发表机构
University of Chicago; Florida State University; University of California, Los Angeles（芝加哥大学; 佛罗里达州立大学; 加州大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对物理系统离散观测下的连续时间轨迹生成问题，提出PhiBE-Flow框架，直接估计随机微分方程的概率速度场，无需模型系数或分数估计，具备收敛保证，在数值系统、Navier-Stokes及真实视频上验证了有效性。
AI 中文摘要
物理系统在时间上连续演化，但其状态通常仅在离散时间点被观测到。要从这类观测中生成与其概率密度一致的轨迹，需要捕捉连续时间的演化过程，而不仅仅是学习连续观测之间的转移映射。我们提出了PhiBE-Flow，一个直接估计控制这种连续时间分布演化的随机微分方程（SDE）所诱导的概率速度场的框架。PhiBE-Flow采用无模型方法从离散观测中学习，既不需要已知的SDE系数，也不需要分数估计。我们为该方法的收敛性提供了保证，同时考虑了时间离散化和有限样本误差。我们在复杂度递增的系统上评估了PhiBE-Flow，从受控随机数值系统到Navier-Stokes动力学和真实世界视频。结果表明，PhiBE-Flow能准确恢复随机动力学的概率流，保留多尺度物理统计量，并在视频生成性能上优于代表性基线。代码可在该https URL获取。
英文摘要
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.
