mlsanityData to 7 Oct 2026

VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models

arXiv 2506.13754 ↗First posted 16 Jun 2025cs.LG cs.AI cs.CVcited by 7

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under full or partial observation, our approach unifies these tasks under a single, flexible generative framework. Specifically, we recast PDE-solving as a generalized inpainting problem, e.g., treating forward prediction as inferring missing spatiotemporal information of future states from initial conditions. To this end, we design a transformer-based architecture that conditions on arbitrary patterns of known data to infer missing values across time and space. Our method proposes pixel-space video diffusion models for fine-grained, high-fidelity inpainting and conditioning, while enhancing computational efficiency through hierarchical modeling. Extensive experiments show that our video inpainting-based diffusion model offers an accurate and versatile solution across a wide range of PDEs and problem setups, outperforming state-of-the-art baselines.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 54 of its 73 references that are in the map. First posted on arXiv 16 Jun 2025.

Builds on

54 of 73 references.

Closest ancestors · 9

Same direction, newest first

  1. 2024Scalable High-Resolution Pixel-Space Image Synthesis with Hourglass Diffusion Transformers21 Jan
  2. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  3. 2022Classifier-Free Diffusion Guidance26 Jul
  4. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  6. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models6 Aug
  7. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  8. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  9. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 45

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,466
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  5. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,286
  6. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  7. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
  8. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  9. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,465
  10. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  11. 2022Denoising Diffusion Restoration Modelscited by 951
  12. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
33 more
  1. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  2. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  3. 2022Latent Video Diffusion Models for High-Fidelity Long Video Generationcited by 385
  4. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  5. 2022MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolationcited by 307
  6. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  7. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  8. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  9. 2023SEINE: Short-to-Long Video Diffusion Model for Generative Transition and Predictioncited by 231
  10. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 225
  11. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 203
  12. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
  13. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 180
  14. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstructioncited by 150
  15. 2022Diffusion Models for Video Prediction and Infillingcited by 134
  16. 2023Inversion-Free Image Editing with Natural Languagecited by 106
  17. 2023VDT: General-purpose Video Diffusion Transformers via Mask Modelingcited by 102
  18. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observationcited by 100
  19. 2021Hierarchical Transformers Are More Efficient Language Modelscited by 99
  20. 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 84
  21. 2023AVID: Any-Length Video Inpainting with Diffusion Modelcited by 81
  22. 2019Physics-Informed Neural Networks for Power Systemscited by 80
  23. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 80
  24. 2021Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equationscited by 68
  25. 2023Neural Inverse Operators for Solving PDE Inverse Problemscited by 61
  26. 2024Gradient-Free Generation for Hard-Constrained Systemscited by 35
  27. 2021A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEscited by 31
  28. 2023Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flowscited by 30
  29. 2023Neural Stress Fields for Reduced-order Elastoplasticity and Fracturecited by 24
  30. 2024Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problemscited by 18
  31. 2022Solving Seismic Wave Equations on Variable Velocity Models with Fourier Neural Operatorcited by 17
  32. 2024Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observationscited by 13
  33. 2025Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulencecited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 5.

7 papers.

  1. 2025PRISMA: Improving the Accuracy-Latency Frontier of Diffusion-based PDE Solvers Using Physics-Informed Spectral Attentioncited by 2
  2. 2025Efficient Generative Transformer Operators For Million-Point PDEscited by 2
  3. 2026Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flowscited by 1
  4. 2026Error-Conditioned Neural Solverscited by 1
  5. 2026Image Editing Models are Numerical Solverscited by 1
  6. 2026Recursive Flow Matchingcited by 0
  7. 2026Generalized Neural Operator for Parametric and Boundary-Value Problemscited by 0

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  4. 2025LanPaint: Training-Free Diffusion Inpainting with Asymptotically Exact and Fast Conditional Sampling
  5. 2026Just-in-Time: Training-Free Spatial Acceleration for Diffusion Transformers
  6. 2025Beyond Blur: A Fluid Perspective on Generative Diffusion Models
  7. 2023Infusion: internal diffusion for inpainting of dynamic textures and complex motion
  8. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems