Thomas Savary

Thomas Savary, François Rozet, Gilles Louppe

Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and observations, but suffer from poor scalability in high dimensions. In this work, we show that diffusion-based emulators of dynamical systems can be used to implement, without additional training, an optimal variant of particle filters that has remained largely unexplored due to implementation challenges with classical numerical solvers. Experiments on nonlinear chaotic systems, including atmospheric dynamics, demonstrate that the proposed approach successfully scales particle filtering to high-dimensional settings.

Thomas Savary, François Rozet, Gilles Louppe

Data assimilation is widely used in many disciplines such as meteorology, oceanography, and robotics to estimate the state of a dynamical system from noisy observations. In this work, we propose a lightweight and general method to perform data assimilation using diffusion models pre-trained for emulating dynamical systems. Our method builds on particle filters, a class of data assimilation algorithms, and does not require any further training. As a guiding example throughout this work, we illustrate our methodology on GenCast, a diffusion-based model that generates global ensemble weather forecasts.