mlsanityData to 7 Oct 2026

Particle-Guided Diffusion Models for Partial Differential Equations

arXiv 2601.23262 ↗First posted 30 Jan 2026cs.LGcited by 4

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedure within a new Sequential Monte Carlo (SMC) framework, yielding a scalable generative PDE solver. Across multiple benchmark PDE systems as well as multiphysics and interacting PDE systems, our method produces solution fields with lower numerical error than existing state-of-the-art generative methods.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 42 of its 78 references that are in the map. First posted on arXiv 30 Jan 2026.

Builds on

42 of 78 references.

Closest ancestors · 9

Same direction, newest first

  1. 2025Generative Latent Neural PDE Solver using Flow Matching28 Mar
  2. 2024On conditional diffusion models for PDE simulations21 Oct
  3. 2024Generative AI for fast and accurate statistical computation of fluids27 Sep
  4. 2023Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models8 Dec
  5. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation4 Sep
  6. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Models30 Jun
  7. 2023A Denoising Diffusion Model for Fluid Field Prediction27 Jan
  8. 2022Flow Matching for Generative Modeling6 Oct
  9. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun

Other references · 33

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  7. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  8. 2014Conditional Generative Adversarial Netscited by 2,152
  9. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  10. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  11. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  12. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
21 more
  1. 2023AudioLDM: Text-to-Audio Generation with Latent Diffusion Modelscited by 592
  2. 2017Generative Adversarial Networks: An Overviewcited by 588
  3. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  4. 2021Machine learning accelerated computational fluid dynamicscited by 461
  5. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  6. 2023Make-An-Audio: Text-To-Audio Generation with Prompt-Enhanced Diffusion Modelscited by 323
  7. 2022A Survey on Generative Diffusion Modelcited by 238
  8. 2023Score-based Data Assimilationcited by 91
  9. 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
  10. 2019Elements of Sequential Monte Carlocited by 60
  11. 2018Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systemscited by 54
  12. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 46
  13. 2017Deep Learning the Physics of Transport Phenomenacited by 26
  14. 2024Conditional sampling within generative diffusion modelscited by 18
  15. 2025A Mixture-Based Framework for Guiding Diffusion Modelscited by 17
  16. 2025Diffusion models for inverse problemscited by 15
  17. 2024Conditioning diffusion models by explicit forward-backward bridgingcited by 11
  18. 2025Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlocited by 9
  19. 2024Sequential Posterior Sampling with Diffusion Modelscited by 6
  20. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  21. 2025Generative diffusion posterior sampling for informative likelihoodscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computingcited by 4
  2. 2026Particle-Guided Diffusion for Gas-Phase Reaction Kineticscited by 1
  3. 2026Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Samplingcited by 0
  4. 2026Interacting particle guidance for sampling reward-tilted generative priorscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observation
  2. 2026Self-Augmented Diffusion Guidance for Physics-Informed Generation
  3. 2024New algorithms for sampling and diffusion models
  4. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulation
  5. 2026Guided Flow Matching for Forward and Inverse PDE Problems with Sparse Observations: Algorithm and Theory
  6. 2023A Unified Sampling Framework for Solver Searching of Diffusion Probabilistic Models
  7. 2024Physics-Informed Diffusion Models
  8. 2026Physics-informed diffusion models in spectral space