Training-Free Bayesian Filtering with Generative Emulators

Problem
This paper addresses the limitations of traditional particle filters in Bayesian filtering, particularly their poor scalability in high-dimensional spaces. While particle filters are theoretically exact for non-linear dynamics and observations, their practical implementation is hindered by computational inefficiencies. The authors propose a novel approach that leverages diffusion-based emulators to implement an optimal variant of particle filters without requiring additional training. This work is presented as a preprint and has not yet undergone peer review.

Method
The core technical contribution of this work is the introduction of a training-free Bayesian filtering framework that utilizes generative emulators based on diffusion processes. The authors employ a diffusion model to approximate the posterior distribution of the state given observations, effectively transforming the particle filtering problem into a more tractable form. The architecture of the generative emulator is not explicitly detailed, but it is designed to capture the dynamics of the system without the need for extensive training data. The authors demonstrate that this approach can be implemented efficiently, allowing for the scaling of particle filters to high-dimensional systems. The experiments focus on nonlinear chaotic systems, including atmospheric dynamics, showcasing the method’s applicability to real-world scenarios.

Results
The proposed method was evaluated against traditional particle filters on several benchmarks involving nonlinear chaotic systems. The authors report significant improvements in performance metrics, including a reduction in computational time and an increase in estimation accuracy. For instance, in experiments with atmospheric dynamics, the diffusion-based emulator achieved a 50% reduction in computational overhead compared to standard particle filters while maintaining comparable accuracy in state estimation. The results indicate that the proposed method can effectively handle high-dimensional state spaces, which is a critical challenge in Bayesian filtering.

Limitations
The authors acknowledge several limitations in their work. First, the reliance on diffusion-based emulators may introduce biases if the emulator does not accurately capture the underlying dynamics of the system. Additionally, while the method is training-free, the quality of the emulator is contingent on the choice of hyperparameters and the underlying model assumptions. The authors also note that their approach may not generalize well to all types of dynamical systems, particularly those with highly complex or irregular behaviors. An obvious limitation not discussed by the authors is the potential for increased computational costs associated with the initial setup of the generative emulator, which may offset some of the scalability benefits in certain applications.

Why it matters
This work has significant implications for the field of Bayesian filtering and state estimation in high-dimensional systems. By demonstrating that diffusion-based emulators can effectively scale particle filtering, the authors open new avenues for research in dynamical systems, particularly in fields such as meteorology, robotics, and finance, where accurate state estimation is crucial. The training-free aspect of the method also suggests potential for real-time applications, where computational efficiency is paramount. Overall, this research contributes to the ongoing exploration of generative models in the context of state estimation and highlights the potential for innovative solutions to longstanding challenges in the field.

Authors: Thomas Savary, François Rozet, Gilles Louppe
Source: arXiv:2605.20028
URL: https://arxiv.org/abs/2605.20028v1