# FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation

arXiv: https://arxiv.org/abs/2501.16642 · HTML: https://mlsanity.com/paper/2501.16642/

## Key facts

- Cited by 18 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 23 of its 78 references that are in the map.
- First posted on arXiv 13 Jan 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, 23 of 23)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [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)
- [MAGVIT: Masked Generative Video Transformer](https://mlsanity.com/paper/2212.05199/) (2022)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolation](https://mlsanity.com/paper/2205.09853/) (2022)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [PreDiff: Precipitation Nowcasting with Latent Diffusion Models](https://mlsanity.com/paper/2307.10422/) (2023)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Conditional Simulation Using Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2202.13460/) (2022)
- [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024)
- [An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems](https://mlsanity.com/paper/2309.00983/) (2023)
- [Deep Generative Data Assimilation in Multimodal Setting](https://mlsanity.com/paper/2404.06665/) (2024)
- [Fuxi-DA: A Generalized Deep Learning Data Assimilation Framework for Assimilating Satellite Observations](https://mlsanity.com/paper/2404.08522/) (2024)
- [Blind Inversion using Latent Diffusion Priors](https://mlsanity.com/paper/2407.01027/) (2024)
- [ADAF: An Artificial Intelligence Data Assimilation Framework for Weather Forecasting](https://mlsanity.com/paper/2411.16807/) (2024)
- [A Score-based Nonlinear Filter for Data Assimilation](https://mlsanity.com/paper/2306.09282/) (2023)
- [FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilation](https://mlsanity.com/paper/2406.01645/) (2024)
- [AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage](https://mlsanity.com/paper/2402.06110/) (2024)
- [Sim2Real in Reconstructive Spectroscopy: Deep Learning with Augmented Device-Informed Data Simulation](https://mlsanity.com/paper/2403.12354/) (2024)

## Built on by (most cited first, 18 of 18)

- [DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants](https://mlsanity.com/paper/2512.00252/) (2025)
- [SerpentFlow: Generative Unpaired Domain Alignment via Shared-Structure Decomposition](https://mlsanity.com/paper/2601.01979/) (2026)
- [LEVDA: Latent Ensemble Variational Data Assimilation via Differentiable Dynamics](https://mlsanity.com/paper/2602.19406/) (2026)
- [Training-Free Bayesian Filtering with Generative Emulators](https://mlsanity.com/paper/2605.20028/) (2026)
- [SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate](https://mlsanity.com/paper/2605.18745/) (2026)
- [Reframing Generative Models for Physical Systems using Stochastic Interpolants](https://mlsanity.com/paper/2509.26282/) (2025)
- [Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective](https://mlsanity.com/paper/2602.05319/) (2026)
- [Variational Optimality of F"ollmer Processes in Generative Diffusions](https://mlsanity.com/paper/2602.10989/) (2026)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (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)
- [PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation](https://mlsanity.com/paper/2609.26890/) (2026)
- [EnJoi: Ensemble Joint Score Filter for Generative Data Assimilation](https://mlsanity.com/paper/2609.35944/) (2026)
- [DAWIS: Data Assimilation with Windowed Inverse Sampling via Multitask Interpolants](https://mlsanity.com/paper/2610.03314/) (2026)
- [A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants](https://mlsanity.com/paper/2610.03396/) (2026)
- [LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2610.04034/) (2026)
- [Xaurora: Generative Weather Forecasting with Denoising Stochastic Interpolants from a Foundation Model Prior](https://mlsanity.com/paper/2610.06509/) (2026)
- [Probabilistic Simulation of Gas-Liquid Interfaces with Coupled Flow Matching on Spherical Harmonics](https://mlsanity.com/paper/2610.16327/) (2026)

## Abstract (arXiv)

Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in practice, while purely data-driven solvers learn a deterministic mapping between observations and states and therefore miss the intrinsic stochasticity of real processes. Recently, score-based diffusion models learn a global diffusion prior and provide a good modeling of the stochastic dynamics, showing new potential for DA. However, their all-at-once generation rather than step-by-step transition limits their performance when dealing with highly complex stochastic processes and lacks physical interpretability. To tackle these drawbacks, we introduce FlowDAS, a generative DA framework that uses stochastic interpolants to directly learn state transition dynamics and achieve step-by-step transition to better model the real dynamics. We also improve the framework by combining the observation, better suiting the DA settings. Directly learning the underlying dynamics from collected data removes restrictive dynamical assumptions, and conditioning on observations at each interpolation step yields stable, measurement-consistent forecasts. Experiments on Lorenz-63, Navier-Stokes super-resolution/sparse-observation scenarios, and large-scale weather forecasting -- where dynamics are partly or wholly unknown -- show that FlowDAS surpasses model-driven methods, neural operators, and score-based baselines in accuracy and physical plausibility.