Variational Streaming Flow: Probabilistic Forecasting in Physical Time

2026-09-30

AI Summary

This study addresses the high computational cost of flow matching and the limitation of conventional flow models to deterministic trajectories, which hinders probabilistic prediction. To overcome these challenges, this work proposes a variational flow model that integrates variational inference into flow-based architectures. By learning latent distributions over physical time and modeling continuous velocity fields, the approach transcends deterministic constraints and functions as a plug-and-play module within Joint Embedding Predictive Architecture (JEPA) world models. The proposed method demonstrates superior accuracy in long-horizon rollouts and bifurcation dynamics while significantly improving motion planning success rates. Ultimately, it achieves an effective balance between computational efficiency and distributional fidelity.

Abstract

Probabilistic forecasting is important for predicting complex dynamical systems because intrinsic randomness and incomplete observations can cause the same observed state to evolve into multiple plausible futures. While flow matching is a flexible approach for probabilistic forecasting, it is computationally expensive. Streaming flow (SF) reformulates this approach to model temporal evolution efficiently by learning a continuous velocity field directly in physical time. However, SF learns a deterministic velocity field. Thus, it provides only a single future trajectory for a given fixed initial state and observation history. To overcome this limitation, we introduce Variational Streaming Flow (VSF). Our approach learns a latent distribution that is conditioned on the dynamics of interest. In turn, this enables probabilistic forecasting. Importantly, we retain the computational efficiency of SF by generating in physical time. Across deterministic and stochastic dynamical systems, VSF demonstrates superior predictive accuracy and distributional fidelity. We demonstrate the advantage for both long-horizon rollouts exceeding 1,000 steps, and settings with bifurcating dynamics. Moreover, VSF can be integrated into existing Joint-Embedding Predictive Architecture (JEPA)-based world models as a plug-and-play predictor to improve temporal dynamics and goal-directed success rate in navigation, motion planning, and manipulation.

Problem

• probabilistic forecasting
• complex dynamical systems
• streaming flow
• deterministic velocity field

Innovation

• Variational Streaming Flow
• Probabilistic Forecasting
• Flow Matching
• Physical Time Generation
• JEPA World Models