arXiv AI June 3, 2026 By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen

Physics-informed diffusion models in spectral space

arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: 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.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.

diffusion

arXiv AI

Jul 24

PILD: Physics-Informed Learning via Diffusion

arXiv:2601. 21284v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in engineering and scientific problems where physical laws must be respected.

By Tianyi Zeng, Tianyi Wang, Jiaru Zhang, Zimo Zeng, Feiyang Zhang, Yiming Xu, Sikai Chen, Junfeng Jiao, Christian Claudel, Xinbo Chen

diffusion safety

arXiv AI

Jun 30

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation

arXiv:2505. 22391v2 Announce Type: replace-cross Abstract: Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems.

By Yi Zhang, Peng Wang, Difan Zou

diffusion efficiency benchmarks

arXiv Machine Learning

5d ago

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).

By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi

rag diffusion benchmarks

arXiv AI

Aug 5

PRISMA: Improving the Accuracy-Latency Frontier of Diffusion-based PDE Solvers Using Physics-Informed Spectral Attention

arXiv:2512. 01370v2 Announce Type: replace-cross Abstract: Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance.

By Medha Sawhney, Abhilash Neog, Mridul Khurana, Anuj Karpatne

diffusion benchmarks

arXiv Machine Learning

Jul 27

Latent PDE mapping for efficient physics-informed learning across geometries with limited data

arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.

By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban

benchmarks

arXiv AI

Jul 15

Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.

By Zixuan Shen (Central South University), Bingchuan Wang (Central South University), Zhi Wang (Nanjing University), Yong Wang (Central South University)

diffusion

Related stories

PILD: Physics-Informed Learning via Diffusion

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

PRISMA: Improving the Accuracy-Latency Frontier of Diffusion-based PDE Solvers Using Physics-Informed Spectral Attention

Latent PDE mapping for efficient physics-informed learning across geometries with limited data

Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance