Problem
Research questions and friction points this paper is trying to address.
continuous-time trajectory generation
discrete observations
stochastic dynamics
probability velocity field
Continuous-Time Trajectory Generation from Discrete Observations with Stochasticity
🤖 AI Summary
This study addresses the limitation of existing methods that predominantly rely on discrete transition maps, making it challenging to generate trajectories consistent with continuous-time probability densities from discrete observations. To overcome this, we propose PhiBE-Flow, a framework integrating stochastic differential equations (SDEs) with flow matching techniques. Without requiring known SDE coefficients or score estimation, PhiBE-Flow directly learns the probability velocity field induced by the SDE, enabling model-free continuous trajectory generation with theoretical convergence guarantees. The proposed method accurately recovers probability flows and captures multi-scale physical statistical properties. Extensive experiments demonstrate that PhiBE-Flow significantly outperforms baseline approaches in both Navier-Stokes dynamics modeling and video generation tasks.
📝 Abstract
Physical systems evolve continuously in time, yet their states are typically observed only at discrete times. Generating trajectories consistent with their probability densities from such observations therefore requires capturing the continuous-time evolution rather than only learning transition mappings between consecutive observations. We propose PhiBE-Flow, a framework that directly estimates the probability velocity field induced by the stochastic differential equation (SDE) which governs this continuous-time distributional evolution. PhiBE-Flow learns from discrete observations using a model-free approach requiring neither known SDE coefficients nor score estimation. We establish convergence guarantees for the method, accounting for both time-discretization and finite-sample errors. We evaluate PhiBE-Flow on systems of increasing complexity, from controlled stochastic numerical systems to Navier--Stokes dynamics and real-world videos. Our results show that PhiBE-Flow accurately recovers probability flows of stochastic dynamics, preserves multiscale physical statistics, and improves video generation performance over representative baselines. The code is available at https://github.com/R1fe/PhiBE-Flow.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Continuous-time trajectory generation
Stochastic differential equations
Probability velocity field
Model-free learning
Score estimation
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