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Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective

Yinan Huang, Hans Hao-Hsun Hsu, Junran Wang, Bo Dai, Pan Li

TL;DR

This work reframes sequential inference in streaming stochastic systems as a Bayesian filtering problem and introduces Sequential Flow Matching, which learns a probability flow transporting the predictive distribution from $p(x_{t-1}|z_{\le t-1})$ to $p(x_t|z_{\le t})$. By leveraging the previous posterior as a principled warm start, the method reduces sampling error compared to restarting from a non-informative base and achieves performance competitive with full-step diffusion using only one or a few sampling steps. Across forecasting, planning/control, and state estimation tasks, it demonstrates favorable fidelity-latency tradeoffs, enabling real-time deployment of flow-based models. The approach provides a principled perspective on efficient sequential inference, with practical gains in latency and robustness, though it relies on a pretraining-generation-finetuning pipeline and could benefit from simulation-free training in future work.

Abstract

Sequential prediction from streaming observations is a fundamental problem in stochastic dynamical systems, where inherent uncertainty often leads to multiple plausible futures. While diffusion and flow-matching models are capable of modeling complex, multi-modal trajectories, their deployment in real-time streaming environments typically relies on repeated sampling from a non-informative initial distribution, incurring substantial inference latency and potential system backlogs. In this work, we introduce Sequential Flow Matching, a principled framework grounded in Bayesian filtering. By treating streaming inference as learning a probability flow that transports the predictive distribution from one time step to the next, our approach naturally aligns with the recursive structure of Bayesian belief updates. We provide theoretical justification that initializing generation from the previous posterior offers a principled warm start that can accelerate sampling compared to naïve re-sampling. Across a wide range of forecasting, decision-making and state estimation tasks, our method achieves performance competitive with full-step diffusion while requiring only one or very few sampling steps, therefore with faster sampling. It suggests that framing sequential inference via Bayesian filtering provides a new and principled perspective towards efficient real-time deployment of flow-based models.

Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective

TL;DR

This work reframes sequential inference in streaming stochastic systems as a Bayesian filtering problem and introduces Sequential Flow Matching, which learns a probability flow transporting the predictive distribution from to . By leveraging the previous posterior as a principled warm start, the method reduces sampling error compared to restarting from a non-informative base and achieves performance competitive with full-step diffusion using only one or a few sampling steps. Across forecasting, planning/control, and state estimation tasks, it demonstrates favorable fidelity-latency tradeoffs, enabling real-time deployment of flow-based models. The approach provides a principled perspective on efficient sequential inference, with practical gains in latency and robustness, though it relies on a pretraining-generation-finetuning pipeline and could benefit from simulation-free training in future work.

Abstract

Sequential prediction from streaming observations is a fundamental problem in stochastic dynamical systems, where inherent uncertainty often leads to multiple plausible futures. While diffusion and flow-matching models are capable of modeling complex, multi-modal trajectories, their deployment in real-time streaming environments typically relies on repeated sampling from a non-informative initial distribution, incurring substantial inference latency and potential system backlogs. In this work, we introduce Sequential Flow Matching, a principled framework grounded in Bayesian filtering. By treating streaming inference as learning a probability flow that transports the predictive distribution from one time step to the next, our approach naturally aligns with the recursive structure of Bayesian belief updates. We provide theoretical justification that initializing generation from the previous posterior offers a principled warm start that can accelerate sampling compared to naïve re-sampling. Across a wide range of forecasting, decision-making and state estimation tasks, our method achieves performance competitive with full-step diffusion while requiring only one or very few sampling steps, therefore with faster sampling. It suggests that framing sequential inference via Bayesian filtering provides a new and principled perspective towards efficient real-time deployment of flow-based models.
Paper Structure (30 sections, 2 theorems, 20 equations, 7 figures, 7 tables, 2 algorithms)

This paper contains 30 sections, 2 theorems, 20 equations, 7 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Bayesian Sequential Flow Matching
  4. Problem Setup and Bayesian Filtering
  5. Sequential Inference with Flow-based Models: Existing Practices
  6. Sequential Flow Matching
  7. Practical Implementation
  8. Related Works
  9. Experiment
  10. Physical System Forecasting
  11. Planning and Control
  12. State Estimation
  13. Performance and Latency Tradeoffs
  14. Ablation Study
  15. Conclusion and Limitations
  16. ...and 15 more sections

Key Result

Proposition 3.1

Denote the short hand for distribution $p(x_{t}|z_{\le t})$ by $p$. Consider flow matching with straight interpolation $x_t(\tau)=(1-\tau)x_t(0)+\tau x_t(1)$ and two different couplings of $(x_t(0),x_t(1))$: (A) independent Gaussian coupling. Suppose $x_t(0)\sim p(x_t|z_{\le t})$ and $x_t(1)\sim \ma which implies $\mathcal{W}_2(p_{\text{Gaussian}}, p)-\mathcal{W}_2(p_{\text{Bayes}}, p)=\operatorna

Figures (7)

  • Figure 1: Illustration of the sequential inference problems using streaming forecasting as examples. A: The sequential inference problem $p(x_t|z_{\le t})$ that predicts future states given historical observations over time $t=1,2,...,T$. B: Bayesian filtering framework refines previous predictions based on latest observations to obtain new estimations. C: Following the idea of Bayesian filtering, sequential flow matching leverages a probability flow to recursively transport from previous belief $p(x_{t-1}|z_{\le t-1})$ to current belief $p(x_t|z_{\le t})$.
  • Figure 2: Inference latency v.s. performance for maze planning under varying sampling steps (1, 2, 3, 4, 5, 8, 10, 20 and 50 steps). DF: Pyramid and DF: Full-sequence refer to two denoising schedules of diffusion forcing. Sequential DF uses full sequence denoising.
  • Figure 3: RMSE of Burgers' equation as a function of forecast lead time.
  • Figure 4: Inference latency for smoke control under varying sampling timesteps (1, 2, 3, 5, 10, and 15 steps). Wall-clock time is computed per instance and averaged across both physical time steps and the test set.
  • Figure 5: Performance as a function of re-noise level $\tau_{\text{renoise}}$ on state estimation. Left and right figures are at different system uncertainty levels.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Proposition 3.1: One-step Sampling Error
  • Lemma A.1: One-step Sampling Distribution
  • proof
  • proof