Diffusion Dynamics

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16 papers in the last four weeks, up 100% on the four weeks before. 0.2% of all new papers.

Jul 13Week of Sep 28

Latest papers 97

May 14, 2026cs.LG

Reading the Cell, Designing the Cure: Perturbation-Conditioned Molecular Diffusion for Function-Oriented Drug Design

When reliable target structures are unavailable at scale or phenotypes arise from dysregulated pathways, transcriptomic perturbations provide a system-level functional readout for drug action. In this work, we formalize \emph{Transcriptome-based Drug Design (TBDD)} as a generative inverse problem: designing drug molecules conditioned on desired transcriptomic state transitions. We analyze the inherently ill-posed nature of this task, which is further complicated by the profound domain gap between biology and chemistry and by the sparsity of transcriptomic signals. To address these challenges, we propose \textbf{\themodel{}} (A \textbf{C}ell\textbf{U}lar \textbf{R}esponse \textbf{E}ngine), a multi-resolution transcriptome-guided diffusion framework. \themodel{} features a specialized \textbf{Transcriptome Perturbation Functional Feature Extractor (TFE)} that (1) distills function-oriented perturbation embeddings from pre/post states, (2) aligns these signatures to dual chemical views to bridge the cross-modal gap, and (3) performs heterogeneity-aware aggregation to extract robust state-specific signals from noisy transcriptomic data. Extensive evaluations on both standard benchmarks and rigorous out-of-distribution protocols demonstrate that \themodel{} consistently outperforms strong baselines in structural quality and functional consistency. Furthermore, we validate its practical utility via a zero-shot gene-inhibitor design task, highlighting the potential of phenotype-driven generative discovery.

Ziyu Xu, Zijian Zhang, Liang Wang +4

NLPR, MAIS, Institute of Automation, Chinese Academy of Sciences, Beijing, China · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing, China · School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China +1

Drug Design Transcriptomics Cells Diffusion Dynamics Diffusion Models

May 12, 2026cs.CV

Improving Diffusion Posterior Samplers with Lagged Temporal Corrections for Image Restoration

Diffusion-based posterior sampling (PS) is a leading framework for imaging inverse problems, combining learned priors with measurement constraints. Yet, its standard formulations rely on instantaneous data-consistent estimates, which induce temporal variability in the reverse dynamics. We reinterpret PS from a dynamical perspective, showing that the standard PS update corresponds to a first-order discretization of the diffusion dynamics plus a residual correction capturing the mismatch between the denoised prediction and the data-consistent estimate. A second-order discretization, however, naturally introduces a temporal correction based on the variation of consecutive estimates. Building on this, we propose LAMP, combining the second-order update with the residual correction characterizing a PS technique. LAMP thus inherits a lagged temporal correction, and it can be implemented as a modular plug-in over the PS backbone. We show that LAMP preserves the structure of a posterior sampler, and we perform a one-step risk analysis to characterize when LAMP improves the reverse transition via a bias-variance trade-off. Experiments across multiple imaging tasks demonstrate consistent improvements over strong baselines such as DiffPIR and DDRM, without increasing the number of denoising evaluations.

Davide Evangelista, Elena Morotti, Francesco Pivi +1

Dept. of Computer Science and Engineering University of Bologna · Dept. of Political and Social Sciences University of Bologna

Posterior Sampling Diffusion Sampling Inverse Problem Image Restoration Diffusion Dynamics Time Discretization

May 12, 2026cs.CV

RealDiffusion: Physics-informed Attention for Multi-character Storybook Generation

While modern diffusion models excel at generating diverse single images, extending this to sequential generation reveals a fundamental challenge: balancing narrative dynamism with multi-character coherence. Existing methods often falter at this trade-off, leading to artifacts where characters lose their identity or the story stagnates. To resolve this critical tension, we introduce RealDiffusion, a unified framework designed to reconcile robust coherence with narrative dynamism. Heat diffusion serves as a dissipative prior that averages neighboring features along the sequence and removes high-frequency noise within the subject region. This suppresses attribute drift and stabilizes identity across frames. A region-aware stochastic process then introduces small perturbations that explore nearby modes and prevent collapse so the story maintains pose change and scene evolution. We thus introduce a lightweight, training-free Physics-informed Attention mechanism that injects controllable physical priors into the self-attention layers during inference. By modeling feature evolution as a configurable physical system, our method regularizes spatio-temporal relationships without suppressing intentional, prompt-driven changes. Extensive experiments demonstrate that RealDiffusion achieves substantial gains in character coherence while preserving narrative dynamism, outperforming state-of-the-art approaches. Code is available at https://github.com/ShmilyQi-CN/RealDiffusion.

Qi Zhao, Jun Chen, Ivor Tsang +1

Xi’an Jiaotong University, China · Zhejiang Normal University, China · SGIT AI Lab, State Grid Corporation of China +1

Narrative Generation Diffusion Dynamics Discourse Coherence Narratives Prior Knowledge Integration

May 12, 2026cs.RO

Coordinated Diffusion: Generating Multi-Agent Behavior Without Multi-Agent Demonstrations

Imitation learning powered by generative models has proven effective for modeling complex single-agent behaviors. However, teaching multi-agent systems, like multiple arms or vehicles, to coordinate through imitation learning is hindered by a fundamental data bottleneck: as the joint state-action space grows exponentially with the number of agents, collecting a sufficient amount of coordinated multi-agent demonstrations becomes extremely costly. In this work, we ask: how can we leverage single-agent demonstration data to learn multi-agent policies? We present Coordinated Diffusion (CoDi), a framework that couples independently trained single-agent diffusion policies through a user-defined multi-agent cost function, without requiring any coordinated demonstrations. We derive a new diffusion-based sampling scheme wherein the diffusion score function decomposes into independent, single-agent pre-trained base policies plus a cost-driven guidance term that coordinates these base policies into cohesive multi-agent behavior. We show that this guidance term can be estimated in a gradient-free manner, making CoDi applicable to black-box, non-differentiable cost functions without additional training. Theoretically and empirically, we analyze the conditions under which this composition can faithfully approximate a target multi-agent behavior. We find a complementary role for demonstration data versus the cost function: single-agent demonstrations must cover the support of the desired multi-agent behavior, while the cost function must promote desired behavior from this product of single-agent policies. Our results in simulation and hardware experiments of a two-arm manipulation task show that CoDi discovers robust coordinated behavior from single-agent data, is more data-efficient than multi-agent baselines, and highlights the importance of joint guidance, base policy support, and cost design.

