mlsanityData to 7 Oct 2026

A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction

arXiv 2211.14680 ↗First posted 26 Nov 2022cs.LG physics.flu-dyncited by 150

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

Abstract (arXiv)

Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning models for high-fidelity data reconstruction require low-fidelity data for model training. Such requirement restrains the application performance of these models, since their data reconstruction accuracy would drop significantly if the low-fidelity input data used in model test has a large deviation from the training data. To overcome this restraint, we propose a diffusion model which only uses high-fidelity data at training. With different configurations, our model is able to reconstruct high-fidelity data from either a regular low-fidelity sample or a sparsely measured sample, and is also able to gain an accuracy increase by using physics-informed conditioning information from a known partial differential equation when that is available. Experimental results demonstrate that our model can produce accurate reconstruction results for 2d turbulent flows based on different input sources without retraining.

Key facts. Cited by 150 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 35 of its 76 references that are in the map. First posted on arXiv 26 Nov 2022.

Builds on

35 of 76 references.

References · 35

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
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  5. 2020Denoising Diffusion Implicit Modelscited by 9,655
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  10. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  11. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
  12. 2019Semantic Image Synthesis with Spatially-Adaptive Normalizationcited by 1,295
23 more
  1. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,155
  2. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  3. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  4. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  5. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  6. 2021Machine learning accelerated computational fluid dynamicscited by 461
  7. 2021SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Modelscited by 415
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  12. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
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  16. 2021Video Super-Resolution Transformercited by 120
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  23. 2020Deep Learning for Efficient Reconstruction of High-Resolution Turbulent DNS Datacited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 22; 2024: 31; 2025: 42; 2026: 55.

150 papers.

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  1. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  2. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observationcited by 100
  3. 2024Physics-Informed Diffusion Modelscited by 88
  4. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 65
  5. 2024On conditional diffusion models for PDE simulationscited by 56
  6. 2023CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problemscited by 54
  7. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 46
  8. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 46
  9. 2024Gradient-Free Generation for Hard-Constrained Systemscited by 35
  10. 2023Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Modelscited by 33
  11. 2023A Denoising Diffusion Model for Fluid Field Predictioncited by 31
  12. 2023Synthetic Lagrangian Turbulence by Generative Diffusion Modelscited by 31
38 more
  1. 2023Physics-Informed Computer Vision: A Review and Perspectivescited by 28
  2. 2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generationcited by 28
  3. 2024Wavelet Diffusion Neural Operatorcited by 28
  4. 2025Generative Latent Neural PDE Solver using Flow Matchingcited by 28
  5. 2025Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraintscited by 26
  6. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulationcited by 25
  7. 2025Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networkscited by 24
  8. 2023Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Modelscited by 22
  9. 2023Physics Informed Token Transformer for Solving Partial Differential Equationscited by 21
  10. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  11. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 19
  12. 2023SuperBench: A Super-Resolution Benchmark Dataset for Scientific Machine Learningcited by 18
  13. 2023Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO)cited by 16
  14. 2024Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observationscited by 16
  15. 2024Diffusion State-Guided Projected Gradient for Inverse Problemscited by 14
  16. 2024Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observationscited by 13
  17. 2024Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operatorcited by 12
  18. 2023Inexpensive High Fidelity Melt Pool Models in Additive Manufacturing Using Generative Deep Diffusioncited by 11
  19. 2025Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approachcited by 11
  20. 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generationcited by 11
  21. 2025Guiding diffusion models to reconstruct flow fields from sparse datacited by 11
  22. 2024PiRD: Physics-informed Residual Diffusion for Flow Field Reconstructioncited by 10
  23. 2024Development of Skip Connection in Deep Neural Networks for Computer Vision and Medical Image Analysis: A Surveycited by 10
  24. 2024Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flowscited by 10
  25. 2024Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networkscited by 10
  26. 2025Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanicscited by 10
  27. 2024Pi-fusion: Physics-informed diffusion model for learning fluid dynamicscited by 9
  28. 2026Decoupled Diffusion Sampling for Inverse Problems on Function Spacescited by 9
  29. 2023Turbulence Scaling from Deep Learning Diffusion Generative Modelscited by 8
  30. 2025Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observationscited by 8
  31. 2025Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environmentscited by 8
  32. 2025VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Modelscited by 7
  33. 2025Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstructioncited by 7
  34. 2024Generative Learning for Forecasting the Dynamics of Complex Systemscited by 6
  35. 2024Generative Diffusion Models for Fast Simulations of Particle Collisions at CERNcited by 6
  36. 2024Conditional score-based diffusion models for solving inverse problems in mechanicscited by 6
  37. 2024Generating Physical Dynamics under Priorscited by 6
  38. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6

50 most cited of 150 All 150 (JSON)

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  2. 2025Rectified Flows for Fast Multiscale Fluid Flow Modeling
  3. 2024Reconstructing 3D Flow from 2D Data with Diffusion Transformer
  4. 2026Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields
  5. 2025Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems
  6. 2026Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance
  7. 2026Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems
  8. 2026Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensors