New method generates smooth trajectories from discrete noisy data
Continuous-Time Trajectory Generation from Discrete Observations with Stochasticity
Machine Learning
Summary
Physical systems change continuously over time, but we often only get snapshots at certain moments. This paper presents PhiBE-Flow, a new way to recreate smooth, realistic paths between those snapshots that match how the system truly behaves over time, even if the process has randomness. Unlike other methods, it doesn’t need to know all the system details or rely on complex calculations about probability gradients. The authors tested their method on both simulated and real data, including fluid flow and videos, showing it can create accurate continuous-time descriptions and improve video generation.
What this means in practice
- •For simulation engineers: Generate smooth trajectories between sparse sensor readings in physical simulations without assuming known system models.
- •For computer vision developers: Improve video frame interpolation and generation by modeling continuous stochastic dynamics from discrete frames.
Authors
Ruifeng Shang, Shu Liu, Yuhua Zhu
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.