Diffusion Models

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Overview

Diffusion models learn a data distribution by gradually corrupting examples with noise and training a denoiser to reverse that process. Major approaches include DDPMs and score-based SDEs, latent diffusion and diffusion Transformers, flow and consistency methods, and discrete masked or continuous-time Markov diffusion; conditioning and guidance adapt them to specific tasks. They are used for images, video, audio, language, molecules, and scientific forecasting, with evaluations ranging from ImageNet FID to language perplexity and domain-specific measures of accuracy and uncertainty. A central tension is how to make sampling faster and generation more controllable without sacrificing quality, calibration, or diversity, while theory and ongoing audits address generalization, memorization, and privacy.

Latest papers

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1,192 papers152 papers in the last four weeks, up 77% on the four weeks before. 0.9% of all new papers.

Nov 5, 2025

Inference-Time Optimization of Prompt Embeddings in Diffusion Models: A Comparison of sep-CMA-ES and Adam

Deep diffusion models have revolutionized image generation by producing high-quality outputs. However, achieving specific objectives with these models often requires costly adaptations such as fine-tuning, which can be resource-intensive and time-consuming. An alternative approach is inference-time control, which involves optimizing the prompt embeddings to guide the generation process without altering the model weights. We explore prompt-embedding search optimization for the Stable Diffusion XL Turbo model, comparing a gradient-free evolutionary approach, the Separable Covariance Matrix Adaptation Evolution Strategy (sep-CMA-ES), against the widely used gradient-based optimizer Adaptive Moment Estimation (Adam). Candidate images are evaluated by a weighted objective that combines LAION Aesthetic Predictor V2 and CLIPScore, enabling explicit trade-offs between aesthetic quality and prompt-image alignment. On 36 prompts sampled from Parti Prompts (P2) under three weight settings (aesthetics-only, balanced, alignment-only), sep-CMA-ES consistently achieves higher objective values than Adam. We additionally analyze divergence from the unoptimized baseline using cosine similarity and SSIM and report the compute and memory footprints. These results suggest that sep-CMA-ES is an effective inference-time optimizer for prompt-embedding search, improving aesthetics-alignment trade-offs and resource usage without model fine-tuning.

Domício Pereira Neto, João Correia, Penousal Machado

University of Coimbra Coimbra, Portugal

T2I GenerationDiffusion Models
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Oct 31, 2025

Rethinking Robust Adversarial Concept Erasure in Diffusion Models

Concept erasure methods aim to remove specific unsafe target concepts in diffusion models while preserving image generation utility. To address the vulnerability that erased concepts can be easily recovered under adversarial attacks, adversarial concept erasure methods integrate adversarial optimization into the concept erasure process. However, existing adversarial concept erasure methods face a trade-off between robustness and computational cost. We attribute this to adversarial optimization techniques that use random samples to approximate the adversarial objective function. Adversarial optimization that uses a small number of samples fails to produce adversarial embeddings that accurately capture the target concept space. To mitigate this limitation, we propose Semantic-Guided Adversarial Optimization, which uses a single sample to produce adversarial embeddings that better capture the target concept space. We also propose Semantic-Guided Concept Erasure, which automatically maps the target concept to a semantically similar surrogate. Extensive experiments on not-safe-for-work content, artistic styles, and object-related concepts demonstrate that our method, S-GRACE (Semantic-Guided Robust Adversarial Concept Erasure) achieves state-of-the-art erasure robustness and superior image generation utility, with significantly lower computational cost than existing methods. Our code is available at https://github.com/Qhong-522/S-GRACE.

Qinghong Yin, Yu Tian, Heming Yang +5

Beijing University of Posts and Telecommunications, China · University of Chinese Academy of Sciences, China · Nanjing University of Aeronautics and Astronautics, China

Adversarial RobustnessDiffusion Model UnlearningConcept ErasureT2I Diffusion ModelsDiffusion Models
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Oct 29, 2025

MedForj: An open, large-scale foundational generative prior for high-resolution 3D brain MRI

This work introduces MedForj, a suite of 3D foundational generative priors based on diffusion models. The MedForj models were trained on 72,65972{,}659 1~mm isotropic 3D T1T_1-weighted MRI human brain image volumes from 38,17438{,}174 subjects, drawn from a curated corpus of 80,67580{,}675 volumes from 42,50642{,}506 subjects spanning 3838 publicly available datasets. These training images were manually inspected to exclude those with poor quality and excessive pathology, and otherwise were minimally processed. The models include six different diffusion training strategies: rectified flow, latent diffusion rectified flow, flow matching, velocity prediction, clean prediction, and noise prediction. Image samples produced by each of these models were compared to each other and against real, ground truth data under downstream segmentation distributions, FID, five inverse problems, and blind human inspection in an observer study. Flow matching was the strongest strategy overall, achieving the best inverse problem solving results at 28.8028.80~dB PSNR and 0.8740.874 SSIM averaged over the five forward problems, the highest rate of reconstructions judged real by blind human raters at 72.6%72.6\%, and the closest per-structure match to real segmented anatomy in a permutation test. It was not best everywhere: rectified flow produced the most convincing unconditional samples in the observer study and the best FID, and the latent rectified-flow model achieved the smallest joint distributional distance to real anatomy. No other strategy, however, performed consistently well across all four evaluations. We therefore recommend flow matching as the default MedForj prior, while releasing every strategy so that the choice can be revisited per application. All model weights and corresponding code are publicly available at https://github.com/piksl-research/medforj.

