AI RESEARCH
Lagrangian Flow Matching: A Least-Action Framework for Principled Path Design
arXiv CS.LG
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ArXi:2605.15419v1 Announce Type: new Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the data distribution. A central design choice is the path itself. Existing constructions, including rectified and optimal-transport-based paths, transport samples along straight lines between coupled endpoints and thus cover only a narrow class of dynamics.