# Flow Matching for Efficient and Scalable Data Assimilation

arXiv: https://arxiv.org/abs/2508.13313 · HTML: https://mlsanity.com/paper/2508.13313/

## Key facts

- Cited by 12 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 24 of its 59 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Coupling techniques for nonlinear ensemble filtering](https://mlsanity.com/paper/1907.00389/) (2019)
- [On the Guidance of Flow Matching](https://mlsanity.com/paper/2502.02150/) (2025)
- [Memorization and Regularization in Generative Diffusion Models](https://mlsanity.com/paper/2501.15785/) (2025)
- [An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems](https://mlsanity.com/paper/2309.00983/) (2023)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Learning Enhanced Ensemble Filters](https://mlsanity.com/paper/2504.17836/) (2025)
- [Ensemble score filter with image inpainting for data assimilation in tracking surface quasi-geostrophic dynamics with partial observations](https://mlsanity.com/paper/2501.12419/) (2025)
- [Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting](https://mlsanity.com/paper/2409.09800/) (2024)
- [Local Flow Matching Generative Models](https://mlsanity.com/paper/2410.02548/) (2024)

## Built on by (most cited first, 12 of 12)

- [DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants](https://mlsanity.com/paper/2512.00252/) (2025)
- [Training-Free Bayesian Filtering with Generative Emulators](https://mlsanity.com/paper/2605.20028/) (2026)
- [Closed-form conditional diffusion models for data assimilation](https://mlsanity.com/paper/2603.21291/) (2026)
- [Second Order Drifting Models](https://mlsanity.com/paper/2608.07924/) (2026)
- [FlowDA: Accurate, Low-Latency Weather Data Assimilation via Flow Matching](https://mlsanity.com/paper/2602.06800/) (2026)
- [Generative Model Proposal based Particle Filtering for Data Assimilation](https://mlsanity.com/paper/2607.01012/) (2026)
- [Ensemble Controlled-Flow Filtering for Implicit Data Assimilation](https://mlsanity.com/paper/2607.12975/) (2026)
- [Generative models for simulation based filtering: Formulations and Empirical Comparisons](https://mlsanity.com/paper/2609.16317/) (2026)
- [FREESIA: Covariance-Aware Posterior Transport for Expressive and Scalable Data Assimilation](https://mlsanity.com/paper/2609.25085/) (2026)
- [Improving Ensemble Filters with Flow Matching](https://mlsanity.com/paper/2609.28015/) (2026)
- [AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation](https://mlsanity.com/paper/2609.32411/) (2026)
- [LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2610.04034/) (2026)

## 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.