mlsanityData to 14 Oct 2026

Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks

arXiv 2504.02843 ↗First posted 19 Mar 2025physics.comp-ph cs.AI physics.flu-dyncited by 25

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

Abstract (arXiv)

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which relevant statistics (e.g., RMS and two-point correlations) can be derived. Here, we propose a graph-based latent diffusion (or alternatively, flow-matching) model that enables direct sampling of states from their equilibrium distribution, given a mesh discretization of the system and its physical parameters. This allows for the efficient computation of flow statistics without running long and expensive numerical simulations. The graph-based structure enables operations on unstructured meshes, which is critical for representing complex geometries with spatially localized high gradients, while latent-space diffusion modeling with a multi-scale GNN allows for efficient learning and inference of entire distributions of solutions. A key finding is that the proposed networks can accurately learn full distributions even when trained on incomplete data from relatively short simulations. We apply this method to a range of fluid dynamics tasks, such as predicting pressure distributions on 3D wing models in turbulent flow, demonstrating both accuracy and computational efficiency in challenging scenarios. The ability to directly sample accurate solutions, and capturing their diversity from short ground-truth simulations, is highly promising for complex scientific modeling tasks.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 44 of its 68 references that are in the map. First posted on arXiv 19 Mar 2025.

Builds on

44 of 68 references.

Closest ancestors · 14

Same direction, newest first

  1. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observation25 Jun
  2. 2023Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models8 Dec
  3. 2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation14 Nov
  4. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers10 Aug
  5. 2023Graph Denoising Diffusion for Inverse Protein Folding29 Jun
  6. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting3 Jun
  7. 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models31 Jan
  8. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction26 Nov
  9. 2022Flow Matching for Generative Modeling6 Oct
  10. 2022Protein structure generation via folding diffusion30 Sep
  11. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  12. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
2 more
  1. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  2. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar

Other references · 30

  1. 2017Attention Is All You Needcited by 60,361
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  5. 2020Denoising Diffusion Implicit Modelscited by 9,781
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  7. 2016Layer Normalizationcited by 5,669
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  9. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,430
  10. 2016Variational Graph Auto-Encoderscited by 1,382
  11. 2018Relational inductive biases, deep learning, and graph networkscited by 1,360
  12. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
18 more
  1. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  2. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  3. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  4. 2017Self-Normalizing Neural Networkscited by 598
  5. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 509
  6. 2019Graph U-Netscited by 492
  7. 2015Variational Dropout and the Local Reparameterization Trickcited by 490
  8. 2021Machine learning accelerated computational fluid dynamicscited by 471
  9. 2023FreeU: Free Lunch in Diffusion U-Netcited by 196
  10. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 138
  11. 2018Deep Fluids: A Generative Network for Parameterized Fluid Simulationscited by 121
  12. 2022MultiScale MeshGraphNetscited by 98
  13. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 91
  14. 2018Efficient collective swimming by harnessing vortices through deep reinforcement learningcited by 73
  15. 2018Deep Dynamical Modeling and Control of Unsteady Fluid Flowscited by 68
  16. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 49
  17. 2022Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNNcited by 45
  18. 2021Generative Modeling of Turbulencecited by 26

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 8; 2026: 17.

25 papers.

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  1. 2025Generative Latent Neural PDE Solver using Flow Matchingcited by 28
  2. 2025Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraintscited by 28
  3. 2025Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanicscited by 10
  4. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 5
  5. 2026Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systemscited by 3
  6. 2025Reframing Generative Models for Physical Systems using Stochastic Interpolantscited by 2
  7. 2025Generative Urban Flow Modeling: From Geometry to Airflow with Graph Diffusioncited by 2
  8. 2026Flow Matching and Diffusion Models via PointNet for Generating Fluid Fields on Irregular Geometriescited by 2
  9. 2025Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Latercited by 1
  10. 2025Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equationscited by 1
  11. 2026GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domainscited by 1
  12. 2026Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEscited by 0
13 more
  1. 2026Deterministic and probabilistic neural surrogates of global hybrid-Vlasov simulationscited by 0
  2. 2026Stable Long-Horizon Spatiotemporal Prediction on Meshes Using Latent Multiscale Recurrent Graph Neural Networkscited by 0
  3. 2026Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervisioncited by 0
  4. 2026Signal-Aware Conditional Diffusion Surrogates for Transonic Wing Pressure Predictioncited by 0
  5. 2026One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributionscited by 0
  6. 2026Inpainting physics: self-supervised learning for context-driven fluid simulationcited by 0
  7. 2026Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomographycited by 0
  8. 2026PCGD: Physics-Guided Conditional Graph Diffusion for TCAD Device Simulationcited by 0
  9. 2026A Shortcut to Statistically Steady-State Turbulence with Flow Matchingcited by 0
  10. 2026Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Lossescited by 0
  11. 2026Fluid-DiT: Graph-Free Diffusion Transformers for Fluid Flow Simulations Learningcited by 0
  12. 2026Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solverscited by 0
  13. 2026Cross-Domain Pretraining for Steady-State Neural CFD Surrogatescited by 0

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  2. 2025Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction
  3. 2026Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domains
  4. 2026FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes
  5. 2025Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks
  6. 2023Diffusion model based data generation for partial differential equations
  7. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation
  8. 2024Generative AI for fast and accurate statistical computation of fluids