Paper
A Long-Short Flow-Map Perspective for Drifting Models
Authors
Zhiqi Li, Bo Zhu
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.20463v1</id>\n <title>A Long-Short Flow-Map Perspective for Drifting Models</title>\n <updated>2026-02-24T01:48:52Z</updated>\n <link href='https://arxiv.org/abs/2602.20463v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.20463v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <published>2026-02-24T01:48:52Z</published>\n <arxiv:comment>25 pages, 7 figures</arxiv:comment>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Zhiqi Li</name>\n </author>\n <author>\n <name>Bo Zhu</name>\n </author>\n </entry>"
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