We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems. We learn the joint distribution of PDE parameters and solutions via a diffusion process in a latent space of scaled spectral representations, where Gaussian noise corresponds to functions with controlled regularity. This spectral formulation enables significant dimensionality reduction compared to grid-based diffusion models and ensures that the induced process in function space remains within a class of functions for which the PDE operators are well defined. Building on diffusion posterior sampling, we enforce physics-informed constraints and measurement conditions during inference, applying Adam-based updates at each diffusion step. We evaluate the proposed approach on Poisson, Helmholtz, and incompressible Navier-Stokes equations, demonstrating improved accuracy and computational efficiency compared with existing diffusion-based PDE solvers, which are state of the art for sparse observations. Code is available at https://github.com/deeplearningmethods/PISD.
STeP-Diff: Spatio-Temporal Physics-Informed Diffusion Models for Mobile Fine-Grained Pollution Forecasting
Shenzhen International Graduate School, Tsinghua University, China（清华大学深圳国际研究生院）；Department of Electronic Engineering, Beijing National Research Center for Information Science and Tech- nology (BNRist), Tsinghua University, China（电子工程系，北京信息科学与技术国家研究中心（BNRist），清华大学）；Shenzhen Smartcity Communication, Shenzhen, China（深圳智慧城市通信）；College of Soil and Water Conservation, Southwest Forestry University, China（水土保持学院，西南林业大学）；College of Civil Engineering, Southwest Forestry University, China（土木工程学院，西南林业大学）
Efficient Diversity-Preserving Diffusion Alignment via Gradient-Informed GFlowNets
Mila, Université de Montréal（蒙特利尔大学Mila实验室）；Max Planck Institute for Intelligent Systems - Tübingen（智能系统马克斯·普朗克研究所（图宾根））；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；University of Tübingen（图宾根大学）；University of Cambridge（剑桥大学）；Microsoft Research（微软研究院）
A Diffusion-Based Kinematics and Dynamics Model for 3D Sign Language Production
Department of Computer Science, University of Bari Aldo Moro（巴里阿尔多·莫罗大学计算机科学系）；Institute for Technological Development and Innovation in Communications, University of Las Palmas de Gran Canaria（拉斯帕尔马斯大加那利大学通信技术发展与创新研究所）
Unpaired Photo-realistic Image Deraining with Energy-informed Diffusion Model
School of Information Engineering, Chang’an University（长安大学信息工程学院）；School of Data Science and Artificial Intelligence, Chang’an University（长安大学数据科学与人工智能学院）
PID: Physics-Informed Diffusion Model for Infrared Image Generation
Research Center for Intelligent Computing Systems, Institute of Computing Technology, Chinese Academy of Sciences（智能计算系统研究中心，计算技术研究所，中国科学院）；School of Computer Science and Technology, University of Chinese Academy of Sciences（计算机科学与技术学院，中国科学院大学）
Stokes-Informed Diffusion for Robust Linear Polarization Estimation
Zhejiang University（浙江大学）；School of Engineering, Westlake University（西湖大学工学院）；School of Automation, Central South University（中南大学自动化学院）；College of Computer Science and Technology, Zhejiang University of Technology（浙江工业大学计算机科学与技术学院）；School of Computer Science, Peking University（北京大学计算机科学学院）
FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling
Institute for Foundations of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Department of Statistics and Data Science, Yale University（统计与数据科学系，耶鲁大学）；Laboratoire Navier, École nationale des ponts et chaussées, Institut Polytechnique de Paris, University Gustave Eiffel, CNRS UMR 8205（纳维实验室，巴黎理工学院，格斯塔夫·埃菲尔大学，CNRS UMR 8205）；Department of Chemical and Environmental Engineering, Yale University（化学与环境工程系，耶鲁大学）
LoCI-DiffCom: Longitudinal Consistency-Informed Diffusion Model for 3D Infant Brain Image Completion
School of Biomedical Engineering, ShanghaiTech University（上海科技大学生物医学工程学院）；Shanghai United Imaging Intelligence Co., Ltd（上海联影智能医疗科技有限公司）；Shanghai Clinical Research and Trail Center（上海临床研究中心）
Noise-Informed Diffusion-Generated Image Detection with Anomaly Attention
School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；New Laboratory of Pattern Recognition (NLPR), Institute of Automation, Chinese Academy of Sciences (CASIA)（中国科学院自动化研究所模式识别实验室）；Nanjing University of Information Science and Technology（南京信息科学技术大学）；State Key Laboratory of Media Convergence and Communication, Communication University of China（中国传媒大学媒体融合与传播国家重点实验室）
School of Mathematics and Computer Sciences, Nanchang University, Nanchang, China（南昌大学数学与计算机科学学院）；School of Information Engineering, Nanchang University, Nanchang, China（南昌大学信息工程学院）；Key Laboratory of Advanced Medical Imaging and Intelligent Computing of Guizhou Province, China（贵州省先进医学影像与智能计算重点实验室）
Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；Xiangtan University（湘潭大学）；National Innovation Center for Advanced Medical Devices（国家高性能医疗器械创新中心）；Nanchang University（南昌大学）；Pazhou Lab（琶洲实验室）
iRadioDiff: Physics-Informed Diffusion Model for Indoor Radio Map Construction and Localization
State Key Laboratory of ISN（信息与通信工程国家重点实验室）；Xidian University（西安电子科技大学）；School of Telecommunications Engineering（电信工程学院）；School of Artificial Intelligence（人工智能学院）；School of Information Science and Technology（信息科学与技术学院）；Southwest Jiaotong University（西南交通大学）；Department of Electrical and Computer Engineering（电气与计算机工程系）
Physics-informed Diffusion Generation for Geomagnetic Map Interpolation
State Key Laboratory of Blockchain and Data Security（区块链与数据安全国家重点实验室）；High-Performance Intelligent Computing Research Center for Ultra-Large Scale Graph Data（超大规模图数据高性能智能计算研究中心）；School of Computer and Computing Science（计算机与计算科学学院）；Hangzhou City University（杭州市大学）；Zhejiang Lab（浙江实验室）
A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
Department of Mathematics \& POSTECH MINDS (Mathematical Institute for Data Science), Pohang University of Science；Graduate School of Artificial Intelligence \& POSTECH MINDS (Mathematical Institute for Data Science), Pohang University of Science