Samuel W. Remedios, Aaron Carass, Jerry L. Prince +1

Image Analysis and Communications Laboratory, Johns Hopkins University · Department of Neurology, Johns Hopkins Hospital

Flow MatchingHealthcare3D Medical ImagingMedical Image SynthesisDiffusion-Based Inverse Problems3D Diffusion Models+1
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Oct 26, 2025

Beyond the Semicircle: Free Diffusion Models with Prescribed Equilibria

A growing class of machine-learning objects -- covariance and Gram matrices, kernel and attention matrices, MIMO channel matrices, density operators -- are naturally spectra rather than coordinate vectors. Building a denoising diffusion model for such data by corrupting eigenvalues coordinatewise is not merely elegant: it converges to the wrong limit, because eigenvalues repel rather than move independently. Free probability theory supplies the correct forward process, with free convolution replacing classical convolution and Voiculescu's conjugate variable replacing the score, but constant-coefficient free diffusions have a hidden limitation of their own: their only possible equilibrium is the semicircular law, whatever the target distribution looks like. We show that state-dependent free volatility removes this restriction. For any sufficiently regular compactly supported target law, we explicitly construct, through a closed-form Hilbert-transform drift, a free Fokker--Planck flow having that law as a stationary spectral distribution. Under an additional convex-potential condition, the construction admits a globally relaxing diffusion interpretation, reverse-time dynamics, and a trainable score. The generalization is genuine rather than cosmetic: no change of spectral variable reduces it to the constant-coefficient case, and it is a Wasserstein gradient flow only for an explicitly characterized family of coefficients that contains no bounded non-constant member. We instantiate the construction on the Marchenko--Pastur law, the limiting spectrum of isotropic sample covariance matrices, and validate it numerically: the free-versus-coordinatewise gap, an exact dimension-independent score driving reverse-time matrix dynamics at several matrix sizes, the designed Marchenko--Pastur equilibrium, and end-to-end generation with a learned score.

Swagatam Das

Random Matrix TheoryDiffusion Models
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Oct 20, 2025

Not Every Time and Frequency Need to Be Forgotten in Diffusion Unlearning

Data unlearning aims to remove the influence of specific training samples from a trained model. In fine-tuning methods, data unlearning relies primarily on loss maximization over forget samples, which often leads to quality degradation or incomplete forgetting. Existing methods perform unlearning uniformly across diffusion stages, ignoring diffusion dynamics from noise to data. Our systematic study of diffusion phases shows that forgetting in diffusion models is uneven across time and frequency, with theoretical justification of distributive distortion and forgetting-utility trade-off. By selectively forgetting time and frequency in diffusion models, we achieve both higher unlearning success rates and improved generation quality across diverse settings, including both conditional and unconditional scenarios. We also introduce an improved SSCD metric that measures dissimilarity using a normalized perturbation distance. Together, we provide practical insights for understanding and improving data unlearning in diffusion models.

Jinseong Park, Mijung Park

Korea Institute for Advanced Study · University of British Columbia

Diffusion Model UnlearningMachine UnlearningDiffusion Models
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Oct 14, 2025

A Connection Between Score Matching and Local Intrinsic Dimension

The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered that diffusion models capture the LID of data through the spectra of their score estimates and through the rate of change of their density estimates under various noise perturbations. While these methods can accurately quantify LID, they require either many forward passes of the diffusion model or use of gradient computation, limiting their applicability in compute- and memory-constrained scenarios. We show that the LID is a lower bound on the denoising score matching loss, motivating use of the denoising score matching loss as a LID estimator. Moreover, we show that the equivalent implicit score matching loss also approximates LID via the normal dimension and is closely related to a recent LID estimator, FLIPD. Our experiments on a manifold benchmark and with Stable Diffusion 3.5 indicate that the denoising score matching loss is a highly competitive and scalable LID estimator, achieving superior accuracy and memory footprint under increasing problem size and quantization level.

Eric Yeats, Aaron Jacobson, Darryl Hannan +4

PNNL · UNC Chapel Hill · UC San Diego

Intrinsic DimensionalityScore MatchingDiffusion Models
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Oct 3, 2025

Multi-task Neural Diffusion Processes

Neural diffusion processes provide a scalable, non-Gaussian approach to modelling distributions over functions, but existing formulations are limited to single-task inference and do not capture dependencies across related tasks. We propose multi-task neural diffusion processes (MT-NDPs), an extension that incorporates a task encoder to enable task-conditioned probabilistic regression and few-shot adaptation across related functions. The task encoder extracts a low-dimensional representation from context observations and conditions the diffusion model on this representation, allowing information sharing across tasks while accommodating variable-sized context sets and preserving permutation invariance with respect to the ordering of context observations. We evaluate MT-NDPs through synthetic experiments and two real-world applications involving wind turbine data and school examination outcomes. The results demonstrate improved predictive accuracy relative to single-task diffusion baselines when context observations are available, alongside competitive performance against neural-process and Gaussian-process alternatives. In the wind-energy application, MT-NDPs achieve the lowest average coverage error among the evaluated models at larger context sizes, demonstrating improved predictive uncertainty calibration. Overall, our findings highlight the potential of task-conditioned diffusion models for uncertainty-aware multi-task regression and few-shot adaptation to previously unseen tasks.

Joseph Rawson, Domniki Ladopoulou, Petros Dellaportas

Department of Statistical Science, University College London, Gower Street, London, WC1E 6BT, United Kingdom. · Department of Statistics, Athens University of Economics and Business, Patission 76, Athens, 104 34, Greece.

Diffusion ModelsMulti-Task LearningFew-Shot Learning
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Oct 1, 2025

Affordance-Guided Diffusion Prior for 3D Hand Reconstruction

How can we reconstruct 3D hand poses when large portions of the hand are heavily occluded by itself or by objects? Humans often resolve such ambiguities by leveraging contextual knowledge -- such as affordances, where an object's shape and function suggest how the object is typically grasped. Inspired by this observation, we propose a generative prior for hand pose refinement guided by affordance-aware textual descriptions of hand-object interactions (HOI). Our method employs a diffusion-based generative model that learns the distribution of plausible hand poses conditioned on affordance descriptions, which are inferred from a large vision-language model (VLM). This enables the refinement of occluded regions into more accurate and functionally coherent hand poses. Extensive experiments on HOGraspNet, a 3D hand-affordance dataset with severe occlusions, demonstrate that our affordance-guided refinement significantly improves hand pose estimation over both recent regression methods and diffusion-based refinement lacking contextual reasoning.

Naru Suzuki, Takehiko Ohkawa, Tatsuro Banno +3

The University of Tokyo · KAIST

3D Hand Pose EstimationHand-Object InteractionDiffusion Models3D Hand Reconstruction
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Sep 30, 2025

DiffAU: Diffusion-Based Ambisonics Upscaling

Spatial audio enhances immersion by reproducing 3D sound fields, with Ambisonics offering a scalable format for this purpose. While first-order Ambisonics (FOA) notably facilitates hardware-efficient acquisition and storage of sound fields as compared to high-order Ambisonics (HOA), its low spatial resolution limits realism, highlighting the need for Ambisonics upscaling (AU) as an approach for increasing the order of Ambisonics signals. In this work we propose DiffAU, a cascaded AU method that leverages recent developments in diffusion models combined with novel adaptation to spatial audio to generate 3rd order Ambisonics from FOA. By learning data distributions, DiffAU provides a principled approach that rapidly and reliably reproduces HOA in various settings. Experiments in anechoic conditions with multiple speakers, show strong objective and perceptual performance.

Amit Milstein, Nir Shlezinger, Boaz Rafaely

ECE School Ben-Gurion University of the Negev, Be’er-Sheva, Israel

Audio Diffusion ModelsSpatial AudioDiffusion Models
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Sep 30, 2025

Data-to-Energy Stochastic Dynamics

The Schrödinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport to the stochastic case, has received attention due to its connections to diffusion models and flow matching, as well as its applications in the natural sciences. However, all existing algorithms allow to infer such dynamics only for cases where samples from both distributions are available. In this paper, we propose the first general method for modelling Schrödinger bridges when one (or both) distributions are given by their unnormalised densities, with no access to data samples. Our algorithm relies on a generalisation of the iterative proportional fitting (IPF) procedure to the data-free case, inspired by recent developments in off-policy reinforcement learning for training of diffusion samplers. We demonstrate the efficacy of the proposed data-to-energy IPF on synthetic problems, finding that it can successfully learn transports between multimodal distributions. As a secondary consequence of our reinforcement learning formulation, which assumes a fixed time discretisation scheme for the dynamics, we find that existing data-to-data Schrödinger bridge algorithms can be substantially improved by learning the diffusion coefficient of the dynamics. Finally, we apply the newly developed algorithm to the problem of sampling posterior distributions in latent spaces of generative models, thus creating a data-free image-to-image translation method. Code: https://github.com/mmacosha/d2e-stochastic-dynamics

Kirill Tamogashev, Esmeralda S. Whitammer

University of Edinburgh

Sampling from Unnormalized DistributionsSchrödinger BridgesDiffusion Models
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Sep 23, 2025

Lavida-O: Elastic Large Masked Diffusion Models for Unified Multimodal Understanding and Generation

We propose Lavida-O, a unified Masked Diffusion Model (MDM) for multimodal understanding and generation. Unlike existing multimodal MDMs such as MMaDa and Muddit which only support simple image-level understanding tasks and low-resolution image generation, Lavida-O presents a single framework that enables image-level understanding, object grounding, image editing, and high-resolution (1024px) text-to-image synthesis. Lavida-O incorporates a novel Elastic Mixture-of-Transformers (Elastic-MoT) architecture that couples a lightweight generation branch with a larger understanding branch, supported by token compression, universal text conditioning and stratified sampling for efficient and high-quality generation. Lavida-O further incorporates planning and iterative self-reflection in image generation and editing tasks, seamlessly boosting generation quality with its understanding capabilities. Lavida-O achieves state-of-the-art performance on a wide range of benchmarks including RefCOCO object grounding, GenEval text-to-image generation, and ImgEdit image editing, outperforming existing autoregressive models and continuous diffusion models such as Qwen2.5-VL and FluxKontext-dev, while offering considerable speedup at inference. These advances establish Lavida-O as a new paradigm for scalable multimodal reasoning and generation.

Shufan Li, Jiuxiang Gu, Kangning Liu +4

Adobe · UCLA

Masked Diffusion ModelsUnified Multimodal ModelsMultimodal Foundation ModelsDiffusion-Based Image EditingT2I Diffusion ModelsDiffusion Models+2
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Sep 19, 2025

Diff-Feat: Diffusion-Based Cross-Modal Feature Extraction for Multi-Label Classification

Multi-label classification has broad applications and depends on powerful representations capable of capturing multiple interactions. We introduce Diff-Feat, a simple yet effective framework that extracts intermediate features from pre-trained diffusion-Transformer models for both images and text, and fuses them for downstream tasks. We observe distinct patterns in optimal feature selection: for vision tasks, the most discriminative intermediate feature along the diffusion process occurs at the middle step and is located at the middle block in Transformer. In contrast, for language tasks, the best feature occurs at the noise-free step and is located at the deepest block. Notably, a consistent phenomenon across diverse datasets: a fixed "Middle Layer" yields the best performance on various downstream classification tasks for images (under DiT-XL/2-256×\times256 and various U-ViT architectures). We further analyze the underlying mechanism and its scaling behavior across model scales. To efficiently select representations, we devise a heuristic local-search algorithm that pinpoints the locally optimal "image-text"×\times"block-timestep" pair among a few candidates, avoiding an exhaustive grid search. A simple fusion-linear projection followed by addition-of the selected representations achieves 46.1% mAP on Visual Genome 500 (with 500 categories) and 80.2% mAP on Pix2Cap-COCO (with 80 categories), consistently outperforming strong baseline methods. Code is available at https://github.com/lt-0123/Diff-Feat.

Tian Lan, Yiming Zheng, Jianxin Yin

School of Statistics, Renmin University of China · Center for Applied Statistics and School of Statistics, Renmin University of China

Multimodal ClassificationMulti-Label ClassificationDiffusion ModelsMultimodal Fusion
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Sep 15, 2025

IS-Diff: Improving Diffusion-Based Inpainting with Better Initial Seed

Diffusion models have shown promising results in free-form inpainting. Recent studies based on refined diffusion samplers or novel architectural designs led to realistic results and high data consistency. However, random initialization seed (noise) adopted in vanilla diffusion process may introduce mismatched semantic information in masked regions, leading to biased inpainting results, e.g., low consistency and low coherence with the other unmasked area. To address this issue, we propose the Initial Seed refined Diffusion Model (IS-Diff), a completely training-free approach incorporating distributional harmonious seeds to produce harmonious results. Specifically, IS-Diff employs initial seeds sampled from unmasked areas to imitate the masked data distribution, thereby setting a promising direction for the diffusion procedure. Moreover, a dynamic selective refinement mechanism is proposed to detect severe unharmonious inpaintings in intermediate latent and adjust the strength of our initialization prior dynamically. We validate our method on both standard and large-mask inpainting tasks using the CelebA-HQ, ImageNet, and Places2 datasets, demonstrating its effectiveness across all metrics compared to state-of-the-art inpainting methods.

Yongzhe Lyu, Yu Wu, Yutian Lin +1

School of Computer Science, Wuhan University, Wuhan 430072, China

Image InpaintingDiffusion ModelsDiffusion Sampling
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Aug 29, 2025

ECHO: Ego-Centric modeling of Human-Object interactions

Modeling human-object interactions (HOI) from an egocentric perspective is a critical yet challenging task, particularly when relying on sparse signals from wearable devices like smart glasses and watches. We present ECHO, the first unified framework to jointly recover human pose, object motion, and contact dynamics solely from head and wrist tracking. To tackle the underconstrained nature of this problem, we introduce a novel tri-variate diffusion process with independent noise schedules that models the mutual dependencies between the human, object, and interaction modalities. This formulation allows ECHO to operate with flexible input configurations, making it robust to intermittent tracking and capable of leveraging partial observations. Crucially, it enables training on a combination of large-scale human motion datasets and smaller HOI collections, learning strong priors while capturing interaction nuances. Furthermore, we employ a smooth inpainting inference mechanism that enables the generation of temporally consistent interactions for arbitrarily long sequences. Extensive evaluations demonstrate that ECHO achieves state-of-the-art performance, significantly outperforming existing methods lacking such flexibility. The project page is available at https://ptrvilya.github.io/echo/.

Ilya A. Petrov, Vladimir Guzov, Riccardo Marin +5

University of Tübingen, Germany · Tübingen AI Center, Germany · Technical University of Munich, Germany +3

HOI Generation3D ReconstructionObject Pose EstimationHuman Pose EstimationDiffusion ModelsHuman-Object Interaction
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Aug 21, 2025

MeSS: City Mesh-Guided Outdoor Scene Generation with Cross-View Consistent Diffusion

Mesh models have become increasingly accessible for numerous cities; however, the lack of realistic textures restricts their application in virtual urban navigation and autonomous driving. To address this, this paper proposes MeSS (Meshbased Scene Synthesis) for generating high-quality, styleconsistent outdoor scenes with city mesh models serving as the geometric prior. While image and video diffusion models can leverage spatial layouts (such as depth maps or HD maps) as control conditions to generate street-level perspective views, they are not directly applicable to 3D scene generation. Video diffusion models excel at synthesizing consistent view sequences that depict scenes but often struggle to adhere to predefined camera paths or align accurately with rendered control videos. In contrast, image diffusion models, though unable to guarantee cross-view visual consistency, can produce more geometry-aligned results when combined with ControlNet. Building on this insight, our approach enhances image diffusion models by improving cross-view consistency. The pipeline comprises three key stages: first, we generate geometrically consistent sparse views using Cascaded Outpainting ControlNets; second, we propagate denser intermediate views via a component dubbed AGInpaint; and third, we globally eliminate visual inconsistencies (e.g., varying exposure) using the GCAlign module. Concurrently with generation, a 3D Gaussian Splatting (3DGS) scene is reconstructed by initializing Gaussian balls on the mesh surface. Our method outperforms existing approaches in both geometric alignment and generation quality. Once synthesized, the scene can be rendered in diverse styles through relighting and style transfer techniques. project page: https://albertchen98.github.io/mess/

Xuyang Chen, Zhijun Zhai, Kaixuan Zhou +10

Huawei Hilbert Research Center · Technical University of Munich, Munich, Germany · Wuhan University, Wuhan, China +1

3D Scene GenerationMulti-View Image SynthesisDiffusion Models
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Aug 13, 2025

EEGDM: Label-Efficient EEG Representation Learning with Generative Diffusion Model

Electroencephalography (EEG) is a critical tool for monitoring brain activity and diagnosing neurological disorders such as epilepsy. However, learning meaningful representations from raw EEG signals remains challenging due to limited annotations, substantial inter-subject variability, and complex temporal dynamics. Recent EEG foundation models (FMs) have demonstrated promising performance through transformer-based architectures and large-scale self-supervised pretraining, yet they often incur substantial computational costs and exhibit diminishing returns with increasing model and dataset scale, limiting their practicality in clinical settings. To address these challenges, we propose EEGDM, a diffusion-based EEG representation learning framework. Specifically, EEGDM introduces a Structured State-Space Model for Diffusion Pretraining (SSMDP) that effectively captures long-range temporal dependencies through generative diffusion training on unlabeled EEG data. The representations are subsequently leveraged for downstream tasks via our Latent Fusion Module (LFM), which integrates multi-layer latent features of SSMDP. We evaluate EEGDM on three EEG benchmarks spanning EEG event classification (TUEV), seizure detection (CHB-MIT), and seizure classification (IIIC). Compared with existing state-of-the-art methods, including EEG FMs, EEGDM achieves competitive performance across diverse tasks and datasets, exceeding existing methods in most cases while requiring substantially fewer samples for both pretraining and downstream adaptation. These results demonstrate that diffusion-based learning can unlock more discriminative EEG representations, with direct implications for epilepsy diagnosis and management. Our source code and pretrained checkpoints are publicly available at: https://github.com/jhpuah/EEGDM.

Jia Hong Puah, Sim Kuan Goh, Ziwei Zhang +6

School of Artificial Intelligence and Robotics, Xiamen University Malaysia · School of Energy and Chemical Engineering, Xiamen University Malaysia · Department of Biomedical Engineering, Universiti Malaya +3

ElectroencephalographyEEG Seizure DetectionRepresentation LearningSelf-Supervised Time Series Representation LearningDiffusion ModelsData-Efficient Learning+1
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Jun 29, 2025

Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks

Urban sensor networks need forecasts that are accurate, carry useful uncertainty, and refresh fast enough to act on as new readings arrive. These goals conflict: deterministic models give no distribution, while diffusion forecasters model uncertainty but denoise from pure noise over many steps. We present Double-Diffusion, which integrates a closed-form graph-heat prior into a denoising diffusion model. The prior is a parameter-free low-pass forecast over the sensor graph, and it serves two roles: it is the residual target the model generates, and it conditions the denoiser. The reverse process therefore starts near the prior and denoises a short warm-started chain instead of synthesizing from pure noise; the name denotes this composition, a graph diffusion feeding a denoising diffusion. A compact denoiser, DD-Net, is trained as a Denoising Diffusion Probabilistic Model (DDPM) in the Resfusion warm-start formulation, so generation refines the prior over a short truncated chain rather than synthesizing from pure noise; a graph-spectral read-out of the prior residual sets its switchable spatial filter per domain from training data alone. On four real-world air quality and traffic networks, Double-Diffusion attains the best CRPS of all probabilistic methods on every dataset and stays competitive in point accuracy with the strongest baselines, at a fraction of the sampling cost of from-noise diffusion. The code is available at: https://github.com/teddyicare/Double-Diffusion

Hanlin Dong, Arian Prabowo, Hao Xue +4

University of New South Wales Sydney, Australia · University of Maryland College Park, United States · The Hong Kong University of Science and Technology (Guangzhou) Guangzhou, China

Spatiotemporal ForecastingDiffusion Model Inference AccelerationProbabilistic Time Series ForecastingDiffusion ModelsGraph Diffusion
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Jun 24, 2025

Generate the Forest before the Trees - A Hierarchical Diffusion model for Climate Downscaling

Downscaling is essential for generating the high-resolution climate data needed for local planning, but traditional methods remain computationally demanding. Recent years have seen impressive results from AI downscaling models, particularly diffusion models, which have attracted attention due to their ability to generate ensembles and overcome the smoothing problem common in other AI methods. However, these models typically remain computationally intensive. We introduce a Hierarchical Diffusion Downscaling (HDD) model, which introduces an easily-extensible hierarchical sampling process to the diffusion framework. A coarse-to-fine hierarchy is imposed via a simple downsampling scheme. HDD achieves competitive accuracy on ERA5 reanalysis datasets and CMIP6 models, significantly reducing computational load by running on up to half as many pixels with competitive results. Additionally, a single model trained at 0.25° resolution transfers seamlessly across multiple CMIP6 models with much coarser resolution. HDD thus offers a lightweight alternative for probabilistic climate downscaling, facilitating affordable large-ensemble high-resolution climate projections. See a full code implementation at: https://github.com/HDD-Hierarchical-Diffusion-Downscaling/HDD-Hierarchical-Diffusion-Downscaling.

Declan J. Curran, Sanaa Hobeichi, Hira Saleem +2

School of Computer Science and Engineering, University of New South Wales, Sydney, New South Wales, Australia · ARC Centre of Excellence for the Weather of the 21st Century and Climate Change Research Centre, University of New South Wales, Sydney, New South Wales, Australia

Climate DownscalingClimate ModelingDiffusion ModelsDiffusion Model Acceleration
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Jun 24, 2025

Diffusion-aided Task-oriented Semantic Communications with Model Inversion Attack

Semantic communication enhances transmission efficiency by conveying semantic information rather than raw input symbol sequences. Task-oriented semantic communication further aims to retain only task-specific information, thereby achieving greater bandwidth savings. However, these neural-network-based communication systems are vulnerable to model inversion attacks, in which adversaries attempt to recover sensitive input information from intercepted semantic features. The key challenge is therefore to preserve privacy while maintaining task accuracy and robustness. We consider a task-confidential setting in which the adversary attempts to reconstruct the original input from intercepted features without knowing the legitimate receiver's task or model. Although PSNR and SSIM are commonly used to assess reconstruction quality, we find that an external classifier can still perform the legitimate receiver's task with nontrivial accuracy on reconstructions with low PSNR or SSIM, indicating that these reconstructions still contain task-level semantic leakage. We therefore propose DiffSem, which splits the diffusion process between controlled transmitter-side self-noising and matched receiver-side reverse denoising. Experiments on the MNIST, CIFAR-10, and CelebA datasets show that DiffSem improves the legitimate receiver's task accuracy without increasing either the transmitted feature size or information leakage.

Xuesong Wang, Mo Li, Xingyan Shi +2

School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong 518172, China

Semantic CommunicationTask-Oriented Semantic CommunicationModel Inversion AttacksDiffusion Models
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Jun 13, 2025

The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis

Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary stochasticity function or a probability flow ODE, corresponding to setting this stochasticity function to zero. In this work, we investigate the effect of this stochasticity on the generation process through the evolution of Kullback-Leibler (KL) divergences, obtaining general KL divergence bounds and a novel analysis of the impact of the time-profile of the score error on model performance. For exact score functions, stochasticity has a contractive effect, decreasing KL divergence along the sampling trajectory. For approximate scores, however, a trade-off arises between correcting accumulated errors and amplifying current score errors, meaning stochasticity can either improve or degrade generation performance. Theoretical considerations indicate that the gain from stochasticity depends on the time-localization of the trained model error. We test this in experiments on both toy and benchmark data sets, also comparing the KL divergence evolution with the obtained bounds. We also present a fully analytical example, where all the relevant quantities can be computed, and the optimal stochasticity function can be characterized via an optimal control analysis.

Bernardo P. Schaeffer, Ricardo M. S. Rosa, Glauco Valle

Instituto de Matem´atica, Universidade Federal do Rio de Janeiro

Stochastic Differential EquationsDiffusion SamplingScore-Based Generative ModelingDiffusion Models
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Jun 11, 2025

ScoreMix: Synthetic Data Generation by Score Composition in Diffusion Models Improves Recognition

Synthetic data generation is increasingly used in machine learning for training and data augmentation. Yet, current strategies often rely on external foundation models or datasets, whose usage is restricted in many scenarios due to policy or legal constraints. We propose ScoreMix, a self-contained synthetic generation method to produce hard synthetic samples for recognition tasks by leveraging the score compositionality of diffusion models. The approach mixes class-conditioned scores along reverse diffusion trajectories, yielding domain-specific data augmentation without external resources. We systematically study class-selection strategies and find that mixing classes distant in the discriminator's embedding space yields larger gains, providing up to 3% additional average improvement, compared to selection based on proximity. Interestingly, we observe that condition and embedding spaces are largely uncorrelated under standard alignment metrics, and the generator's condition space has a negligible effect on downstream performance. Across 8 public face recognition benchmarks, ScoreMix improves accuracy by up to 7 percentage points, without hyperparameter search, highlighting both robustness and practicality. Our method provides a simple yet effective way to maximize discriminator performance using only the available dataset, without reliance on third-party resources. Paper website: https://parsa-ra.github.io/scoremix/.

Parsa Rahimi, Sebastien Marcel

1EPFL, Switzerland · 2Idiap, Switzerland

Synthetic Data AugmentationSynthetic Data GenerationFace RecognitionScore-Based Generative ModelingDiffusion ModelsDiffusion-Based Data Augmentation
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Jun 11, 2025

ELBO-T2IAlign: A Generic ELBO-Based Method for Calibrating Pixel-level Text-Image Alignment in Diffusion Models

Diffusion models excel at image generation. Recent studies have shown that these models not only generate high-quality images but also encode text-image alignment information through attention maps or loss functions. This information is valuable for various downstream tasks, including segmentation, text-guided image editing, and compositional image generation. However, current methods heavily rely on the assumption of perfect text-image alignment in diffusion models, which is not the case. In this paper, we propose using zero-shot referring image segmentation as a proxy task to evaluate the pixel-level image and class-level text alignment of popular diffusion models. We conduct an in-depth analysis of pixel-text misalignment in diffusion models from the perspective of training data bias. We find that misalignment occurs in images with small-sized, occluded, or rare object classes. Therefore, we propose ELBO-T2IAlign--a simple yet effective method to calibrate pixel-text alignment in diffusion models based on the evidence lower bound (ELBO) of likelihood. ELBO-T2IAlign is training-free and generic: it requires no additional annotations, model retraining, or architectural modifications, and it can be directly applied to different diffusion backbones. Extensive experiments on zero-shot referring image segmentation, text-guided image editing, and compositional image generation verify that the proposed calibration improves pixel-text alignment across complementary downstream tasks.

