mlsanityData to 7 Oct 2026

Flow Matching for Efficient and Scalable Data Assimilation

arXiv 2508.13313 ↗First posted 18 Aug 2025stat.ML cs.LG math.OCcited by 11

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

Abstract (arXiv)

Data assimilation (DA) estimates a dynamical system's state from noisy observations. Recent generative models like the ensemble score filter (EnSF) improve DA in high-dimensional nonlinear settings but are computationally expensive. We introduce the ensemble flow filter (EnFF), a training-free, flow matching (FM)-based framework that accelerates sampling and offers flexibility in flow design. EnFF uses Monte Carlo estimators for the marginal flow field, localized guidance for observation assimilation, and utilizes a novel flow path that exploits the Bayesian DA formulation. It generalizes classical filters such as the bootstrap particle filter and ensemble Kalman filter. Experiments on high-dimensional benchmarks demonstrate EnFF's improved cost-accuracy tradeoffs and scalability, highlighting FM's potential for efficient, scalable DA. Code is available at https://github.com/Utah-Math-Data-Science/Data-Assimilation-Flow-Matching.

Key facts. Cited by 11 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 24 of its 59 references that are in the map. First posted on arXiv 18 Aug 2025.

Builds on

24 of 59 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025On the Guidance of Flow Matching4 Feb
  2. 2025Ensemble score filter with image inpainting for data assimilation in tracking surface quasi-geostrophic dynamics with partial observations20 Jan
  3. 2024Local Flow Matching Generative Models3 Oct
  4. 2024DiffDA: a Diffusion Model for Weather-scale Data Assimilation11 Jan
  5. 2023An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems2 Sep
  6. 2023Improving and generalizing flow-based generative models with minibatch optimal transport1 Feb
  7. 2022Flow Matching for Generative Modeling6 Oct
  8. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 16

  1. 2020Denoising Diffusion Implicit Modelscited by 9,655
  2. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,455
  3. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  5. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  6. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  7. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Modelscited by 441
  8. 2023Stochastic interpolants with data-dependent couplingscited by 94
  9. 2023Score-based Data Assimilationcited by 91
  10. 2016Variational Fourier features for Gaussian processescited by 85
  11. 2019Coupling techniques for nonlinear ensemble filteringcited by 48
  12. 2025Memorization and Regularization in Generative Diffusion Modelscited by 39
4 more
  1. 2024Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Datacited by 20
  2. 2025Learning Enhanced Ensemble Filterscited by 11
  3. 2024LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observationscited by 10
  4. 2024Accuracy of the Ensemble Kalman Filter in the Near-Linear Settingcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 10.

11 papers.

  1. 2025DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolantscited by 3
  2. 2026Closed-form conditional diffusion models for data assimilationcited by 3
  3. 2026Training-Free Bayesian Filtering with Generative Emulatorscited by 2
  4. 2026Second Order Drifting Modelscited by 1
  5. 2026FlowDA: Accurate, Low-Latency Weather Data Assimilation via Flow Matchingcited by 0
  6. 2026Generative Model Proposal based Particle Filtering for Data Assimilationcited by 0
  7. 2026Ensemble Controlled-Flow Filtering for Implicit Data Assimilationcited by 0
  8. 2026Generative models for simulation based filtering: Formulations and Empirical Comparisonscited by 0
  9. 2026FREESIA: Covariance-Aware Posterior Transport for Expressive and Scalable Data Assimilationcited by 0
  10. 2026Improving Ensemble Filters with Flow Matchingcited by 0
  11. 2026AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations
  2. 2026EnJoi: Ensemble Joint Score Filter for Generative Data Assimilation
  3. 2024A competitive baseline for deep learning enhanced data assimilation using conditional Gaussian ensemble Kalman filtering
  4. 2025FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation
  5. 2026A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systems
  6. 2026A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants
  7. 2026DAWIS: Data Assimilation with Windowed Inverse Sampling via Multitask Interpolants
  8. 2026Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Video Flow-matching