Lasse Peters, Laura Ferranti, Andrea Bajcsy +1

University of California, Berkeley · Delft University of Technology · Carnegie Mellon University

Diffusion Policies Imitation Learning Diffusion Dynamics Agent Behavior Modeling

May 10, 2026q-bio.BM

TD3B: Transition-Directed Discrete Diffusion for Allosteric Binder Generation

Protein function is often controlled by ligands that bias the direction of state transitions, such as agonists and antagonists, rather than stabilizing a single conformation. This is especially important for clinically relevant G protein-coupled receptors (GPCRs), where therapeutic efficacy depends on functional directionality. Structure-based design methods optimize binding to static conformations and cannot represent non-reversible, directional effects or systematically distinguish agonist from antagonist behavior. To address this gap, we introduce Transition-Directed Discrete Diffusion for Allosteric Binder Design (TD3B), a sequence-based generative framework that designs binders with specified agonist or antagonist behavior via a directional transition control objective. TD3B combines a target-aware Direction Oracle, a soft binding-affinity gate, and amortized fine-tuning of a pre-trained discrete diffusion model, enabling targeted agonist and antagonist generation decoupled from binding affinity and unattainable by equilibrium-based or inference-only guidance baselines. The code and checkpoints are available at https://huggingface.co/ChatterjeeLab/TD3B.

Hanqun Cao, Aastha Pal, Sophia Tang +4

Department of Computer Science and Engineering, The Chinese University of Hong Kong · Department of Bioengineering, University of Pennsylvania · Department of Computer and Information Science, University of Pennsylvania +1

Diffusion Dynamics

May 10, 2026cs.AI

Primal-Dual Guided Decoding for Constrained Discrete Diffusion

Discrete diffusion models generate structured sequences by progressively unmasking tokens, but enforcing global property constraints during generation remains an open challenge. We propose primal-dual guided decoding, an inference-time method that formulates constrained generation as a KL-regularised optimisation problem and solves it online via adaptive Lagrangian multipliers. At each denoising step, the method modifies token logits through an additive, constraint-dependent bias, with multipliers updated by mirror descent based on constraint violation. The bias arises as the optimal KL-regularised projection of the constraint, so the constrained distribution remains as close as possible to the model's unconstrained distribution while still satisfying the constraint. The method requires no retraining and no additional model evaluations beyond standard sampling, supports multiple simultaneous constraints, and provides formal bounds on constraint violation. We evaluate our approach on topical text generation, molecular design, and music playlist generation, showing that a single algorithm instantiated via domain-specific scoring functions improves constraint satisfaction while preserving relevant domain-specific quality metrics.

Federico Tomasi, Dmitrii Moor, Alice Wang +1

Spotify

Diffusion Models Diffusion Dynamics Decoding Biases

May 6, 2026cs.CV

Computer-Aided Design Generation by Cascaded Discrete Diffusion Model

Recent deep learning approaches seek to automate CAD creation by representing a model as a sequence of discrete commands and parameters, and then generating them using autoregressive models or continuous diffusion operating in Euclidean embedding space. However, continuous diffusion perturbs representations in a continuous Euclidean domain that does not reflect the inherently discrete and heterogeneous nature of CAD tokens, often producing perturbed representations that map to semantically invalid symbols. To overcome this limitation, we propose a cascaded discrete diffusion framework for CAD generation, which consists of a command diffusion for generating CAD commands and a parameter diffusion conditioned on CAD commands. Unlike isotropic Gaussian perturbation, the forward process of our approach operates directly over categorical token distributions using delicate transition matrices. For commands, we adopt an absorbing-state transition matrix that progressively corrupts tokens to a designated symbol; for parameters, we introduce specific transition matrices tailored to heterogeneous attributes: a Gaussian kernel for coordinate continuity, a scale-invariant kernel for dimensional values, and a prior-preserving kernel for boolean attributes. The reverse process is achieved by two denoising networks: a Transformer-based encoder for command recovery, and a parameter network with extra local self-attention for command-level interaction and cross-attention for conditional injection. Experiments on the DeepCAD dataset show that the proposed approach surpasses existing autoregressive and continuous diffusion models on unconditional generation metrics, while qualitative results validate effective controllability in conditional generation tasks. Source codes will be released.

Honghu Pan, Xiaoling Luo, Yongyong Chen +2

School of Artificial Intelligence and Robotics, Hunan University · College of Computer Science and Software Engineer, Shenzhen University · School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen +1

Diffusion Models Diffusion Dynamics Single-Token Output Distributions Deep Learning

May 6, 2026cs.CV

Structured 3D Latents Are Surprisingly Powerful: Unleashing Generalizable Style with 2D Diffusion

3D asset generation plays a pivotal role in fields such as gaming and virtual reality, enabling the rapid synthesis of high-fidelity 3D objects from a single or multiple images. Building on this capability, enabling style-controllable generation naturally emerges as an important and desirable direction. However, existing approaches typically rely on style images that lie within or are similar to the training distribution of 3D generation models. When presented with out-of-distribution (OOD) styles, their performance degrades significantly or even fails. To address this limitation, we introduce \textbf{DiLAST}: 2D Diffusion-based Latent Awakening for 3D Style Transfer. Specifically, we leverage a pretrained 2D diffusion model as a teacher to provide rich and generalizable style priors. By aligning rendered views with the target style under diffusion-based guidance, our method optimizes the structured 3D latent representations for stylization. We observe that this limitation stems not from insufficient model capacity, but from the underutilization of structured 3D latents, which are inherently expressive. Despite being trained on comparatively limited data, 3D generation models can leverage 2D diffusion guidance to steer denoising toward specific directions in latent space, thereby producing diverse, OOD styles. Extensive experiments across diverse data and multiple 3D generation backbones demonstrate the effectiveness and plug-and-play nature of our approach.

Yiran Qiao, Yiren Lu, Yunlai Zhou +5

Case Western Reserve University

High-Fidelity 3D Generation Photorealistic Style Transfer Style Diffusion Dynamics

May 5, 2026cs.CV

GeoTopoDiff: Learning Geometry--Topology Graph Priors through Boundary-Constrained Mixed Diffusion for Sparse-Slice 3D Porous Reconstruction

Diffusion-based voxel prior modelling is challenging for the reconstruction of large-scale 3D porous microstructures. Due to the demanding requirements for simultaneously modelling both the continuous pore morphology and the discrete pore-throat topology, the diffusion models require fully observed CT scans to provide topology-faithful priors, which results in an inherent trade-off among throughput, topological fidelity, and field of view in practical industrial applications. We propose GeoTopoDiff, a graph diffusion-based framework for reconstructing 3D porous microstructures from sparse CT slices. GeoTopoDiff transfers the learning of diffusion priors from a voxel-based space to a mixed graph state space, which simultaneously encompasses continuous pore geometry and discrete pore-throat topology. A topology-aware partial graph prior from sparsely observed CT slices is introduced to constrain the reverse denoising process. Experiments on anisotropic PTFE and Fontainebleau sandstone show that GeoTopoDiff reduces morphology-related errors by 19.8% and topology-sensitive transport errors by 36.5% on average. Our findings suggest that the mixed graph state space promotes the diffusion denoising process to reduce posterior uncertainty under a sparse observations. All models and code have been made publicly available to facilitate the exploration of diffusion models in the field of 3D porous microstructures simulation.

Yue Shi, Peng Wang, Mingzhe Yu +5

Manchester Metropolitan University, Manchester M1 5GD, U.K. · University of Surrey, Surrey, GU2 7XH, U.K. · Johnson Matthey Billingham, TS23 1LB, U.K. +1

Diffusion Priors Porous Media Geometric Reconstruction Diffusion Dynamics Cone-Beam Computed Tomography 3D Reconstruction+2

May 4, 2026physics.med-ph

TRACED: In vivo imaging of extracellular intrinsic diffusivity, tortuosity, cell size distribution and cell density in human glioma patients

The lack of analytical models describing diffusion time dependence at intermediate time scales in complex tissue microstructure limits the accurate quantification of extracellular diffusivity and tissue microstructure. We introduce TRACED, a biophysical model that incorporates diffusion time dependence in cell distributions to quantify pathologically-relevant properties in solid tumors. Neural networks were trained on Monte Carlo diffusion simulations using sphere distribution-based geometries to enable the rapid computation of time-dependent diffusion MRI signals in cell populations of variable cell size. Model sensitivity and fit performance were assessed via simulation. Diffusion data from eight mixed-grade glioma patients was fitted using the TRACED model. Data fitting was performed using a novel physics-informed transfer learning pipeline, Sim2PINN. In two patients, cell size measurements were compared directly with image-localized histology. Simulation results indicate improved parameter estimation compared to the simple two-compartment model. TRACED enabled the simultaneous in vivo quantification of intracellular volume fraction, cell size distribution, extracellular intrinsic diffusivity, and tortuosity in glioma patients. Neural network implementations of diffusion time-dependence and tortuosity showed behavior consistent with coarse-graining and effective medium theory, respectively. Future work will explore the clinical utility of TRACED parameters in additional patients.

Joshua K. Marchant, Hong-Hsi Lee, Elizabeth R. Gerstner +2

Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Boston, United States of America · Harvard-MIT Program in Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, United States of America · Harvard Medical School, Boston, United States of America +2

Glioma Diffusion Dynamics Porous Media

May 3, 2026cs.IT

Optimization of CV-QKD Under Practical Constraints

Using reinforcement learning, we optimize for practical hardware constraints, including limited FIR filter taps at the transmitter and receiver, mean photon number and finite DAC/ADC resolution. Under these realistic conditions, the proposed approach achieves significant performance improvements.

Svitlana Matsenko, Amirhossein Ghazisaeidi, Marcin Jarzyna +2

DTU Electro, Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark · Nokia Bell Labs, 91300 Massy, France · Centre for Quantum Optical Technologies, CeNT, University of Warsaw, 02-097 Warszawa, Poland +1

Source-Channel Coding Single-Photon Avalanche Diode Diffusion Dynamics

May 3, 2026cs.CV

Disentangled Anatomy-Disease Diffusion (DADD) for Controllable Ulcerative Colitis Progression Synthesis

Synthesizing longitudinal medical images at controllable disease stages while preserving patient-specific anatomy is hindered by the entanglement of pathological textures and structural features. We address this challenge for ulcerative colitis (UC) endoscopy, where severity follows a continuous ordinal progression along the Mayo Endoscopic Score (MES). Our framework, Disentangled Anatomy-Disease Diffusion (DADD), conditions a latent diffusion model on two complementary embeddings: a pretrained image encoder for patient anatomy and a separately trained ordinal embedder for cumulative disease severity. Since image embeddings inevitably capture disease information, we introduce a Feature Purifier, a cross-attention-based erasure mechanism that identifies and suppresses disease-correlated channels, yielding purified anatomical representations. These cleaned anatomy tokens and target disease tokens are injected into the denoising network via a Triple-Pathway Cross-Attention mechanism with resolution-dependent routing gates. This architecture leverages the U-Net hierarchy, in which different network depths encode global structure versus fine-grained pathological texture. Furthermore, we introduce Delta Steering, a training-free directional signal derived from the ordinal embeddings that enables explicit, single-pass control over disease transitions at inference without requiring additional forward passes. Validated on the LIMUC dataset, our approach produces high-fidelity images across all severity levels and effectively rebalances skewed class distributions, enhancing performance for downstream classification tasks. The dataset is available at zenodo.org/records/5827695 and the code base at github.com/umutdundar99/progressive-stable-diffusion

Umut Dundar, Alptekin Temizel

Graduate School of Informatics Middle East Technical University, Turkey

Longitudinal Imaging U-Net Diffusion Dynamics Synthesis Embedder

Apr 29, 2026cs.LG

Language Diffusion Models are Associative Memories Capable of Retrieving Unseen Data

When do language diffusion models memorize their training data, and how to quantitatively assess their true generative regime? We address these questions by showing that Uniform-based Discrete Diffusion Models (UDDMs) fundamentally behave as Associative Memories (AMs)

\textit{with emergent creative capabilities}

. The core idea of an AM is to reliably recover stored data points as

\textit{memories}

by establishing distinct basins of attraction around them. Historically, models like Hopfield networks use an explicit energy function to guarantee these stable attractors. We broaden this perspective by leveraging the observation that energy is not strictly necessary, as basins of attraction can also be formed via conditional likelihood maximization. By evaluating token recovery of

\textit{training}

and

\textit{test}

examples, we identify in UDDMs a sharp memorization-to-generalization transition governed by the size of the training dataset: as it increases, basins around training examples shrink and basins around unseen test examples expand, until both later converge to the same level. Crucially, we can detect this transition using only the conditional entropy of predicted token sequences: memorization is characterized by vanishing conditional entropy, while in the generalization regime the conditional entropy of most tokens remains finite. Thus, conditional entropy offers a practical probe for the memorization-to-generalization transition in deployed models.

Bao Pham, Mohammed J. Zaki, Luca Ambrogioni +2

1Rensselaer Polytechnic Institute (RPI) · 2Donders Institute for Brain, Cognition, and Behaviour, Radboud University · 3Dynamical Mind +1

Diffusion Language Models Memorization Diffusion Dynamics Entropy

Apr 28, 2026cs.RO

FlowS: One-Step Motion Prediction via Local Transport Conditioning

Generative motion prediction must satisfy three simultaneous requirements for real-world autonomy: high accuracy, diverse multimodal futures, and strictly bounded latency. Diffusion models meet the first two but violate the third, requiring tens to hundreds of denoising steps. We identify a conditioning strategy that resolves this tension: \textit{single-step integration is accurate when the underlying transport problem is local}. A model that must both discover the correct behavioral mode and traverse a long displacement in one step accumulates large discretization errors; conditioning the base distribution to lie near plausible futures reduces the problem to short-range refinement, the regime where a single Euler step suffices. We instantiate this \emph{local transport conditioning} in FlowS, a conditional flow matching framework with two mechanisms. First, an online, scene-conditioned learned prior emits

K

calibrated anchor trajectories per agent, each already near a plausible future, converting mode discovery into local correction. Second, a step-consistent displacement field enforces semigroup self-consistency, guaranteeing that a single step inherits multi-step accuracy. Crucially, anchoring this field at learned priors along straight-line paths yields a {stable, low-variance} training target, unlike prior self-consistency methods that suffer from {high-variance bootstrap} signals on curved diffusion paths. On the Waymo Open Motion Dataset, FlowS achieves state-of-the-art Soft mAP {(0.4804) and mAP (0.4703) with ensemble at 75,FPS} with single-step inference, demonstrating that local transport conditioning makes one-step generative motion prediction practical for safety-critical autonomy. Code and pretrained models will be released upon acceptance.

Leandro Di Bella, Adrian Munteanu, Bruno Cornelis

Department of Electronics and Informatics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium · IMEC, Kapeldreef 75, B-3001 Leuven, Belgium

Human Motion Prediction Stable Transport Motion Diffusion Dynamics

Apr 27, 2026cs.CV

DiffuSAM: Diffusion-Based Prompt-Free SAM2 for Few-Shot and Source-Free Medical Image Segmentation

Segmentation models such as Segment Anything Model (SAM) and SAM2 achieve strong prompt-driven zero-shot performance. However, their training on natural images limits domain transfer to medical data. Consequently, accurate segmentation typically requires extensive fine-tuning and expert-designed prompts. We propose DiffuSAM, a diffusion-based adaptation of SAM2 for prompt-free medical image segmentation. Our framework synthesizes SAM2-compatible segmentation mask-like embeddings via a lightweight diffusion-prior from off-the-shelf frozen SAM2 image features. The generated embeddings are integrated into SAM2's mask decoder to produce accurate segmentations, thereby eliminating the need for user prompts. The diffusion prior is further conditioned on previously segmented slices, enforcing spatial consistency across volumes. Evaluated on the BTCV and CHAOS datasets for CT and MRI under Source-Free Unsupervised Domain Adaptation (SF-UDA) and Few-Shot settings, DiffuSAM achieves competitive performance with efficient training and inference. Code is available upon request from the corresponding author.

Tal Grossman, Noa Cahan, Lev Ayzenberg +1

School of Electrical Engineering, Tel Aviv University, Israel · School of Biomedical Engineering, Tel Aviv University, Israel

Semi-Supervised Medical Image Segmentation Magnetic Resonance Imaging Diffusion Dynamics

Apr 27, 2026stat.ML

Conditional Score-Based Modeling of Effective Langevin Dynamics

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time trajectory increments, state-space partitioning, or repeated simulation of candidate models, which become unreliable or computationally expensive for high-dimensional systems, coarse temporal sampling, or unevenly sampled data. We introduce a data-driven calibration method based on a novel relationship between the coefficients of a stochastic reduced model and the conditional score of the finite-time transition density, defined as the gradient of the logarithm of the transition density with respect to the initial state. The resulting identity expresses derivatives of lagged correlation functions as stationary expectations over observed lagged pairs involving this conditional score and the unknown model coefficients. This formulation allows the drift and diffusion structure to be constrained directly from finite-lag statistics, without differentiating trajectories, partitioning state space, or repeatedly integrating candidate reduced models during calibration, yielding a least-squares fitting problem over stationary lagged pairs. We validate the approach on three systems of increasing complexity: an analytically tractable Cox--Ingersoll--Ross diffusion, a two-dimensional nonequilibrium diffusion with affine multiplicative noise, and a periodic soft-spin stochastic Landau--Lifshitz chain. Across these tests, the inferred models preserve the invariant statistics while reproducing finite-lag dynamical correlations. The framework provides a scalable route for learning stochastic reduced-order models from data that reproduce prescribed statistical and dynamical properties.

Ludovico T. Giorgini

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Langevin Dynamics Reduced-Order Models Latent Dynamics Spatial Photonic Ising Machines Diffusion Dynamics

Apr 26, 2026cs.LG

Symmetric Equilibrium Propagation for Thermodynamic Diffusion Training

The reverse process in score-based diffusion models is formally equivalent to overdamped Langevin dynamics in a time-dependent energy landscape. In our prior work we showed that a bilinearly-coupled analog substrate can physically realize this dynamics at a projected three-to-four orders of magnitude energy advantage over digital inference by replacing dense skip connections with low-rank inter-module couplings. Whether the \emph{training} loop can be closed on the same substrate -- without routing gradients through an external digital accelerator -- has remained open. We resolve this affirmatively: Equilibrium Propagation applied directly to the bilinear energy yields an unbiased estimator of the denoising score-matching gradient in the zero-nudge limit. For finite nudging we derive a sharp bias bound controlled solely by substrate stiffness, local curvature, and the norm of the loss-gradient signal, with a bilinear-specific corollary showing that one dominant bias term vanishes identically for coupling-parameter updates. Symmetric nudging further upgrades the leading bias from

\mathcal{O}(β)

to

\mathcal{O}(β^2)

at negligible extra cost. Under realistic finite-relaxation budgets this upgrade is essential, as one-sided EqProp produces anti-correlated gradients while symmetric EqProp yields well-aligned updates. Bias-variance analysis determines the optimal operating point, and end-to-end physical-unit accounting projects a

10^3

-

10^4\times

energy advantage per training step over a matched GPU baseline. Symmetric bilinear EqProp is the first local, readout-only training rule that preserves the low-rank coupling enabling scalable thermodynamic diffusion models.

Aditi De

Diffusion Dynamics Langevin Dynamics Energy Resources

Apr 23, 2026cs.CV

Pre-process for segmentation task with nonlinear diffusion filters

This paper deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. We first show an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, we propose a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. We also prove that our filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edge-preserving process. Under the conditions established for the diffusivity and using a stopping criterion for the diffusion time, we get piecewise constant images with a low computational effort. Finally, we test our filter with real images and we illustrate the effects of our diffusivity function as a method to get piecewise constant images. The code is available at https://github.com/cplatero/NonlinearDiffusion.

Javier Sanguino, Carlos Platero, Olga Velasco

Health Science Technology Group, Technical University of Madrid, Ronda de Valencia 3, 28012, Madrid, Spain.

Diffusion-Based Image Editing Diffusion Dynamics

Apr 22, 2026cs.CV

LLaDA2.0-Uni: Unifying Multimodal Understanding and Generation with Diffusion Large Language Model

We present LLaDA2.0-Uni, a unified discrete diffusion large language model (dLLM) that supports multimodal understanding and generation within a natively integrated framework. Its architecture combines a fully semantic discrete tokenizer, a MoE-based dLLM backbone, and a diffusion decoder. By discretizing continuous visual inputs via SigLIP-VQ, the model enables block-level masked diffusion for both text and vision inputs within the backbone, while the decoder reconstructs visual tokens into high-fidelity images. Inference efficiency is enhanced beyond parallel decoding through prefix-aware optimizations in the backbone and few-step distillation in the decoder. Supported by carefully curated large-scale data and a tailored multi-stage training pipeline, LLaDA2.0-Uni matches specialized VLMs in multimodal understanding while delivering strong performance in image generation and editing. Its native support for interleaved generation and reasoning establishes a promising and scalable paradigm for next-generation unified foundation models. Codes and models are available at https://github.com/inclusionAI/LLaDA2.0-Uni.

Inclusion AI, Tiwei Bie, Haoxing Chen +15

AGI Research Center, Inclusion AI

Diffusion Language Models Multimodal Understanding Large Language Model Backbones Diffusion Dynamics

Apr 22, 2026cs.LG

Structure-Aware Variational Learning of a Class of Generalized Diffusions

Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct regression of governing equations or velocity fields, which can be sensitive to noise and external perturbations and may fail when observations are incomplete. In this work, we propose a structure-aware, energy-based learning framework for inferring unknown potential functions in generalized diffusion processes, grounded in the energetic variational approach. Starting from the energy-dissipation law associated with the Fokker-Planck equation, we construct loss functions based on the De Giorgi dissipation functional, which consistently couple the free energy and the dissipation mechanism of the system. This formulation avoids explicit enforcement of the governing partial differential equation and preserves the underlying variational structure of the dynamics. Through numerical experiments in one, two, and three dimensions, we demonstrate that the proposed energy-based loss exhibits enhanced robustness with respect to observation time, noise level, and the diversity and amount of available training data. These results highlight the effectiveness of energy-dissipation principles as a reliable foundation for learning stochastic diffusion dynamics from data.

Yubin Lu, Xiaofan Li, Chun Liu +2

School of Mathematics, South China University of Technology, Guangzhou 510640, China. · Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616 United States · School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332 United States +1

Variational Fokker--Planck Equation Diffusion Dynamics Stochastic Gradient Descent Structure-Aware

Apr 20, 2026cs.CV

DiffuSAM: Diffusion Guided Zero-Shot Object Grounding for Remote Sensing Imagery

Diffusion models have emerged as powerful tools for a wide range of vision tasks, including text-guided image generation and editing. In this work, we explore their potential for object grounding in remote sensing imagery. We propose a hybrid pipeline that integrates diffusion-based localization cues with state-of-the-art segmentation models such as RemoteSAM and SAM3 to obtain more accurate bounding boxes. By leveraging the complementary strengths of generative diffusion models and foundational segmentation models, our approach enables robust and adaptive object localization across complex scenes. Experiments demonstrate that our pipeline significantly improves localization performance, achieving over a 14% increase in Acc@0.5 compared to existing state-of-the-art methods.

Geet Sethi, Panav Shah, Ashutosh Gandhe +1

Indian Institute of Technology Bombay

Remote Sensing Image Segmentation Object Localization Diffusion Models Objects Diffusion Dynamics

Apr 20, 2026cs.CV

AnyLift: Scaling Motion Reconstruction from Internet Videos via 2D Diffusion

Reconstructing 3D human motion and human-object interactions (HOI) from Internet videos is a fundamental step toward building large-scale datasets of human behavior. Existing methods struggle to recover globally consistent 3D motion under dynamic cameras, especially for motion types underrepresented in current motion-capture datasets, and face additional difficulty recovering coherent human-object interactions in 3D. We introduce a two-stage framework leveraging 2D diffusion that reconstructs 3D human motion and HOI from Internet videos. In the first stage, we synthesize multi-view 2D motion data for each domain, leveraging 2D keypoints extracted from Internet videos to incorporate human motions that rarely appear in existing MoCap datasets. In the second stage, a camera-conditioned multi-view 2D motion diffusion model is trained on the domain-specific synthetic data to recover 3D human motion and 3D HOI in the world space. We demonstrate the effectiveness of our method on Internet videos featuring challenging motions such as gymnastics, as well as in-the-wild HOI videos, and show that it outperforms prior work in producing realistic human motion and human-object interaction.

Hongjie Li, Heng Yu, Jiaman Li +4

Stanford University · H. Li is now with Peking University

Training-Set Long-Tail Motions Articulated Objects Structure-From-Motion In-The-Wild Videos Motion Long Videos+1

Apr 18, 2026stat.ML

Extraction of informative statistical features in the problem of forecasting time series generated by It{ô}-type processes

In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{ô} stochastic differential equations with unknown random drift and diffusion coefficients. We do not attract any additional information and use only the information contained in the time series as it is. Therefore, as additional features, we use the parameters of statistically adjusted mixture-type models of the observed regularities of the behavior of the time series. Several algorithms of construction of these parameters are discussed. These algorithms are based on statistical reconstruction of the coefficients which, in turn, is based on statistical separation of normal mixtures. We obtain two types of parameters by the techniques of the uniform and non-uniform statistical reconstruction of the coefficients of the underlying It{ô} process. The reconstructed coefficients obtained by uniform techniques do not depend on the current value of the process, while the non-uniform techniques reconstruct the coefficients with the account of their dependence on the value of the process. Actually, the non-uniform techniques used in this paper represent a stochastic analog of the Taylor expansion for the time series. The efficiency of the obtained additional features is compared by using them in the autoregressive algorithms of prediction of time series. In order to obtain pure conclusion that is not affected by unwanted factors, say, related to a special choice of the architecture of the neural network prediction methods, we used only simple autoregressive algorithms. We show that the use of additional statistical features improves the prediction.

Victor Korolev, Mikhail Ivanov, Tatiana Kukanova +4

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics · Moscow Center for Fundamental and Applied Mathematics · Federal Research Center “Computer Science and Control”, Russian Academy of Sciences +2

Time Series Forecasting Stochastic Differential Equations Time Series Autoregressive Model Mixture Models Diffusion Dynamics+1

Apr 3, 2026cs.LG

Understanding Latent Diffusability via Fisher Geometry

Diffusion models often degrade in latent spaces, yet the formal causes remain poorly understood. We quantify latent-space diffusability via the rate of change of the Minimum Mean Squared Error (MMSE) along the diffusion trajectory. Our framework decomposes this MMSE rate into contributions from Fisher Information (FI) and Fisher Information Rate (FIR). We show that isometric embeddings preserve intrinsic FI and establish quantitative intrinsic-FI bounds for a broader class of bi-Lipschitz encoders with controlled weak volume distortion, whereas FIR is governed by the interplay between encoder and data geometries. Our analysis separates four geometric contributions in local stability bounds for Gaussian-smoothed FIR: dimensional compression, tangential distortion, high-frequency encoder curvature, and curvature of data manifold. Experiments across diverse autoencoding architectures provide qualitative support for the geometric mechanisms identified by the theory and show that empirical FI and FIR track several measures of generation quality and latent-space geometry in the settings tested. We establish FI and FIR as a comprehensive analytical framework for understanding latent diffusability.

Jing Gu, Morteza Mardani, Wonjun Lee +2

School of Mathematics, University of Minnesota · NVIDIA · Department of Mathematics, The Ohio State University +1

Discriminative Congruence Transform Diffusion Dynamics Fisher Information Matrix

Mar 28, 2026math.OC

Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control

Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing a control under SDE constraints. In this work, we revisit and generalize Adjoint Matching, a recently proposed SOC-based method for learning optimal controls, and place it on a rigorous footing by deriving it from the Stochastic Maximum Principle (SMP). We formulate a general Hamiltonian adjoint matching objective for SOC problems with control-dependent drift and diffusion and convex running costs, and show that its expected value has the same first variation as the original SOC objective. As a consequence, critical points satisfy the Hamilton--Jacobi--Bellman (HJB) stationarity conditions. In the important practical case of state- and control-independent diffusion, we recover the lean adjoint matching loss previously introduced, which avoids second-order terms and whose critical points coincide with the optimal control under mild uniqueness assumptions. Numerical experiments confirm that the extra terms it discards become necessary once the diffusion is state-dependent. Finally, we show that adjoint matching can be precisely interpreted as a continuous-time method of successive approximations induced by the SMP, yielding a practical and implementable alternative to classical SMP-based algorithms, which are obstructed by intractable martingale terms in the stochastic setting. These results are also of independent interest to the stochastic control community, providing new implementable objectives and a viable pathway for SMP-based iterations in stochastic problems.

Carles Domingo-Enrich, Jiequn Han

Microsoft Research New England · Flatiron Institute

Adjoint Matching Stochastic Optimal Control Optimal Control Stochastic Optimization Stochastic Differential Equations Conditional Flow Matching+2

Feb 16, 2026cs.LG

Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees

Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a continuous-time Markov chain (CTMC) formulation, with a focus on

τ

-leaping-based samplers. We establish sharp convergence guarantees for attaining

\varepsilon

accuracy in Kullback-Leibler (KL) divergence for both uniform and masking noising processes. For uniform discrete diffusion, we show that the

τ

-leaping algorithm achieves an iteration complexity of order

\tilde O(d/\varepsilon)

, with

d

the ambient dimension of the target distribution, eliminating linear dependence on the vocabulary size

S

and improving existing bounds by a factor of

d

; moreover, we establish a matching algorithmic lower bound showing that linear dependence on the ambient dimension is unavoidable in general. For masking discrete diffusion, we introduce a modified

τ

-leaping sampler whose convergence rate is governed by an intrinsic information-theoretic quantity, termed the effective total correlation, which is bounded by

d \log S

but can be sublinear or even constant for structured data. As a consequence, the sampler provably adapts to low-dimensional structure without prior knowledge or algorithmic modification, yielding sublinear convergence rates for various practical examples (such as hidden Markov models, image data, and random graphs). Our analysis requires no boundedness or smoothness assumptions on the score estimator beyond control of the score entropy loss.

Daniil Dmitriev, Zhihan Huang, Yuting Wei

Department of Statistics and Data Science, the Wharton School, University of Pennsylvania

Score-Based Diffusion Model Diffusion Dynamics Diffusion Models Markov

Jan 21, 2026cs.RO

TIDAL: Temporally Interleaved Diffusion and Action Loop for High-Frequency VLA Control

Large-scale Vision-Language-Action (VLA) models offer semantic generalization but suffer from high inference latency because they adopt a low-frequency batch-and-execute paradigm. This frequency mismatch creates an execution blind spot, causing failures in dynamic environments where targets move during the open-loop execution window. We propose TIDAL (Temporally Interleaved Diffusion and Action Loop), a hierarchical framework that decouples semantic reasoning from high-frequency actuation. TIDAL operates as a backbone-agnostic scheduler for diffusion-based VLAs, using a dual-frequency architecture to redistribute the computational budget. Specifically, a low-frequency macro-intent loop caches semantic embeddings, while a high-frequency micro-control loop interleaves single-step flow integration with execution, conditioning on the latest state fused with motion cues. To handle the resulting latency shift, we introduce a temporally misaligned training strategy where the policy learns stalenessaware compensation, conditioning on stale semantic intent alongside real-time proprioception. TIDAL is architectural, making it orthogonal to system-level optimizations. Experiments show an average 2.5x performance gain over open-loop baselines in dynamic interception tasks. Despite a slight decrease in static success rates, our approach yields a 4x increase in feedback frequency and extends the effective horizon of semantic embeddings beyond the native action chunk size. Under nonpaused physics and on a real robot, TIDAL remains robust to unmodeled dynamics, while standard open-loop baselines fail due to latency-induced error accumulation.

Yuteng Sun, Haoran Wang, Ruofei Bai +4

Institute for Infocomm Research (I2R), A*STAR, Singapore · 2Tsinghua University, Beijing, China · 3Nanyang Technological University, Singapore

Diffusion-Based Vision-Language-Actions Inference Latency Diffusion Policies Human Motion Prediction Diffusion Dynamics

Jan 5, 2026cs.LG

Prior Diffusiveness and Regret in the Linear-Gaussian Bandit

We prove that Thompson sampling exhibits

\tilde{O}(σd \sqrt{T} + d r \sqrt{\mathrm{Tr}(Σ_0)})

Bayesian regret in the linear-Gaussian bandit with a

\mathcal{N}(μ_0, Σ_0)

prior distribution on the coefficients, where

d

is the dimension,

T

is the time horizon,

r

is the maximum

\ell_2

norm of the actions, and

σ^2

is the noise variance. In contrast to existing regret bounds, this shows that to within logarithmic factors, the prior-dependent

burn-in'' term $d r \sqrt{\mathrm{Tr}(Σ_0)}$ decouples additively from the minimax (long run) regret $σd \sqrt{T}$. Previous regret bounds exhibit a multiplicative dependence on these terms. We establish these results via a new

elliptical potential'' lemma, and also provide a lower bound indicating that the burn-in term is unavoidable.

Yifan Zhu, John C. Duchi, Benjamin Van Roy

Department of Electrical Engineering, Stanford University, California, United States.

Thompson Sampling Regret Prior Knowledge Integration Diffusion Dynamics

Dec 30, 2025math.ST

Fast Score-Based Sampling via Log-Concave Reductions

Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities. It depends on availability of (approximate) Stein score functions for various levels of additive noise. We show how in some generality, the availability of scores allows the general problem to be ``reduced'' to sampling from an adaptively constructed sequence of

K

strongly log-concave (SLC) sub-problems. The reduction is simple, constructive and algorithm-independent, so that any SLC sampler can be used as a subroutine. Various bounds on score-based sampling complexity follow directly: for instance, high-accuracy SLC samplers yield

\tilde{\mathcal{O}}(K \sqrt{d} \operatorname{polylog}(1/\varepsilon))

guarantees for accuracy

\varepsilon

in dimension

d

, where randomized midpoint SLC schemes yield

\tilde{\mathcal{O}}(K d^{1/3} \operatorname{poly}(1/\varepsilon))

guarantees. When the original distribution itself is SLC, we prove that

K \leq 1 + \log_2(κ)

, thereby obtaining the first efficient procedure with logarithmic dependence on condition number

κ

; for general distributions, the quantity

K

depends on the geometry of score Hessian across the trajectory. Our analysis is direct and simple, involving techniques and insights complementary to those in standard analyses of discretized diffusions.

M. J. Wainwright

Laboratory for Information and Decision Systems · Statistics and Data Science Center · EECS & Mathematics +1

Log-Concave Distributions Optimal Sample Complexity Score-Based Diffusion Model Uncertainty Score Diffusion Dynamics

Dec 22, 2025physics.comp-ph

Adaptive Probability Flow Residual Minimization for High-Dimensional Fokker-Planck Equations

Solving high-dimensional Fokker-Planck (FP) equations remains a challenging problem in computational physics and stochastic dynamics, due to the curse of dimensionality, unbounded domains, and complex probability landscapes. In this work, we propose an adaptive probability flow residual minimization (A-PFRM) method for this problem. The second-order FP equation is reformulated as an equivalent first-order continuity equation associated with the probability flow ordinary differential equation, based on which a loss function is constructed to train neural network approximations without Hessian computation. To further improve the computational efficiency, the Hutchinson trace estimator is applied to compute the divergence in the corresponding score function, such that the training time can be dimension-independent on GPUs. Adaptive sampling strategies are employed to generate the collocation points, and our analysis shows that the Kullback-Leibler divergence between our A-PFRM approximation and the exact solution is bounded by the residual loss weighted by the estimated density function. Numerical experiments are presented to demonstrate the performance of A-PFRM, which include Ornstein-Uhlenbeck (OU) processes problems, Brownian motions with time-varying diffusion, and Geometric OU processes featuring non-Gaussian solutions up to one hundred dimensions.

Xiaolong Wu, Qifeng Liao

School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China

Fokker--Planck Equation Hessian Diffusion Dynamics

Dec 9, 2025cs.CV

GimbalDiffusion: Gravity-Aware Camera Control for Video Generation

Recent progress in text-to-video generation has achieved remarkable realism, yet fine-grained control over camera motion and orientation remains elusive, especially with extreme trajectories (e.g., a 180-degree turnaround, or looking directly up or down). Existing approaches typically encode camera trajectories using relative or ambiguous representations, limiting precise geometric control and offering limited support for large rotations. We introduce GimbalDiffusion, a framework that enables camera control grounded in physical-world coordinates, using gravity as a global reference. Instead of describing motion relative to previous frames, our method defines camera trajectories in an absolute coordinate system, allowing accurate, interpretable control over camera parameters. Using panoramic 360-degree videos for training, we cover the full sphere of possible viewpoints, including combinations of extreme pitch and roll that are out-of-distribution of conventional video data. To improve camera control, we introduce null-pitch conditioning, a strategy that prevents the model from overriding camera specifications in the presence of conflicting prompt content (e.g., generating grass while the camera points toward the sky). Finally, we propose new benchmarks to evaluate gravity-aware camera-controlled video generation, assessing models' ability to generate extreme camera angles and quantify their input prompt entanglement.

Frédéric Fortier-Chouinard, Yannick Hold-Geoffroy, Valentin Deschaintre +2

Université Laval, Québec, Canada · Adobe, San Jose, USA

Camera Control Camera Trajectories Video Generation Human Motion Generation Diffusion Dynamics

Oct 20, 2025cs.LG

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 Models Diffusion Dynamics Forgetting Frequency

Jun 29, 2025cs.LG

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

Probabilistic Forecasting Diffusion Dynamics Denoising Diffusion Probabilistic Model Uncertainty

Jun 25, 2025cs.LG

Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models

We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling complex multiscale dynamical systems without a clear scale separation, for which numerically resolving all scales is prohibitively expensive, e.g., for engineering turbulent flows. While classical closure modeling methods leverage domain knowledge to approximate subgrid-scale phenomena, their deterministic and local assumptions can be too restrictive in regimes lacking a clear scale separation. Recent developments of diffusion-based stochastic models have shown promise in the context of closure modeling, but their prohibitive computational inference cost limits practical applications in many real-world settings. This work addresses this limitation by jointly training convolutional autoencoders with conditional diffusion models in latent space, significantly reducing the dimensionality of the sampling process while preserving essential physical characteristics. Numerical results demonstrate that the joint training approach helps discover a proper latent space that not only guarantees small reconstruction errors but also ensures good performance of the diffusion model in the latent space. When integrated into numerical simulations, the proposed stochastic modeling framework via latent conditional diffusion models achieves significant computational acceleration while maintaining comparable predictive accuracy to standard diffusion models in physical space.

Xinghao Dong, Huchen Yang, Jin-Long Wu

Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA

Multiscale Dynamics Latent Dynamics Diffusion Dynamics Nonlinear Dynamics Latent Space Stochastic+1

May 29, 2025math.NA

A Jump-Diffusion Framework for Irregular Time Series Generation

We propose a framework for generative modeling of continuous-time processes from irregularly and asynchronously recorded data. It is based on the matching of generators and accommodates discontinuous trajectories. Analytical formulas for diffusion and jump bridges yield a family of reference generators that a neural network is trained to match. The key ingredient is that, for our constructed jump bridge, a parametrization of the jump kernel densities by scaled Gaussians admits closed-form expressions for the Kullback-Leibler divergence, allowing simulation-free training.

O. Pfohl, J. Chemseddine, P. Hagemann +3

Department of Mathematics, Humboldt-Universität zu Berlin, 12489, Berlin, Germany · Department of Mathematics, Technische Universität Berlin, 10623, Berlin, Germany · Bundesanstalt für Materialforschung und -prüfung, 12205, Berlin, Germany +1

Time-Series Generation Stochastic Processes Generative Models Diffusion Dynamics Kullback-Leibler Divergence

May 24, 2025cs.CV

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 Models Diffusion Dynamics Repair-Assignment Problem Improvement

Sep 28, 2022stat.ML

Spectral Diffusion Processes

Diffusion models have proven to be a flexible and effective framework for modelling probability distributions on finite-dimensional spaces. However, many physical modelling problems such as time series are naturally described over function spaces. In this work we apply diffusion models to such stochastic processes. To do so we consider a spectral representation of the data, obtained using a kernel, thereby dissociating the stochastic part of the processes from their space-time structure. As a result, the stochasticity of the processes is entirely encoded in the spectral coefficients, which we truncate and model using standard finite-dimensional diffusion models. By truncating the representation in the spectral domain we ensure our resulting model defines valid stochastic processes, thereby naturally satisfying consistency and exchangeability criteria. Projecting our spectral diffusion models back to the original input space, we show that for any given marginals our approach corresponds to a diffusion model with correlated noise, with explicit covariance matrix given by the kernel. We demonstrate our method's effectiveness for modelling various multimodal datasets as well as conditional sampling by amortising our models with respect to a context set.

Angus Phillips, Thomas Seror, Michael Hutchinson +3

Dept. of Statistics, University of Oxford, Oxford, UK. · Dept. of Computer Science ENS, CNRS, PSL University Paris, France. · Dept. of Engineering, University of Cambridge, Cambridge, UK.

Stochastic Processes Diffusion Dynamics Diffusion Models Covariance