Qin Zhou, Zhiyang Zhang, Jinglong Wang +5

School of Software, Beihang University, Beijing 100191, China · College of Computer and Cyber Security, Hebei Normal University, Hebei 050024, China · Department of Computer Science, The University of Hong Kong, Hong Kong

Diffusion Model AlignmentText-Image AlignmentDiffusion Models
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Jun 1, 2025

Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis

Despite the empirical success of Diffusion Models (DMs) and Variational Autoencoders (VAEs), their generalization performance remains theoretically underexplored, especially lacking a full consideration of the shared encoder-generator structure. Leveraging recent information-theoretic tools, we propose a unified theoretical framework that provides guarantees for the generalization of both the encoder and generator by treating them as randomized mappings. This framework further enables (1) a refined analysis for VAEs, accounting for the generator's generalization, which was previously overlooked; (2) illustrating an explicit trade-off in generalization terms for DMs that depends on the diffusion time TT; and (3) providing computable bounds for DMs based solely on the training data, allowing the selection of the optimal TT and the integration of such bounds into the optimization process to improve model performance. Empirical results on both synthetic and real datasets illustrate the validity of the proposed theory.

Qi Chen, Jierui Zhu, Florian Shkurti

Department of Computer Science, University of Toronto · Data Science Institute · Vector Institute +2

Variational AutoencodersNeural Network GeneralizationInformation-Theoretic Generalization BoundsDiffusion ModelsGeneralization Bounds
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May 28, 2025

Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion

Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the limitations of near-term quantum devices. Following our previous work on QDMs, here we propose and implement two physics-inspired protocols. In the first, we use the formalism of quantum stochastic walks, showing that a specific interplay of quantum and classical dynamics in the forward process produces statistically more robust models generating sets of MNIST images with lower Fréchet Inception Distance (FID) than using totally classical dynamics. In the second approach, we realize an algorithm to generate images by exploiting the intrinsic noise of real IBM quantum hardware with only four qubits. Our work could be a starting point to pave the way for new scenarios for large-scale algorithms in quantum Generative AI, where quantum noise is neither mitigated nor corrected, but instead exploited as a useful resource.

Marco Parigi, Stefano Martina, Francesco Aldo Venturelli +1

Department of Physics and Astronomy, University of Florence, Via Sansone 1, Sesto Fiorentino, 50019, Florence, Italy. · LENS - European Laboratory for Non-Linear Spectroscopy, University of Florence, Via Nello Carrara 1, Sesto Fiorentino, 50019, Florence, Italy. · Department of Engineering, Pompeu Fabra, T`anger 122-140, Barcelona, 08018, Barcelona, Spain.

Quantum Generative ModelingDiffusion-Based Image GenerationDiffusion Models
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May 24, 2025

Improved Immiscible Diffusion: Accelerate Diffusion Training by Reducing Its Miscibility

The substantial training cost of diffusion models hinders their deployment. Immiscible Diffusion recently showed that reducing diffusion trajectory mixing in the noise space via linear assignment accelerates training by simplifying denoising. To extend immiscible diffusion beyond the inefficient linear assignment under high batch sizes and high dimensions, we refine this concept to a broader miscibility reduction at any layer and by any implementation. Specifically, we empirically demonstrate the bijective nature of the denoising process with respect to immiscible diffusion, ensuring its preservation of generative diversity. Moreover, we provide thorough analysis and show step-by-step how immiscibility eases denoising and improves efficiency. Extending beyond linear assignment, we propose a family of implementations including K-nearest neighbor (KNN) noise selection and image scaling to reduce miscibility, achieving up to >4x faster training across diverse models and tasks including unconditional/conditional generation, image editing, and robotics planning. Furthermore, our analysis of immiscibility offers a novel perspective on how optimal transport (OT) enhances diffusion training. By identifying trajectory miscibility as a fundamental bottleneck, we believe this work establishes a potentially new direction for future research into high-efficiency diffusion training. The code is available at https://github.com/yhli123/Immiscible-Diffusion.

Yiheng Li, Feng Liang, Dan Kondratyuk +3

UC Berkeley, Berkeley CA 94720, USA · UT Austin, Austin TX 78712, USA · Rekursiv.ai, Mountain View CA, 94041

Diffusion Model AccelerationDiffusion Models
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May 16, 2025

Diffusion-based Evolutionary Optimization for 3D Multi-Objective Molecular Generation

De novo 3D molecular design with multiple properties and fragment-retention constraints is formulated as a constrained multi-objective optimization problem. Existing 3D diffusion models provide strong capabilities for generating novel molecules, but adapting them to new conditions and multi-objective optimization tasks remains difficult. We present Diffusion-based Evolutionary Molecular Optimization (DEMO), a framework that draws solely on the unconditional molecular prior of a frozen pretrained diffusion model to generate chemically valid 3D candidates, while evolutionary search handles conditional generation and constrained multi-objective optimization, without retraining or fine-tuning. DEMO performs crossover and mutation on intermediate diffusion states through an Evolutionary-Guided Diffusion (EGD) operator, combines 2D topology and 3D geometry in Structure-Aware Environmental Selection (SAES) to preserve structural diversity, and uses three cooperating populations to coordinate structural exploration, fragment-constraint satisfaction, and property optimization. Experimental results demonstrate that EGD outperforms task-specific conditional generators in property targeting; SAES preserves structural diversity while retaining competitive hypervolume in multi-objective optimization; and DEMO improves objective convergence and generates diverse feasible molecules under fragment constraints. These results show how evolutionary search can reuse existing diffusion models for diverse molecular design requirements.

Ruiqing Sun, Dawei Feng, Sen Yang +5

College of Computer Science and Technology, National University of Defense Technology, 410073, Changsha, China · Bioinformatics Center, Academy of Military Medical Sciences (AMMS), 100080, Beijing, China

3D Molecular GenerationConstrained Generative ModelingMulti-Objective Evolutionary OptimizationDiffusion ModelsDiffusion Guidance
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May 10, 2025

StableMotion: One-Step Motion Estimation with Diffusion Prior

We present StableMotion, a novel framework that leverages geometric and content priors from pretrained large-scale image diffusion models for motion estimation in single-image rectification tasks such as Stitched Image Rectangling (SIR) and Rolling Shutter Correction (RSC). Specifically, StableMotion takes a text-to-image Stable Diffusion (SD) model as its backbone and repurposes it as an image-to-motion estimator. To mitigate inconsistent outputs produced by diffusion models, we propose Adaptive Ensemble Strategy (AES), which consolidates multiple outputs into a cohesive, high-fidelity result. Additionally, we present Sampling Steps Disaster (SSD), a counterintuitive phenomenon in which increasing the number of sampling steps can lead to poorer outcomes, motivating our one-step inference design. StableMotion is evaluated on two image rectification tasks and delivers state-of-the-art performance on both, while also showing promising transferability through qualitative examples and no-reference evaluations on unseen SIR-OOD and real-captured RSC benchmarks. Supported by SSD, StableMotion achieves efficient one-step inference, offering over 100×\times speedup compared to previous diffusion model-based methods even when combined with the optional AES post-processing. Code and weights are available at https://github.com/ivowang/StableMotion.

Ziyi Wang, Haipeng Li, Lin Sui +5

Yingcai Honors College, University of Electronic Science and Technology of China, Chengdu 611731, China · School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China · 4Paradigm Inc., Beijing 100080, China +2

Diffusion Models
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May 7, 2025

Localized Diffusion Models

Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, a task that in principle suffers from the curse of dimensionality. It is therefore important to understand how low-dimensional structure in the target distribution can be exploited in these models. Here we consider locality structure, which describes certain sparse conditional dependencies among the target random variables. Given some locality structure, the score function is effectively low-dimensional, so that it can be estimated by a localized neural network with significantly reduced sample complexity. This observation motivates the localized diffusion model, where a localized score matching loss is used to train the score function within a localized hypothesis space. We prove that such localization enables diffusion models to circumvent the curse of dimensionality with dimension-independent error bounds, at the price of additional localization error. Under realistic sample size scaling, we then show both theoretically and numerically that a moderate localization radius can balance the statistical and localization errors, yielding better overall performance. Locality structure also facilitates parallel training, making localized diffusion models potentially more efficient for large-scale applications.

Georg A. Gottwald, Shuigen Liu, Youssef Marzouk +2

School of Mathematics and Statistics, The University of Sydney · Department of Mathematics, National University of Singapore · Laboratory for Information and Decision Systems, Massachusetts Institute of Technology +1

Curse of DimensionalityScore-Based Generative ModelingDiffusion Models
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May 7, 2025

Riemannian Denoising Diffusion Probabilistic Models

We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing methods for generative modeling on manifolds rely on substantial geometric information such as geodesic curves or eigenfunctions of the Laplace-Beltrami operator and, as a result, they are limited to manifolds where such information is available. In contrast, our method, built on a projection scheme, can be applied to more general manifolds, as it only requires being able to evaluate the value and the first order derivatives of the function that defines the submanifold. We provide a theoretical analysis of our method in the continuous-time limit, which elucidates the connection between our RDDPMs and score-based generative models on manifolds. The capability of our method is demonstrated on datasets from previous studies and on new datasets sampled from two high-dimensional manifolds, i.e. SO(10)\mathrm{SO}(10) and the configuration space of molecular system alanine dipeptide with fixed dihedral angle.

Zichen Liu, Wei Zhang, Christof Schütte +1

Center for Data Science, Peking University, Beijing 100871, P.R. China · Zuse Institute Berlin, Takustrasse 7, Berlin 14195, Germany · Institute of Mathematics, Freie Universität Berlin and Zuse Institute Berlin, Takustrasse 7, Berlin 14195, Germany +1

Generative ModelingScore-Based Generative ModelingRiemannian GeometryDiffusion Models
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Apr 30, 2025

The Linear Geometry of Interpretable Tokens: Jailbreaking Attacks and Defenses for Unlearned Diffusion Models

Diffusion models excel at generating high-quality images but can memorize and reproduce harmful concepts when prompted. Although fine-tuning methods have been proposed to unlearn a target concept, they struggle to fully erase it while maintaining generation quality on other concepts, leaving models vulnerable to jailbreak attacks. Existing jailbreak methods demonstrate this vulnerability but offer limited insight into how unlearned models retain harmful concepts, limiting progress on effective defenses. In this work, we show that a coherent, interpretable, attack-accessible linear residual of the erased concept can be recovered in the token embedding space, and that both an attack and a defense follow from this structure. We introduce SubAttack, a novel jailbreaking attack that reads out this subspace by learning an orthogonal set of attack token embeddings, each being a linear combination of human-interpretable textual elements, revealing that unlearned models still retain the target concept through related textual components. Furthermore, our attack is also more powerful and transferable across text prompts, initial noises, and unlearned models than prior attacks. Conversely, projecting out the same subspace yields SubDefense, a lightweight plug-and-play defense mechanism that suppresses the residual concept in unlearned models. SubDefense provides stronger robustness than existing defenses while better preserving safe generation quality. Extensive experiments across multiple unlearning methods, concepts, and attack types demonstrate that our approach advances both understanding and mitigation of vulnerabilities in diffusion unlearning.

Siyi Chen, Yimeng Zhang, Sijia Liu +1

University of Michigan · Michigan State University

Jailbreak AttacksDiffusion Model UnlearningMachine UnlearningDiffusion Models
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