通过长短流图分解重释漂移模型，提升对动态系统演化建模的准确性。
A Long-Short Flow-Map Perspective for Drifting Models
- 将全局传输过程分解为长时流图与短时终端流图
- 终端区间趋零时精确恢复漂移场与保守冲量项
- 适用于需要精准建模动态演化过程的研究者
本文通过半群一致性的时间-空间流图因子分解，重新诠释了漂移模型~\cite{deng2026generative}。我们证明全局传输过程可分解为一个长时流图与一个具有闭式最优速度表示的短时终端流图；当终端区间长度趋于零时，恰好恢复漂移场及保证流图一致性的保守冲量项。基于此视角，我们提出一种新的似然学习公式，使长短流图分解与传输下的密度演化相匹配。通过理论分析和基准测试的实证评估验证了该框架的有效性，并对特征空间优化提供了理论解释，同时指出了若干待解决的开放问题。
原文摘要 · Abstract (English)
This paper provides a reinterpretation of the Drifting Model~\cite{deng2026generative} through a semigroup-consistent long-short flow-map factorization. We show that a global transport process can be decomposed into a long-horizon flow map followed by a short-time terminal flow map admitting a closed-form optimal velocity representation, and that taking the terminal interval length to zero recovers exactly the drifting field together with a conservative impulse term required for flow-map consistency. Based on this perspective, we propose a new likelihood learning formulation that aligns the long-short flow-map decomposition with density evolution under transport. We validate the framework through both theoretical analysis and empirical evaluations on benchmark tests, and further provide a theoretical interpretation of the feature-space optimization while highlighting several open problems for future study.
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