A Long-Short Flow-Map Perspective for Drifting Models

• URL: http://arxiv.org/abs/2602.20463v1
• Date: Tue, 24 Feb 2026 01:48:52 GMT
• Title: A Long-Short Flow-Map Perspective for Drifting Models
• Authors: Zhiqi Li, Bo Zhu,
• Abstract summary: We show that a global transport process can be decomposed into a long-horizon flow map followed by a short-time terminal flow map.<n>We propose a new likelihood learning formulation that aligns the long-short flow-map decomposition with density evolution under transport.
• Score: 10.305612650249804
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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