Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective

Sequential probabilistic inference from streaming observations requires tracking distributions over future trajectories as new observations arrive. Although diffusion models can effectively capture complex distributions, their generation in streaming settings typically requires repeatedly transporting a non-informative source such as Gaussian noise to the target distribution. This noise-to-target transport incurs substantial inference latency and makes efficient high-fidelity sampling challenging. 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, as consecutive posteriors share common structure, the sequential flow only needs to learn the distributional update which enables substantially faster sampling than na\"ive 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 5-20 times fewer sampling steps, substantially reducing inference latency.