mlsanityData to 7 Oct 2026

Text2PDE: Latent Diffusion Models for Accessible Physics Simulation

arXiv 2410.01153 ↗First posted 2 Oct 2024cs.LGcited by 25

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

Abstract (arXiv)

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to ~3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.

Key facts. Cited by 25 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 57 of its 83 references that are in the map. First posted on arXiv 2 Oct 2024.

Builds on

57 of 83 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observation25 Jun
  2. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers10 Aug
  3. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting3 Jun
  4. 2023A Denoising Diffusion Model for Fluid Field Prediction27 Jan
  5. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction26 Nov

Other references · 52

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  5. 2019RoBERTa: A Robustly Optimized BERT Pretraining Approachcited by 13,266
  6. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  7. 2020Denoising Diffusion Implicit Modelscited by 9,655
  8. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  9. 2021Masked Autoencoders Are Scalable Vision Learnerscited by 7,339
  10. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  11. 2020Scaling Laws for Neural Language Modelscited by 6,411
  12. 2022Scalable Diffusion Models with Transformerscited by 5,931
38 more
  1. 2022Classifier-Free Diffusion Guidancecited by 5,717
  2. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  3. 2020Taming Transformers for High-Resolution Image Synthesiscited by 3,229
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  5. 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,526
  6. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  7. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  8. 2023Consistency Modelscited by 1,778
  9. 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,725
  10. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,465
  11. 2021Perceiver: General Perception with Iterative Attentioncited by 1,089
  12. 2022Tune-A-Video: One-Shot Tuning of Image Diffusion Models for Text-to-Video Generationcited by 958
  13. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  14. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  15. 2022On Distillation of Guided Diffusion Modelscited by 721
  16. 2023Text2Video-Zero: Text-to-Image Diffusion Models are Zero-Shot Video Generatorscited by 666
  17. 2023Structure and Content-Guided Video Synthesis with Diffusion Modelscited by 589
  18. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
  19. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
  20. 2022Masked Autoencoders As Spatiotemporal Learnerscited by 428
  21. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speedcited by 344
  22. 2023Common Diffusion Noise Schedules and Sample Steps are Flawedcited by 308
  23. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  24. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  25. 2021Factorized Fourier Neural Operatorscited by 237
  26. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  27. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
  28. 2018Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flowscited by 147
  29. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 137
  30. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  31. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 90
  32. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
  33. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
  34. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 46
  35. 2024AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fieldscited by 38
  36. 2024Strategies for Pretraining Neural Operatorscited by 14
  37. 2024Masked Autoencoders are PDE Learnerscited by 11
  38. 2024CaFA: Global Weather Forecasting with Factorized Attention on Spherecited by 6

50 most cited of 52 All 52 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 9; 2026: 14.

25 papers.

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  1. 2025Generative Latent Neural PDE Solver using Flow Matchingcited by 28
  2. 2025Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulationcited by 19
  3. 2024NeuralDEM -- Real-time Simulation of Industrial Particulate Flowscited by 10
  4. 2024Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogatescited by 8
  5. 2025Text-Trained LLMs Can Zero-Shot Extrapolate PDE Dynamics, Revealing a Three-Stage In-Context Learning Mechanismcited by 7
  6. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6
  7. 2026OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inferencecited by 4
  8. 2025Controllable Motion Generation via Diffusion Modal Couplingcited by 2
  9. 2025Point-wise Diffusion Models for Physical Systems with Shape Variations: Application to Spatio-temporal and Large-scale systemcited by 2
  10. 2025Efficient Generative Transformer Operators For Million-Point PDEscited by 2
  11. 2026Flow Matching and Diffusion Models via PointNet for Generating Fluid Fields on Irregular Geometriescited by 2
  12. 2025Hamiltonian Neural PDE Solvers through Functional Approximationcited by 0
13 more
  1. 2025Learning Mappings in Mesh-based Simulationscited by 0
  2. 2025GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometriescited by 0
  3. 2026LinkD: AutoRegressive Diffusion Model for Mechanical Linkage Synthesiscited by 0
  4. 2026Coupled Diffusion-Encoder Models for Reconstruction of Flow Fieldscited by 0
  5. 2026Generative Neural Operators through Diffusion Last Layercited by 0
  6. 2026An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interactioncited by 0
  7. 2026Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systemscited by 0
  8. 2026MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functionscited by 0
  9. 2026Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidancecited by 0
  10. 2026Large language models for partial differential equation workflowscited by 0
  11. 2026Learnable composition for neural operatorscited by 0
  12. 2026Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEscited by 0
  13. 2026Cross-Domain Pretraining for Steady-State Neural CFD Surrogatescited by 0

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  5. 2025CodePDE: An Inference Framework for LLM-driven PDE Solver Generation
  6. 2026AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Design
  7. 2026Bias-Constrained Diffusion Schedules for PDE Emulations: Reconstruction Error Minimization and Efficient Unrolled Training
  8. 2026Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains