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arXiv · 2609.25839

Gaussian Flow-Matching Schedules: Implications for Sampling and Training

Arsène Claustre·Hugo Negrel·Claire Boyer·Kimia Nadjahi·Eric Vanden-Eijnden
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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.

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Arsène Claustre, Hugo Negrel, Claire Boyer, Kimia Nadjahi, Eric Vanden-Eijnden. 2026-09-22. Gaussian Flow-Matching Schedules: Implications for Sampling and Training. https://arxiv.org/abs/2609.25839

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