# Ensemble score filter with image inpainting for data assimilation in tracking surface quasi-geostrophic dynamics with partial observations

arXiv: https://arxiv.org/abs/2501.12419 · HTML: https://mlsanity.com/paper/2501.12419/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- First posted on arXiv 20 Jan 2025.

## Placed in

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

## Built on by (most cited first, 10 of 10)

- [Flow Matching for Efficient and Scalable Data Assimilation](https://mlsanity.com/paper/2508.13313/) (2025)
- [DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants](https://mlsanity.com/paper/2512.00252/) (2025)
- [A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions](https://mlsanity.com/paper/2508.06834/) (2025)
- [The Ensemble Schr"odinger Bridge filter for Nonlinear Data Assimilation](https://mlsanity.com/paper/2512.18928/) (2025)
- [A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systems](https://mlsanity.com/paper/2603.14863/) (2026)
- [Diffusion Model-Based Data Assimilation for Real-World Energy Consumption Forecasting](https://mlsanity.com/paper/2605.29072/) (2026)
- [Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Video Flow-matching](https://mlsanity.com/paper/2608.05103/) (2026)
- [FREESIA: Covariance-Aware Posterior Transport for Expressive and Scalable Data Assimilation](https://mlsanity.com/paper/2609.25085/) (2026)
- [Data-Assimilation-Assisted Reinforcement Learning for Power Grid Control under Load Uncertainty](https://mlsanity.com/paper/2609.27229/) (2026)
- [DAWIS: Data Assimilation with Windowed Inverse Sampling via Multitask Interpolants](https://mlsanity.com/paper/2610.03314/) (2026)

## Abstract (arXiv)

Data assimilation plays a pivotal role in understanding and predicting turbulent systems within geoscience and weather forecasting, where data assimilation is used to address three fundamental challenges, i.e., high-dimensionality, nonlinearity, and partial observations. Recent advances in machine learning (ML)-based data assimilation methods have demonstrated encouraging results. In this work, we develop an ensemble score filter (EnSF) that integrates image inpainting to solve the data assimilation problems with partial observations. The EnSF method exploits an exclusively designed training-free diffusion models to solve high-dimensional nonlinear data assimilation problems. Its performance has been successfully demonstrated in the context of having full observations, i.e., all the state variables are directly or indirectly observed. However, because the EnSF does not use a covariance matrix to capture the dependence between the observed and unobserved state variables, it is nontrivial to extend the original EnSF method to the partial observation scenario. In this work, we incorporate various image inpainting techniques into the EnSF to predict the unobserved states during data assimilation. At each filtering step, we first use the diffusion model to estimate the observed states by integrating the likelihood information into the score function. Then, we use image inpainting methods to predict the unobserved state variables. We demonstrate the performance of the EnSF with inpainting by tracking the Surface Quasi-Geostrophic (SQG) model dynamics under a variety of scenarios. The successful proof of concept paves the way to more in-depth investigations on exploiting modern image inpainting techniques to advance data assimilation methodology for practical geoscience and weather forecasting problems.