# AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation

arXiv: https://arxiv.org/abs/2609.32411 · HTML: https://mlsanity.com/paper/2609.32411/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance](https://mlsanity.com/paper/2402.02149/) (2024)
- [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)
- [A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems](https://mlsanity.com/paper/2410.03108/) (2024)
- [Flow Matching for Efficient and Scalable Data Assimilation](https://mlsanity.com/paper/2508.13313/) (2025)
- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Bifidelity Parameter Estimation Using Conditional Diffusion Models](https://mlsanity.com/paper/2504.01894/) (2025)
- [Diffusion Path Samplers via Sequential Monte Carlo](https://mlsanity.com/paper/2601.21951/) (2026)
- [A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions](https://mlsanity.com/paper/2508.06834/) (2025)
- [A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systems](https://mlsanity.com/paper/2603.14863/) (2026)
- [Closed-form conditional diffusion models for data assimilation](https://mlsanity.com/paper/2603.21291/) (2026)
- [Exact Conditional Score-Guided Generative Modeling for Amortized Inference in Uncertainty Quantification](https://mlsanity.com/paper/2506.18227/) (2025)
- [Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solver](https://mlsanity.com/paper/2508.02964/) (2025)
- [Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance](https://mlsanity.com/paper/2601.21104/) (2026)

## Abstract (arXiv)

Bayesian state estimation for high-dimensional nonlinear dynamical systems entails a fundamental tension between statistical fidelity and computational tractability, as particle weights can collapse, while Gaussian ensemble updates can miss non-Gaussian posterior structure. Score-based diffusion filters offer a sampling-based alternative, but existing training-free score filters often rely on heuristic likelihood corrections, which can compromise posterior accuracy by neglecting uncertainty about the system state associated with each noisy reverse particle. To address these issues, we propose AECSF, a training-free adaptive ensemble conditional score filter. AECSF constructs an analytically tractable score estimator from the conditional Tweedie identity, which recasts noisy posterior score estimation as estimating the conditional mean of the system state given a noisy reverse particle and the observation. To estimate these conditional means efficiently, AECSF employs a shared adaptive weighted proposal ensemble, while particle-specific conditional weights yield an estimate for each noisy reverse particle without separate proposal sampling. The proposal ensemble is updated using reverse-particle information within the same reverse-diffusion run to improve conditional-mean estimation. Theoretically, we characterize when a fixed weighted proposal measure yields the exact noisy posterior score. Under stated assumptions, we establish a bound relating conditional-mean estimation errors to reverse-sampling endpoint error. Numerical experiments demonstrate that AECSF improves the accuracy of posterior sampling and nonlinear filtering in high-dimensional problems with limited forecast ensembles.