# A Score-based Nonlinear Filter for Data Assimilation

arXiv: https://arxiv.org/abs/2306.09282 · HTML: https://mlsanity.com/paper/2306.09282/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2023.

## Built on by (most cited first, 8 of 8)

- [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025)
- [Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation](https://mlsanity.com/paper/2310.14458/) (2023)
- [Bifidelity Parameter Estimation Using Conditional Diffusion Models](https://mlsanity.com/paper/2504.01894/) (2025)
- [A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics](https://mlsanity.com/paper/2407.12168/) (2024)
- [SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate](https://mlsanity.com/paper/2605.18745/) (2026)
- [Pathwise Learning of Stochastic Dynamical Systems with Partial Observations](https://mlsanity.com/paper/2601.21860/) (2026)
- [Diffusion Model-Based Data Assimilation for Real-World Energy Consumption Forecasting](https://mlsanity.com/paper/2605.29072/) (2026)
- [EnJoi: Ensemble Joint Score Filter for Generative Data Assimilation](https://mlsanity.com/paper/2609.35944/) (2026)

## Abstract (arXiv)

We introduce a score-based generative sampling method for solving the nonlinear filtering problem with robust accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low stability. To overcome this issue, we adopt the diffusion model framework to solve the nonlinear filtering problem. In stead of storing the information of the filtering density in finite number of Monte Carlo samples, in the score-based filter we store the information of the filtering density in the score model. Then, via the reverse-time diffusion sampler, we can generate unlimited samples to characterize the filtering density. Moreover, with the powerful expressive capabilities of deep neural networks, it has been demonstrated that a well trained score in diffusion model can produce samples from complex target distributions in very high dimensional spaces. Extensive numerical experiments show that our score-based filter could potentially address the curse of dimensionality in very high dimensional problems.