A Long-Short Flow-Map Perspective for Drifting Models
This provides a theoretical reinterpretation of drifting models for researchers in generative modeling and transport processes, though it appears incremental as it builds on existing drifting model frameworks.
The paper tackles the problem of modeling drifting processes by reinterpreting them through a long-short flow-map factorization, showing that global transport can be decomposed into long-horizon and short-time terminal flow maps with a closed-form optimal velocity. The result is a new likelihood learning formulation validated through theoretical analysis and empirical evaluations on benchmark tests.
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.