Generative Model Proposal based Particle Filtering for Data Assimilation

Data assimilation (DA) models state dynamics conditioned on sequential observations, with wide-ranging scientific applications. In filtering, the goal is to model the posterior over the current state given all observations so far. Classical solutions make simplifying distributional or functional assumptions, e.g., linear-Gaussian systems, which can be inaccurate. In principle, particle filters remove these assumptions, yet often collapse in high dimensions. Recent generative DA approaches learn conditional state transitions, but typically incorporate observations through approximate guidance, so errors can accumulate over long horizons. We introduce Flow Proposal Particle Filters (FPPF), which learn a conditional generative-model-based proposal approximating the variance-minimizing optimal proposal. Conditioning on observations steers particles toward high-likelihood regions before weighting, reducing weight variance and delaying degeneracy. Since our proposal admits tractable likelihood evaluation, FPPF computes accurate importance weights and retains a Bayesian update. We further introduce L-FPPF, which uses localization to scale FPPF to high-dimensional systems where global particle filters collapse. Experiments on chaotic dynamical systems and multimodal observations of severe convective storms show that FPPF improves accuracy and calibration over several statistical baselines and other generative DA methods, especially in strongly nonlinear settings, and remains stable over long horizons.