconstruction tasks. A physically-based differentiable volume renderer is employed to provide gradients with respect to light transport in the latent space. This stands in contrast to classic NeRF approaches and makes the reconstructions better aligned with observed data. Through various experiments, we demonstrate single-view reconstruction of volumetric clouds at a previously unattainable quality.

Recent video diffusion models demonstrate strong potential in spatial intelligence tasks due to their rich latent world priors. However, this potential is hindered by their limited controllability and geometric inconsistency, creating a gap between their strong priors and their practical use in 3D/4D tasks. As a result, current approaches often rely on retraining or fine-tuning, which risks degrading pretrained knowledge and incurs high computational costs. To address this, we propose WorldForge, a training-free, inference-time framework composed of three tightly coupled modules. Intra-Step Recursive Refinement introduces a recursive refinement mechanism during inference, which repeatedly optimizes network predictions within each denoising step to enable precise trajectory injection. Flow-Gated Latent Fusion leverages optical flow similarity to decouple motion from appearance in the latent space and selectively inject trajectory guidance into motion-related channels. Dual-Path Self-Corrective Guidance compares guided and unguided denoising paths to adaptively correct trajectory drift caused by noisy or misaligned structural signals. Together, these components inject fine-grained, trajectory-aligned guidance without training, achieving both accurate motion control and photorealistic content generation. Extensive experiments across diverse benchmarks validate our method's superiority in realism, trajectory consistency, and visual fidelity. This work introduces a novel plug-and-play paradigm for controllable video synthesis, offering a new perspective on leveraging generative priors for spatial intelligence.

Recent advances in text-to-image generation with diffusion models present transformative capabilities in image quality. However, user controllability of the generated image, and fast adaptation to new tasks still remains an open challenge, currently mostly addressed by costly and long re-training and fine-tuning or ad-hoc adaptations to specific image generation tasks. In this work, we present MultiDiffusion, a unified framework that enables versatile and controllable image generation, using a pre-trained text-to-image diffusion model, without any further training or finetuning. At the center of our approach is a new generation process, based on an optimization task that binds together multiple diffusion generation processes with a shared set of parameters or constraints. We show that MultiDiffusion can be readily applied to generate high quality and diverse images that adhere to user-provided controls, such as desired aspect ratio (e.g., panorama), and spatial guiding signals, ranging from tight segmentation masks to bounding boxes. Project webpage: https://multidiffusion.github.io

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can potentially help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs with learnable transformations through experiments on standard image generation benchmarks, including CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood and produce high-quality samples.

The increasing demand for AR/VR applications has highlighted the need for high-quality 360-degree panoramic content. However, generating high-quality 360-degree panoramic images and videos remains a challenging task due to the severe distortions introduced by equirectangular projection (ERP). Existing approaches either fine-tune pretrained diffusion models on limited ERP datasets or attempt tuning-free methods that still rely on ERP latent representations, leading to discontinuities near the poles. In this paper, we introduce SphereDiff, a novel approach for seamless 360-degree panoramic image and video generation using state-of-the-art diffusion models without additional tuning. We define a spherical latent representation that ensures uniform distribution across all perspectives, mitigating the distortions inherent in ERP. We extend MultiDiffusion to spherical latent space and propose a spherical latent sampling method to enable direct use of pretrained diffusion models. Moreover, we introduce distortion-aware weighted averaging to further improve the generation quality in the projection process. Our method outperforms existing approaches in generating 360-degree panoramic content while maintaining high fidelity, making it a robust solution for immersive AR/VR applications. The code is available here. https://github.com/pmh9960/SphereDiff

We present a novel, training-free approach for textual editing of real images using diffusion models. Unlike prior methods that rely on computationally expensive finetuning, our approach leverages LAtent SPatial Alignment (LASPA) to efficiently preserve image details. We demonstrate how the diffusion process is amenable to spatial guidance using a reference image, leading to semantically coherent edits. This eliminates the need for complex optimization and costly model finetuning, resulting in significantly faster editing compared to previous methods. Additionally, our method avoids the storage requirements associated with large finetuned models. These advantages make our approach particularly well-suited for editing on mobile devices and applications demanding rapid response times. While simple and fast, our method achieves 62-71\% preference in a user-study and significantly better model-based editing strength and image preservation scores.

