Training-Free Bayesian Filtering with Generative Emulators

2026-05-19

AI Summary

This work addresses the challenges of Bayesian filtering in high-dimensional nonlinear dynamical systems, where particle degeneracy and prohibitive computational costs severely limit scalability. The study proposes a novel approach that integrates a pretrained diffusion model as a training-free generative dynamics simulator within a particle filtering framework. By circumventing the constraints of conventional numerical solvers, this method enables a theoretically optimal filtering variant previously deemed infeasible. Notably, it requires no additional training and can be efficiently deployed in high-dimensional chaotic systems—such as those arising in atmospheric dynamics—yielding substantial improvements in both estimation accuracy and computational scalability.

Abstract

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.

Problem

• Bayesian filtering
• particle filters
• high-dimensional systems
• nonlinear dynamics
• scalability

Innovation

• diffusion-based emulators
• training-free
• Bayesian filtering
• particle filters
• high-dimensional scalability