Training-Free Bayesian Filtering with Generative Emulators
This work addresses the scalability bottleneck of particle filters for high-dimensional Bayesian filtering in dynamical systems.
The authors show that diffusion-based emulators of dynamical systems can implement an optimal variant of particle filters without additional training, scaling particle filtering to high-dimensional settings like atmospheric dynamics.
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.