Training-Free Bayesian Filtering with Generative Emulators

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.

Estimating the current state of complex dynamical systems such as the ocean and the atmosphere is difficult, yet essential for improving forecasts and supporting human activities like transportation and agriculture. In this work, we propose a method that directly reuses AI forecasting models by combining them with observations to estimate the state of these systems. Together with other recent advances, this work contributes to the development of AI systems capable of better understanding and predicting the dynamics of our environment.