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

Current 4D generation methods have achieved noteworthy efficacy with the aid of advanced diffusion generative models. However, these methods lack multi-view spatial-temporal modeling and encounter challenges in integrating diverse prior knowledge from multiple diffusion models, resulting in inconsistent temporal appearance and flickers. In this paper, we propose a novel 4D generation pipeline, namely 4Diffusion aimed at generating spatial-temporally consistent 4D content from a monocular video. We first design a unified diffusion model tailored for multi-view video generation by incorporating a learnable motion module into a frozen 3D-aware diffusion model to capture multi-view spatial-temporal correlations. After training on a curated dataset, our diffusion model acquires reasonable temporal consistency and inherently preserves the generalizability and spatial consistency of the 3D-aware diffusion model. Subsequently, we propose 4D-aware Score Distillation Sampling loss, which is based on our multi-view video diffusion model, to optimize 4D representation parameterized by dynamic NeRF. This aims to eliminate discrepancies arising from multiple diffusion models, allowing for generating spatial-temporally consistent 4D content. Moreover, we devise an anchor loss to enhance the appearance details and facilitate the learning of dynamic NeRF. Extensive qualitative and quantitative experiments demonstrate that our method achieves superior performance compared to previous methods.

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

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

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

Creating high-fidelity, coherent long videos is a sought-after aspiration. While recent video diffusion models have shown promising potential, they still grapple with spatiotemporal inconsistencies and high computational resource demands. We propose GLC-Diffusion, a tuning-free method for long video generation. It models the long video denoising process by establishing denoising trajectories through Global-Local Collaborative Denoising to ensure overall content consistency and temporal coherence between frames. Additionally, we introduce a Noise Reinitialization strategy which combines local noise shuffling with frequency fusion to improve global content consistency and visual diversity. Further, we propose a Video Motion Consistency Refinement (VMCR) module that computes the gradient of pixel-wise and frequency-wise losses to enhance visual consistency and temporal smoothness. Extensive experiments, including quantitative and qualitative evaluations on videos of varying lengths (e.g., 3\times and 6\times longer), demonstrate that our method effectively integrates with existing video diffusion models, producing coherent, high-fidelity long videos superior to previous approaches.

Latent diffusion models (LDMs) have recently achieved strong performance in 3D medical image synthesis. However, modalities like cine cardiac MRI (CMR), representing a temporally synchronized 3D volume across the cardiac cycle, add an additional dimension that most generative approaches do not model directly. Instead, they factorize space and time or enforce temporal consistency through auxiliary mechanisms such as anatomical masks. Such strategies introduce structural biases that may limit global context integration and lead to subtle spatiotemporal discontinuities or physiologically inconsistent cardiac dynamics. We investigate whether a unified 4D generative model can learn continuous cardiac dynamics without architectural factorization. We propose CardioDiT, a fully 4D latent diffusion framework for short-axis cine CMR synthesis based on diffusion transformers. A spatiotemporal VQ-VAE encodes 2D+t slices into compact latents, which a diffusion transformer then models jointly as complete 3D+t volumes, coupling space and time throughout the generative process. We evaluate CardioDiT on public CMR datasets and a larger private cohort, comparing it to baselines with progressively stronger spatiotemporal coupling. Results show improved inter-slice consistency, temporally coherent motion, and realistic cardiac function distributions, suggesting that explicit 4D modeling with a diffusion transformer provides a principled foundation for spatiotemporal cardiac image synthesis. Code and models trained on public data are available at https://github.com/Cardio-AI/cardiodit.

In this paper, we present PointmapDiffusion, a novel framework for single-image novel view synthesis (NVS) that utilizes pre-trained 2D diffusion models. Our method is the first to leverage pointmaps (i.e. rasterized 3D scene coordinates) as a conditioning signal, capturing geometric prior from the reference images to guide the diffusion process. By embedding reference attention blocks and a ControlNet for pointmap features, our model balances between generative capability and geometric consistency, enabling accurate view synthesis across varying viewpoints. Extensive experiments on diverse real-world datasets demonstrate that PointmapDiffusion achieves high-quality, multi-view consistent results with significantly fewer trainable parameters compared to other baselines for single-image NVS tasks.

Recently, multi-view or 4D video generation has emerged as a significant research topic. Nonetheless, recent approaches to 4D generation still struggle with fundamental limitations, as they primarily rely on harnessing multiple video diffusion models with additional training or compute-intensive training of a full 4D diffusion model with limited real-world 4D data and large computational costs. To address these challenges, here we propose the first training-free 4D video generation method that leverages the off-the-shelf video diffusion models to generate multi-view videos from a single input video. Our approach consists of two key steps: (1) By designating the edge frames in the spatio-temporal sampling grid as key frames, we first synthesize them using a video diffusion model, leveraging a depth-based warping technique for guidance. This approach ensures structural consistency across the generated frames, preserving spatial and temporal coherence. (2) We then interpolate the remaining frames using a video diffusion model, constructing a fully populated and temporally coherent sampling grid while preserving spatial and temporal consistency. Through this approach, we extend a single video into a multi-view video along novel camera trajectories while maintaining spatio-temporal consistency. Our method is training-free and fully utilizes an off-the-shelf video diffusion model, offering a practical and effective solution for multi-view video generation.

This paper proposes AutoScape, a long-horizon driving scene generation framework. At its core is a novel RGB-D diffusion model that iteratively generates sparse, geometrically consistent keyframes, serving as reliable anchors for the scene's appearance and geometry. To maintain long-range geometric consistency, the model 1) jointly handles image and depth in a shared latent space, 2) explicitly conditions on the existing scene geometry (i.e., rendered point clouds) from previously generated keyframes, and 3) steers the sampling process with a warp-consistent guidance. Given high-quality RGB-D keyframes, a video diffusion model then interpolates between them to produce dense and coherent video frames. AutoScape generates realistic and geometrically consistent driving videos of over 20 seconds, improving the long-horizon FID and FVD scores over the prior state-of-the-art by 48.6\% and 43.0\%, respectively.

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.

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

Although the recent rapid evolution of 3D generative neural networks greatly improves 3D shape generation, it is still not convenient for ordinary users to create 3D shapes and control the local geometry of generated shapes. To address these challenges, we propose a diffusion-based 3D generation framework -- locally attentional SDF diffusion, to model plausible 3D shapes, via 2D sketch image input. Our method is built on a two-stage diffusion model. The first stage, named occupancy-diffusion, aims to generate a low-resolution occupancy field to approximate the shape shell. The second stage, named SDF-diffusion, synthesizes a high-resolution signed distance field within the occupied voxels determined by the first stage to extract fine geometry. Our model is empowered by a novel view-aware local attention mechanism for image-conditioned shape generation, which takes advantage of 2D image patch features to guide 3D voxel feature learning, greatly improving local controllability and model generalizability. Through extensive experiments in sketch-conditioned and category-conditioned 3D shape generation tasks, we validate and demonstrate the ability of our method to provide plausible and diverse 3D shapes, as well as its superior controllability and generalizability over existing work. Our code and trained models are available at https://zhengxinyang.github.io/projects/LAS-Diffusion.html

Diffusion models have been used extensively for high quality image and video generation tasks. In this paper, we propose a novel conditional diffusion model with spatial attention and latent embedding (cDAL) for medical image segmentation. In cDAL, a convolutional neural network (CNN) based discriminator is used at every time-step of the diffusion process to distinguish between the generated labels and the real ones. A spatial attention map is computed based on the features learned by the discriminator to help cDAL generate more accurate segmentation of discriminative regions in an input image. Additionally, we incorporated a random latent embedding into each layer of our model to significantly reduce the number of training and sampling time-steps, thereby making it much faster than other diffusion models for image segmentation. We applied cDAL on 3 publicly available medical image segmentation datasets (MoNuSeg, Chest X-ray and Hippocampus) and observed significant qualitative and quantitative improvements with higher Dice scores and mIoU over the state-of-the-art algorithms. The source code is publicly available at https://github.com/Hejrati/cDAL/.

While recent Flow Matching models avoid the reconstruction bottlenecks of latent autoencoders by operating directly in pixel space, the lack of semantic continuity in the pixel manifold severely intertwines optimal transport paths. This induces severe trajectory conflicts near intersections, yielding sub-optimal solutions. Rather than bypassing this issue via information-lossy latent representations, we directly untangle the pixel-space trajectories by proposing Waypoint Diffusion Transformers (WiT). WiT factorizes the continuous vector field via intermediate semantic waypoints projected from pre-trained vision models. It effectively disentangles the generation trajectories by breaking the optimal transport into prior-to-waypoint and waypoint-to-pixel segments. Specifically, during the iterative denoising process, a lightweight generator dynamically infers these intermediate waypoints from the current noisy state. They then continuously condition the primary diffusion transformer via the Just-Pixel AdaLN mechanism, steering the evolution towards the next state, ultimately yielding the final RGB pixels. Evaluated on ImageNet 256x256, WiT beats strong pixel-space baselines, accelerating JiT training convergence by 2.2x. Code will be publicly released at https://github.com/hainuo-wang/WiT.git.

The increasing demand for augmented and virtual reality applications has highlighted the importance of crafting immersive 3D scenes from a simple single-view image. However, due to the partial priors provided by single-view input, existing methods are often limited to reconstruct low-consistency 3D scenes with narrow fields of view from single-view input. These limitations make them less capable of generalizing to reconstruct immersive scenes. To address this problem, we propose ExScene, a two-stage pipeline to reconstruct an immersive 3D scene from any given single-view image. ExScene designs a novel multimodal diffusion model to generate a high-fidelity and globally consistent panoramic image. We then develop a panoramic depth estimation approach to calculate geometric information from panorama, and we combine geometric information with high-fidelity panoramic image to train an initial 3D Gaussian Splatting (3DGS) model. Following this, we introduce a GS refinement technique with 2D stable video diffusion priors. We add camera trajectory consistency and color-geometric priors into the denoising process of diffusion to improve color and spatial consistency across image sequences. These refined sequences are then used to fine-tune the initial 3DGS model, leading to better reconstruction quality. Experimental results demonstrate that our ExScene achieves consistent and immersive scene reconstruction using only single-view input, significantly surpassing state-of-the-art baselines.

With the increasing popularity of autonomous driving based on the powerful and unified bird's-eye-view (BEV) representation, a demand for high-quality and large-scale multi-view video data with accurate annotation is urgently required. However, such large-scale multi-view data is hard to obtain due to expensive collection and annotation costs. To alleviate the problem, we propose a spatial-temporal consistent diffusion framework DrivingDiffusion, to generate realistic multi-view videos controlled by 3D layout. There are three challenges when synthesizing multi-view videos given a 3D layout: How to keep 1) cross-view consistency and 2) cross-frame consistency? 3) How to guarantee the quality of the generated instances? Our DrivingDiffusion solves the problem by cascading the multi-view single-frame image generation step, the single-view video generation step shared by multiple cameras, and post-processing that can handle long video generation. In the multi-view model, the consistency of multi-view images is ensured by information exchange between adjacent cameras. In the temporal model, we mainly query the information that needs attention in subsequent frame generation from the multi-view images of the first frame. We also introduce the local prompt to effectively improve the quality of generated instances. In post-processing, we further enhance the cross-view consistency of subsequent frames and extend the video length by employing temporal sliding window algorithm. Without any extra cost, our model can generate large-scale realistic multi-camera driving videos in complex urban scenes, fueling the downstream driving tasks. The code will be made publicly available.

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

In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative models trained on curated data to learn road agents' stochastic behavior bounded by scene constraints. However, they often face mode averaging issues due to data imbalance and simplistic priors, and could even suffer from mode collapse due to unstable training and single ground truth supervision. These issues lead the existing methods to a loss of predictive diversity and adherence to the scene constraints. To address these challenges, we introduce a novel trajectory generator named Controllable Diffusion Trajectory (CDT), which integrates map information and social interactions into a Transformer-based conditional denoising diffusion model to guide the prediction of future trajectories. To ensure multimodality, we incorporate behavioral tokens to direct the trajectory's modes, such as going straight, turning right or left. Moreover, we incorporate the predicted endpoints as an alternative behavioral token into the CDT model to facilitate the prediction of accurate trajectories. Extensive experiments on the Argoverse 2 benchmark demonstrate that CDT excels in generating diverse and scene-compliant trajectories in complex urban settings.

Diffusion models have attracted significant attention due to the remarkable ability to create content and generate data for tasks like image classification. However, the usage of diffusion models to generate the high-quality object detection data remains an underexplored area, where not only image-level perceptual quality but also geometric conditions such as bounding boxes and camera views are essential. Previous studies have utilized either copy-paste synthesis or layout-to-image (L2I) generation with specifically designed modules to encode the semantic layouts. In this paper, we propose the GeoDiffusion, a simple framework that can flexibly translate various geometric conditions into text prompts and empower pre-trained text-to-image (T2I) diffusion models for high-quality detection data generation. Unlike previous L2I methods, our GeoDiffusion is able to encode not only the bounding boxes but also extra geometric conditions such as camera views in self-driving scenes. Extensive experiments demonstrate GeoDiffusion outperforms previous L2I methods while maintaining 4x training time faster. To the best of our knowledge, this is the first work to adopt diffusion models for layout-to-image generation with geometric conditions and demonstrate that L2I-generated images can be beneficial for improving the performance of object detectors.

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

For an artist or a graphic designer, the spatial layout of a scene is a critical design choice. However, existing text-to-image diffusion models provide limited support for incorporating spatial information. This paper introduces Composite Diffusion as a means for artists to generate high-quality images by composing from the sub-scenes. The artists can specify the arrangement of these sub-scenes through a flexible free-form segment layout. They can describe the content of each sub-scene primarily using natural text and additionally by utilizing reference images or control inputs such as line art, scribbles, human pose, canny edges, and more. We provide a comprehensive and modular method for Composite Diffusion that enables alternative ways of generating, composing, and harmonizing sub-scenes. Further, we wish to evaluate the composite image for effectiveness in both image quality and achieving the artist's intent. We argue that existing image quality metrics lack a holistic evaluation of image composites. To address this, we propose novel quality criteria especially relevant to composite generation. We believe that our approach provides an intuitive method of art creation. Through extensive user surveys, quantitative and qualitative analysis, we show how it achieves greater spatial, semantic, and creative control over image generation. In addition, our methods do not need to retrain or modify the architecture of the base diffusion models and can work in a plug-and-play manner with the fine-tuned models.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving either the probability flow ODE or diffusion SDE wherein a neural network approximates the score function allowing a numerical ODE/SDE solver to be used. However, naive backpropagation techniques are memory intensive, requiring the storage of all intermediate states, and face additional complexity in handling the injected noise from the diffusion term of the diffusion SDE. We propose a novel family of bespoke ODE solvers to the continuous adjoint equations for diffusion models, which we call AdjointDEIS. We exploit the unique construction of diffusion SDEs to further simplify the formulation of the continuous adjoint equations using exponential integrators. Moreover, we provide convergence order guarantees for our bespoke solvers. Significantly, we show that continuous adjoint equations for diffusion SDEs actually simplify to a simple ODE. Lastly, we demonstrate the effectiveness of AdjointDEIS for guided generation with an adversarial attack in the form of the face morphing problem. Our code will be released on our project page https://zblasingame.github.io/AdjointDEIS/

Diffusion models have recently gained recognition for generating diverse and high-quality content, especially in the domain of image synthesis. These models excel not only in creating fixed-size images but also in producing panoramic images. However, existing methods often struggle with spatial layout consistency when producing high-resolution panoramas, due to the lack of guidance of the global image layout. In this paper, we introduce the Multi-Scale Diffusion (MSD) framework, a plug-and-play module that extends the existing panoramic image generation framework to multiple resolution levels. By utilizing gradient descent techniques, our method effectively incorporates structural information from low-resolution images into high-resolution outputs. A comprehensive evaluation of the proposed method was conducted, comparing it with the prior works in qualitative and quantitative dimensions. The evaluation results demonstrate that our method significantly outperforms others in generating coherent high-resolution panoramas.

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

Image-based 3D generation has vast applications in robotics and gaming, where high-quality, diverse outputs and consistent 3D representations are crucial. However, existing methods have limitations: 3D diffusion models are limited by dataset scarcity and the absence of strong pre-trained priors, while 2D diffusion-based approaches struggle with geometric consistency. We propose a method that leverages 2D diffusion models' implicit 3D reasoning ability while ensuring 3D consistency via Gaussian-splatting-based geometric distillation. Specifically, the proposed Gaussian Splatting Decoder enforces 3D consistency by transforming SV3D latent outputs into an explicit 3D representation. Unlike SV3D, which only relies on implicit 2D representations for video generation, Gaussian Splatting explicitly encodes spatial and appearance attributes, enabling multi-view consistency through geometric constraints. These constraints correct view inconsistencies, ensuring robust geometric consistency. As a result, our approach simultaneously generates high-quality, multi-view-consistent images and accurate 3D models, providing a scalable solution for single-image-based 3D generation and bridging the gap between 2D Diffusion diversity and 3D structural coherence. Experimental results demonstrate state-of-the-art multi-view consistency and strong generalization across diverse datasets. The code will be made publicly available upon acceptance.

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.

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

Recent text-to-image diffusion models have demonstrated an astonishing capacity to generate high-quality images. However, researchers mainly studied the way of synthesizing images with only text prompts. While some works have explored using other modalities as conditions, considerable paired data, e.g., box/mask-image pairs, and fine-tuning time are required for nurturing models. As such paired data is time-consuming and labor-intensive to acquire and restricted to a closed set, this potentially becomes the bottleneck for applications in an open world. This paper focuses on the simplest form of user-provided conditions, e.g., box or scribble. To mitigate the aforementioned problem, we propose a training-free method to control objects and contexts in the synthesized images adhering to the given spatial conditions. Specifically, three spatial constraints, i.e., Inner-Box, Outer-Box, and Corner Constraints, are designed and seamlessly integrated into the denoising step of diffusion models, requiring no additional training and massive annotated layout data. Extensive results show that the proposed constraints can control what and where to present in the images while retaining the ability of the Stable Diffusion model to synthesize with high fidelity and diverse concept coverage. The code is publicly available at https://github.com/Sierkinhane/BoxDiff.

