Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective

TL;DR

This paper introduces Sequential Bayesian Flow Matching, a Bayesian filtering-inspired framework that accelerates probabilistic inference in streaming settings by reducing sampling steps and inference latency.

Contribution

It presents a novel recursive Bayesian filtering approach for flow matching, enabling faster sampling in high-dimensional probabilistic models for real-time applications.

Findings

Achieves comparable distributional performance with fewer sampling steps.

Reduces inference latency significantly in scientific forecasting tasks.

Demonstrates effectiveness across diverse real-world applications.

Abstract

Sequential probabilistic inference from streaming observations requires modeling distributions over future trajectories as new observations arrive. Although diffusion and flow-matching models are effective at capturing high-dimensional, multimodal distributions, their deployment in real-time streaming settings typically relies on repeatedly sampling from a non-informative initial distribution. This results in substantial inference latency, particularly when multiple samples are needed to characterize the predictive distribution. In this work, we introduce Sequential Bayesian Flow Matching, a framework inspired by Bayesian filtering. By learning a probability flow that transports the posterior distribution from one time step to the next time step conditioned on new observations, it mirrors the recursive structure of Bayesian belief updates. Crucially, by using the previous belief as an informative source distribution, it enables substantially faster sampling than naive resampling from scratch. Across scientific forecasting tasks spanning accelerator beam spill dynamics, fluid dynamics, and weather forecasting, as well as decision-making benchmarks, our method achieves performance competitive with full-step diffusion on distributional metrics while using far fewer sampling steps, substantially reducing inference latency. Our code is available at https://github.com/Graph-COM/Sequential_Flow_Matching.