mlsanityData to 14 Oct 2026

DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting

arXiv 2306.01984 ↗First posted 3 Jun 2023cs.LG cs.AI stat.MLcited by 109

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

Abstract (arXiv)

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

Key facts. Cited by 109 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 52 of its 79 references that are in the map. First posted on arXiv 3 Jun 2023.

Builds on

52 of 79 references.

Closest ancestors · 2

Same direction, newest first

  1. 2023PFGM++: Unlocking the Potential of Physics-Inspired Generative Models8 Feb
  2. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting28 Jan

Other references · 50

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2020Denoising Diffusion Implicit Modelscited by 9,781
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  6. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  7. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  10. 2022Video Diffusion Modelscited by 2,305
  11. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,778
  12. 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,742
38 more
  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  2. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  3. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  4. 2021Machine learning accelerated computational fluid dynamicscited by 471
  5. 2022Message Passing Neural PDE Solverscited by 386
  6. 2023ClimaX: A foundation model for weather and climatecited by 337
  7. 2021Skillful Precipitation Nowcasting using Deep Generative Models of Radarcited by 311
  8. 2022MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolationcited by 309
  9. 2022Flexible Diffusion Modeling of Long Videoscited by 294
  10. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 276
  11. 2020WeatherBench: A benchmark dataset for data-driven weather forecastingcited by 275
  12. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 267
  13. 2021Factorized Fourier Neural Operatorscited by 249
  14. 2022Diffusion Probabilistic Modeling for Video Generationcited by 238
  15. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 204
  16. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
  17. 2022Forecasting Global Weather with Graph Neural Networkscited by 168
  18. 2022Generative Modelling With Inverse Heat Dissipationcited by 167
  19. 2019Implicit Deep Learningcited by 124
  20. 2022Soft Diffusion: Score Matching for General Corruptionscited by 102
  21. 2017Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledgecited by 96
  22. 2018Neural networks for post-processing ensemble weather forecastscited by 95
  23. 2022Clifford Neural Layers for PDE Modelingcited by 92
  24. 2022Blurring Diffusion Modelscited by 91
  25. 2023Reflected Diffusion Modelscited by 87
  26. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 84
  27. 2019Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Predictioncited by 67
  28. 2023Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformerscited by 57
  29. 2021Quantifying Uncertainty in Deep Spatiotemporal Forecastingcited by 48
  30. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 38
  31. 2022SwinVRNN: A Data-Driven Ensemble Forecasting Model via Learned Distribution Perturbationcited by 32
  32. 2021An Extensible Benchmark Suite for Learning to Simulate Physical Systemscited by 24
  33. 2020Learning Accurate Long-term Dynamics for Model-based Reinforcement Learningcited by 21
  34. 2022WeatherBench Probability: A benchmark dataset for probabilistic medium-range weather forecasting along with deep learning baseline modelscited by 17
  35. 2023Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systemscited by 14
  36. 2020Learning Stable Models for Prediction and Controlcited by 12
  37. 2022AutoML for Climate Change: A Call to Actioncited by 3
  38. 2023Inductive biases in deep learning models for weather predictioncited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 28; 2025: 43; 2026: 35.

109 papers.

Sort:

By area:

  1. 2024Foundation Models for Time Series Analysis: A Tutorial and Surveycited by 239
  2. 2024Rolling Diffusion Modelscited by 104
  3. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 71
  4. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 67
  5. 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 66
  6. 2024On conditional diffusion models for PDE simulationscited by 60
  7. 2024AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fieldscited by 39
  8. 2023Foundation Models for Weather and Climate Data Understanding: A Comprehensive Surveycited by 34
  9. 2024Continuous Ensemble Weather Forecasting with Diffusion modelscited by 30
  10. 2024Wavelet Diffusion Neural Operatorcited by 29
  11. 2024Generative Diffusion-based Downscaling for Climatecited by 25
  12. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulationcited by 25
38 more
  1. 2025Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networkscited by 25
  2. 2023AI Foundation Models for Weather and Climate: Applications, Design, and Implementationcited by 21
  3. 2024Probabilistic Emulation of a Global Climate Model with Spherical DYffusioncited by 21
  4. 2025Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networkscited by 20
  5. 2025Diffusion Dynamics Models with Generative State Estimation for Cloth Manipulationcited by 19
  6. 2025Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulationcited by 19
  7. 2024DiffPhyCon: A Generative Approach to Control Complex Physical Systemscited by 17
  8. 2024Diffusion Model for Planning: A Systematic Literature Reviewcited by 17
  9. 2025Deep Learning and Foundation Models for Weather Prediction: A Surveycited by 16
  10. 2024Geometric Trajectory Diffusion Modelscited by 15
  11. 2025Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamicscited by 13
  12. 2024Elucidating the Design Choice of Probability Paths in Flow Matching for Forecastingcited by 12
  13. 2025Machine learning for modelling unstructured grid data in computational physics: a reviewcited by 12
  14. 2025Diffusion Models for Time Series Forecasting: A Surveycited by 11
  15. 2025Binned Spectral Power Loss for Improved Prediction of Chaotic Systemscited by 10
  16. 2025Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Reviewcited by 10
  17. 2025Hierarchical Implicit Neural Emulatorscited by 10
  18. 2025Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanicscited by 10
  19. 2024Parametric model reduction of mean-field and stochastic systems via higher-order action matchingcited by 9
  20. 2025Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Modelscited by 9
  21. 2025FLEX: A Backbone for Diffusion-Based Modeling of Spatio-temporal Physical Systemscited by 8
  22. 2025FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modelingcited by 8
  23. 2025Multimodal Atmospheric Super-Resolution With Deep Generative Modelscited by 8
  24. 2025Generative emulation of chaotic dynamics with coherent priorcited by 7
  25. 2026Probabilistic Retrofitting of Learned Simulatorscited by 7
  26. 2024Generative Learning for Forecasting the Dynamics of Complex Systemscited by 6
  27. 2025LaDCast: A Latent Diffusion Model for Medium-Range Ensemble Weather Forecastingcited by 6
  28. 2025Training-Free Data Assimilation with GenCastcited by 5
  29. 2025Predicting partially observable dynamical systems via diffusion models with a multiscale inference schemecited by 5
  30. 2024Diffusion models as probabilistic neural operators for recovering unobserved states of dynamical systemscited by 4
  31. 2025Flow marching for a generative PDE foundation modelcited by 4
  32. 2026Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flowscited by 4
  33. 2024Alternators For Sequence Modelingcited by 3
  34. 2024Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogatescited by 3
  35. 2024AI Foundation Model for Heliophysics: Applications, Design, and Implementationcited by 3
  36. 2025When do World Models Successfully Learn Dynamical Systems?cited by 3
  37. 2025ArchesClimate: Probabilistic Decadal Ensemble Generation With Flow Matchingcited by 3
  38. 2026Tadpole: Autoencoders as Foundation Models for 3D PDEs with Online Learningcited by 3

50 most cited of 109 All 109 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2025Generating time-consistent dynamics with discriminator-guided image diffusion models
  2. 2026Differencing the Diffusion Trajectory toward Uncertain Components for Time Series Forecasting
  3. 2025ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes
  4. 2025HydroDiffusion: Diffusion-Based Probabilistic Streamflow Forecasting with a State Space Backbone
  5. 2025SimDiff: Simpler Yet Better Diffusion Model for Time Series Point Forecasting
  6. 2026GLIDE: Graph-guided Leap Inference for Diffusion Estimation of Spatio-Temporal Point Processes
  7. 2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation
  8. 2025Non-stationary Diffusion For Probabilistic Time Series Forecasting