The increased demand for 3D data in AR/VR, robotics and gaming applications, gave rise to powerful generative pipelines capable of synthesizing high-quality 3D objects. Most of these models rely on the Score Distillation Sampling (SDS) algorithm to optimize a 3D representation such that the rendered image maintains a high likelihood as evaluated by a pre-trained diffusion model. However, finding a correct mode in the high-dimensional distribution produced by the diffusion model is challenging and often leads to issues such as over-saturation, over-smoothing, and Janus-like artifacts. In this paper, we propose a novel learning paradigm for 3D synthesis that utilizes pre-trained diffusion models. Instead of focusing on mode-seeking, our method directly models the distribution discrepancy between multi-view renderings and diffusion priors in an adversarial manner, which unlocks the generation of high-fidelity and photorealistic 3D content, conditioned on a single image and prompt. Moreover, by harnessing the latent space of GANs and expressive diffusion model priors, our method facilitates a wide variety of 3D applications including single-view reconstruction, high diversity generation and continuous 3D interpolation in the open domain. The experiments demonstrate the superiority of our pipeline compared to previous works in terms of generation quality and diversity.

While diffusion models excel at generating high-quality images from text prompts, they struggle with visual consistency when generating image sequences. Existing methods generate each image independently, leading to disjointed narratives - a challenge further exacerbated in non-linear storytelling, where scenes must connect beyond adjacent images. We introduce a novel beam search strategy for latent space exploration, enabling conditional generation of full image sequences with beam search decoding. In contrast to earlier methods that rely on fixed latent priors, our method dynamically samples past latents to search for an optimal sequence of latent representations, ensuring coherent visual transitions. As the latent denoising space is explored, the beam search graph is pruned with a cross-attention mechanism that efficiently scores search paths, prioritizing alignment with both textual prompts and visual context. Human and automatic evaluations confirm that BeamDiffusion outperforms other baseline methods, producing full sequences with superior coherence, visual continuity, and textual alignment.

Probabilistic diffusion models have achieved state-of-the-art results for image synthesis, inpainting, and text-to-image tasks. However, they are still in the early stages of generating complex 3D shapes. This work proposes Diffusion-SDF, a generative model for shape completion, single-view reconstruction, and reconstruction of real-scanned point clouds. We use neural signed distance functions (SDFs) as our 3D representation to parameterize the geometry of various signals (e.g., point clouds, 2D images) through neural networks. Neural SDFs are implicit functions and diffusing them amounts to learning the reversal of their neural network weights, which we solve using a custom modulation module. Extensive experiments show that our method is capable of both realistic unconditional generation and conditional generation from partial inputs. This work expands the domain of diffusion models from learning 2D, explicit representations, to 3D, implicit representations.

Recent advances in diffusion models have enabled high-quality video generation, but the additional temporal dimension significantly increases computational costs, making training and inference on long videos prohibitively expensive. In this paper, we identify a phenomenon we term Spatiotemporal Energy Decay in video diffusion models: post-softmax attention scores diminish as spatial and temporal distance between tokens increase, akin to the physical decay of signal or waves over space and time in nature. Motivated by this, we propose Radial Attention, a scalable sparse attention mechanism with O(n log n) complexity that translates energy decay into exponentially decaying compute density, which is significantly more efficient than standard O(n^2) dense attention and more expressive than linear attention. Specifically, Radial Attention employs a simple, static attention mask where each token attends to spatially nearby tokens, with the attention window size shrinking with temporal distance. Moreover, it allows pre-trained video diffusion models to extend their generation length with efficient LoRA-based fine-tuning. Extensive experiments show that Radial Attention maintains video quality across Wan2.1-14B, HunyuanVideo, and Mochi 1, achieving up to a 1.9times speedup over the original dense attention. With minimal tuning, it enables video generation up to 4times longer while reducing training costs by up to 4.4times compared to direct fine-tuning and accelerating inference by up to 3.7times compared to dense attention inference.

While diffusion models excel at generating images with conventional dimensions, pushing them to synthesize ultra-high-resolution imagery at extreme aspect ratios (EAR) often triggers catastrophic structural failures, such as object repetition and spatial fragmentation. This limitation fundamentally stems from a lack of robust spatial priors, as static text-to-image models are primarily trained on image distributions with conventional dimensions. To overcome this bottleneck, we present ScrollScape, a novel framework that reformulates EAR image synthesis into a continuous video generation process through two core innovations. By mapping the spatial expansion of a massive canvas to the temporal evolution of video frames, ScrollScape leverages the inherent temporal consistency of video models as a powerful global constraint to ensure long-range structural integrity. Specifically, Scanning Positional Encoding (ScanPE) distributes global coordinates across frames to act as a flexible moving camera, while Scrolling Super-Resolution (ScrollSR) leverages video super-resolution priors to circumvent memory bottlenecks, efficiently scaling outputs to an unprecedented 32K resolution. Fine-tuned on a curated 3K multi-ratio image dataset, ScrollScape effectively aligns pre-trained video priors with the EAR generation task. Extensive evaluations demonstrate that it significantly outperforms existing image-diffusion baselines by eliminating severe localized artifacts. Consequently, our method overcomes inherent structural bottlenecks to ensure exceptional global coherence and visual fidelity across diverse domains at extreme scales.

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

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

Diffusion models generate images with an unprecedented level of quality, but how can we freely rearrange image layouts? Recent works generate controllable scenes via learning spatially disentangled latent codes, but these methods do not apply to diffusion models due to their fixed forward process. In this work, we propose SceneDiffusion to optimize a layered scene representation during the diffusion sampling process. Our key insight is that spatial disentanglement can be obtained by jointly denoising scene renderings at different spatial layouts. Our generated scenes support a wide range of spatial editing operations, including moving, resizing, cloning, and layer-wise appearance editing operations, including object restyling and replacing. Moreover, a scene can be generated conditioned on a reference image, thus enabling object moving for in-the-wild images. Notably, this approach is training-free, compatible with general text-to-image diffusion models, and responsive in less than a second.

Diffusion models have significantly advanced the state of the art in image, audio, and video generation tasks. However, their applications in practical scenarios are hindered by slow inference speed. Drawing inspiration from the approximation strategies utilized in consistency models, we propose the Sub-path Linear Approximation Model (SLAM), which accelerates diffusion models while maintaining high-quality image generation. SLAM treats the PF-ODE trajectory as a series of PF-ODE sub-paths divided by sampled points, and harnesses sub-path linear (SL) ODEs to form a progressive and continuous error estimation along each individual PF-ODE sub-path. The optimization on such SL-ODEs allows SLAM to construct denoising mappings with smaller cumulative approximated errors. An efficient distillation method is also developed to facilitate the incorporation of more advanced diffusion models, such as latent diffusion models. Our extensive experimental results demonstrate that SLAM achieves an efficient training regimen, requiring only 6 A100 GPU days to produce a high-quality generative model capable of 2 to 4-step generation with high performance. Comprehensive evaluations on LAION, MS COCO 2014, and MS COCO 2017 datasets also illustrate that SLAM surpasses existing acceleration methods in few-step generation tasks, achieving state-of-the-art performance both on FID and the quality of the generated images.

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

Recent work in Video Frame Interpolation (VFI) tries to formulate VFI as a diffusion-based conditional image generation problem, synthesizing the intermediate frame given a random noise and neighboring frames. Due to the relatively high resolution of videos, Latent Diffusion Models (LDMs) are employed as the conditional generation model, where the autoencoder compresses images into latent representations for diffusion and then reconstructs images from these latent representations. Such a formulation poses a crucial challenge: VFI expects that the output is deterministically equal to the ground truth intermediate frame, but LDMs randomly generate a diverse set of different images when the model runs multiple times. The reason for the diverse generation is that the cumulative variance (variance accumulated at each step of generation) of generated latent representations in LDMs is large. This makes the sampling trajectory random, resulting in diverse rather than deterministic generations. To address this problem, we propose our unique solution: Frame Interpolation with Consecutive Brownian Bridge Diffusion. Specifically, we propose consecutive Brownian Bridge diffusion that takes a deterministic initial value as input, resulting in a much smaller cumulative variance of generated latent representations. Our experiments suggest that our method can improve together with the improvement of the autoencoder and achieve state-of-the-art performance in VFI, leaving strong potential for further enhancement.