Gaussian Flow-Matching Schedules: Implications for Sampling and Training

Abstract:Flow-matching schedules affect both sampling dynamics and the variance of the regression target. For centered commuting Gaussians, we show that a direction-dependent schedule decomposes into two independent design choices: a variance path, which fully determines the intermediate laws and probability flow, and a factorization, which leaves this flow unchanged while controlling irreducible regression variance. On the sampling side, we analyze finite-step Euler accuracy and derive a necessary drift bound for exact N -step sampling, connecting the geodesic and the logarithmic path. On the training side, for any fixed path, we derive closed-form factorizations that either minimize time-averaged regression variance or make it constant along the path.

Machine Learning (cs.LG)

arXiv:2609.25839 [cs.LG]

(or arXiv:2609.25839v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.25839 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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