arXiv：cs.LG· Soon Hoe Lim, Shizheng Lin, Michael W. Mahoney, N. Benjamin Erichson·· 16 小时前
流匹配只是轨迹重放？FreeFM 给出无训练闭式参考实现
Is Flow Matching Just Trajectory Replay for Sequential Data?
AI 导读
研究推导了序列数据上经验流匹配（FM）目标所指向的最优速度场，证明其采样器是一个非参数、记忆增强的连续时间动力系统，速度场可写成由观测转移决定的瞬时速度加权混合的闭式表达。基于此提出 FreeFM——该目标的闭式、免训练实现，可直接由历史转移生成概率预测，为研究序列 FM 提供透明参考。
正文
Abstract:Flow matching (FM) is increasingly used in scientific domains for time series generation and forecasting, where data often arise from underlying dynamical systems. However, it is not well-understood whether it learns transferable dynamical structure or simply performs an effective ''trajectory replay''. We study this question by deriving the optimal velocity field targeted by the empirical FM objective on sequential data. For the Gaussian conditional paths commonly used in practice, we show that the resulting sampler is an ODE whose dynamics describe a nonparametric, memory-augmented continuous-time dynamical system. The driving velocity field admits a closed-form expression as a weighted mixture of instantaneous velocities determined by observed transitions. This characterization provides an interpretable view of neural FM models as parametric estimation of an underlying nonparametric target and naturally leads to FreeFM: a closed-form, training-free realization of this target. FreeFM provides a transparent reference for studying sequential FM while yielding effective probabilistic forecasts directly from historical transitions.
| Comments: | 60 pages |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD) |
| Cite as: | arXiv:2602.08318 [stat.ML] |
| (or arXiv:2602.08318v3 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2602.08318 arXiv-issued DOI via DataCite |
Submission history
From: Soon Hoe Lim [view email]
[v1]
Mon, 9 Feb 2026 06:48:45 UTC (14,234 KB)
[v2]
Thu, 7 May 2026 12:57:02 UTC (5,906 KB)
[v3]
Wed, 14 Oct 2026 03:01:43 UTC (5,803 KB)
来源：arXiv：cs.LG · arxiv.org