mlsanityData to 7 Oct 2026

State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics

arXiv 2407.21314 ↗First posted 31 Jul 2024cs.LG stat.MLcited by 7

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

Abstract (arXiv)

Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical and observational models. To address this challenge, a novel generative model, termed the State-Observation Augmented Diffusion (SOAD) model is proposed for data-driven assimilation. The marginal posterior associated with SOAD has been derived and then proved to match the true posterior distribution under mild assumptions, suggesting its theoretical advantages over previous score-based approaches. Experimental results also indicate that SOAD may offer improved performance compared to existing data-driven methods.

Key facts. Cited by 7 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 54 of its 94 references that are in the map. First posted on arXiv 31 Jul 2024.

Builds on

54 of 94 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Data29 Apr
  2. 2024Controllable seismic velocity synthesis using generative diffusion models9 Feb
  3. 2023An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems2 Sep
  4. 2023Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation29 May
  5. 2022Diffusion Models Beat GANs on Topology Optimization20 Aug

Other references · 49

  1. 2017Attention Is All You Needcited by 59,932
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  3. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  4. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  6. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 13,958
  7. 2021Swin Transformer: Hierarchical Vision Transformer using Shifted Windowscited by 12,082
  8. 2020Denoising Diffusion Implicit Modelscited by 9,655
  9. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  10. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  11. 2023Segment Anythingcited by 8,158
  12. 2022Classifier-Free Diffusion Guidancecited by 5,717
37 more
  1. 2023A Survey of Large Language Modelscited by 2,537
  2. 2015Variational Inference with Normalizing Flowscited by 2,161
  3. 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,725
  4. 2015Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcastingcited by 1,428
  5. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  6. 2014On the Properties of Neural Machine Translation: Encoder-Decoder Approachescited by 1,303
  7. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  8. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  9. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  10. 2017Generative Adversarial Networks: An Overviewcited by 588
  11. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
  12. 2016Tutorial on Variational Autoencoderscited by 404
  13. 2022Understanding Diffusion Models: A Unified Perspectivecited by 337
  14. 2016Ladder Variational Autoencoderscited by 315
  15. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  16. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  17. 2023FuXi: A cascade machine learning forecasting system for 15-day global weather forecastcited by 237
  18. 2022FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operatorscited by 188
  19. 2023FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Leadcited by 170
  20. 2022Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecastcited by 164
  21. 2015Deep Kalman Filterscited by 163
  22. 2021An Introduction to Deep Generative Modelingcited by 104
  23. 2023Score-based Data Assimilationcited by 91
  24. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  25. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 58
  26. 2023Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion modelscited by 48
  27. 2020Combining data assimilation and machine learning to infer unresolved scale parametrisationcited by 40
  28. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 37
  29. 2023Foundation Models for Weather and Climate Data Understanding: A Comprehensive Surveycited by 32
  30. 2021Latent Space Data Assimilation by using Deep Learningcited by 29
  31. 2022Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Modelscited by 24
  32. 2021Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimationcited by 20
  33. 2022Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systemscited by 12
  34. 2023Score-based Data Assimilation for a Two-Layer Quasi-Geostrophic Modelcited by 11
  35. 2020Data Assimilation in the Latent Space of a Neural Networkcited by 9
  36. 2023Latent assimilation with implicit neural representations for unknown dynamicscited by 8
  37. 2024Data Assimilation in Chaotic Systems Using Deep Reinforcement Learningcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 3.

7 papers.

  1. 2024LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observationscited by 10
  2. 2025MODS: Multi-source Observations Conditional Diffusion Model for Meteorological State Downscalingcited by 3
  3. 2026Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilationcited by 3
  4. 2025Divergence-kernel method for linear responses of densities and generative modelscited by 0
  5. 2025Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascadecited by 0
  6. 2026Ensemble Controlled-Flow Filtering for Implicit Data Assimilationcited by 0
  7. 2026Variational Parameter Calibration with Physics-Aware Latent-Space Surrogatescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation
  2. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate
  3. 2026EnJoi: Ensemble Joint Score Filter for Generative Data Assimilation
  4. 2026Closed-form conditional diffusion models for data assimilation
  5. 2024Deep Bayesian Filter for Bayes-faithful Data Assimilation
  6. 2026DAWIS: Data Assimilation with Windowed Inverse Sampling via Multitask Interpolants
  7. 2025PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems
  8. 2026A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants