mlsanityData to 14 Oct 2026

Score-based Data Assimilation

arXiv 2306.10574 ↗First posted 18 Jun 2023cs.LG stat.MLcited by 96

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Cited by 43 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have been proposed to solve this problem, including particle-based and variational methods. However, most algorithms depend on the transition dynamics for inference, which becomes intractable for long time horizons or for high-dimensional systems with complex dynamics, such as oceans or atmospheres. In this work, we introduce score-based data assimilation for trajectory inference. We learn a score-based generative model of state trajectories based on the key insight that the score of an arbitrarily long trajectory can be decomposed into a series of scores over short segments. After training, inference is carried out using the score model, in a non-autoregressive manner by generating all states simultaneously. Quite distinctively, we decouple the observation model from the training procedure and use it only at inference to guide the generative process, which enables a wide range of zero-shot observation scenarios. We present theoretical and empirical evidence supporting the effectiveness of our method.

Key facts. Cited by 96 papers in the map (data through 14 Oct 2026). Builds on 41 of its 73 references that are in the map. First posted on arXiv 18 Jun 2023.

Builds on

41 of 73 references.

References · 41

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  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. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  7. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  8. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  9. 2016Layer Normalizationcited by 5,669
  10. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  11. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  12. 2022Video Diffusion Modelscited by 2,305
29 more
  1. 2023Consistency Modelscited by 1,822
  2. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,778
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  4. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  5. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,163
  6. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 950
  7. 2022Pseudo Numerical Methods for Diffusion Models on Manifoldscited by 700
  8. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 532
  9. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  10. 2021Machine learning accelerated computational fluid dynamicscited by 471
  11. 2021Skillful Precipitation Nowcasting using Deep Generative Models of Radarcited by 311
  12. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 267
  13. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  14. 2022It's Raw! Audio Generation with State-Space Modelscited by 171
  15. 2015Deep Kalman Filterscited by 166
  16. 2020Dynamical Variational Autoencoders: A Comprehensive Reviewcited by 128
  17. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 113
  18. 2017Variational Sequential Monte Carlocited by 95
  19. 2017Filtering Variational Objectivescited by 91
  20. 2020Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 modelcited by 74
  21. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 60
  22. 2020Combining data assimilation and machine learning to infer unresolved scale parametrisationcited by 40
  23. 2020Learning Variational Data Assimilation Models and Solverscited by 36
  24. 2015Black box variational inference for state space modelscited by 31
  25. 2021Variational Data Assimilation with a Learned Inverse Observation Operatorcited by 28
  26. 2022SIXO: Smoothing Inference with Twisted Objectivescited by 22
  27. 2022Posterior samples of source galaxies in strong gravitational lenses with score-based priorscited by 20
  28. 2021Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilationcited by 15
  29. 2021Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problemscited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 4; 2024: 22; 2025: 27; 2026: 43.

96 papers.

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  1. 2024All-in-one simulation-based inferencecited by 74
  2. 2024DiffDA: a Diffusion Model for Weather-scale Data Assimilationcited by 61
  3. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 61
  4. 2024On conditional diffusion models for PDE simulationscited by 60
  5. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 46
  6. 2024Variational Diffusion Posterior Sampling with Midpoint Guidancecited by 32
  7. 2024Deep Generative Data Assimilation in Multimodal Settingcited by 29
  8. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priorscited by 28
  9. 2024Generative Data Assimilation of Sparse Weather Station Observations at Kilometer Scalescited by 27
  10. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  11. 2024Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Datacited by 22
  12. 2023Towards an end-to-end artificial intelligence driven global weather forecasting systemcited by 21
38 more
  1. 2025Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilationcited by 20
  2. 2025Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulationcited by 19
  3. 2025FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilationcited by 18
  4. 2024Translation Equivariant Transformer Neural Processescited by 13
  5. 2025Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamicscited by 13
  6. 2023Score-based Data Assimilation for a Two-Layer Quasi-Geostrophic Modelcited by 12
  7. 2024A Generative Framework for Probabilistic, Spatiotemporally Coherent Downscaling of Climate Simulationcited by 12
  8. 2025Flow Matching for Efficient and Scalable Data Assimilationcited by 12
  9. 2024LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observationscited by 11
  10. 2025PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systemscited by 10
  11. 2024Neural Approximate Mirror Maps for Constrained Diffusion Modelscited by 9
  12. 2024Compositional simulation-based inference for time seriescited by 9
  13. 2025Kinetic Langevin Diffusion for Crystalline Materials Generationcited by 9
  14. 2024PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimationcited by 8
  15. 2024FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilationcited by 8
  16. 2024State-observation augmented diffusion model for nonlinear assimilation with unknown dynamicscited by 8
  17. 2024Nonlinear Assimilation via Score-based Sequential Langevin Samplingcited by 8
  18. 2025Multimodal Atmospheric Super-Resolution With Deep Generative Modelscited by 8
  19. 2025Generative emulation of chaotic dynamics with coherent priorcited by 7
  20. 2025Optimization Benchmark for Diffusion Models on Dynamical Systemscited by 7
  21. 2026Probabilistic Retrofitting of Learned Simulatorscited by 7
  22. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  23. 2025Ensemble Kalman filter in latent space using a variational autoencoder paircited by 5
  24. 2025Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferencescited by 5
  25. 2025Predicting partially observable dynamical systems via diffusion models with a multiscale inference schemecited by 5
  26. 2025DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolantscited by 5
  27. 2026Particle-Guided Diffusion Models for Partial Differential Equationscited by 5
  28. 2026LEVDA: Latent Ensemble Variational Data Assimilation via Differentiable Dynamicscited by 4
  29. 2026Training-Free Bayesian Filtering with Generative Emulatorscited by 4
  30. 2024Neural Incremental Data Assimilationcited by 3
  31. 2025Latent Twinscited by 3
  32. 2026Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilationcited by 3
  33. 2026Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systemscited by 3
  34. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 3
  35. 2023Echoes in the Noise: Posterior Samples of Faint Galaxy Surface Brightness Profiles with Score-Based Likelihoods and Priorscited by 2
  36. 2024VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilationcited by 2
  37. 2025Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulencecited by 2
  38. 2025PIRF: Physics-Informed Reward Fine-Tuning for Diffusion Modelscited by 2

50 most cited of 96 All 96 (JSON)

Similar, not cited

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  1. 2024Deep Bayesian Filter for Bayes-faithful Data Assimilation
  2. 2025Reinforcement learning based data assimilation for unknown state model
  3. 2025Prequential posteriors
  4. 2025Training-Free Data Assimilation with GenCast
  5. 2026A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systems
  6. 2026Generative models for simulation based filtering: Formulations and Empirical Comparisons
  7. 2026Correct then Forecast: Observer State-Space Models for Time Series Forecasting
  8. 2026Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds