# Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective

arXiv: https://arxiv.org/abs/2602.05319 · HTML: https://mlsanity.com/paper/2602.05319/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 49 of its 75 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 49)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [GenAD: Generalized Predictive Model for Autonomous Driving](https://mlsanity.com/paper/2403.09630/) (2024)
- [Consistency Models Made Easy](https://mlsanity.com/paper/2406.14548/) (2024)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Model Predictive Path Integral Control using Covariance Variable Importance Sampling](https://mlsanity.com/paper/1509.01149/) (2015)

## Built on by (most cited first, 1 of 1)

- [Variational Streaming Flow: Probabilistic Forecasting in Physical Time](https://mlsanity.com/paper/2610.00976/) (2026)

## Abstract (arXiv)

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.