Gaussian Flow-Matching Schedules: Implications for Sampling and Training

2026-09-22

AI Summary

研究通过方向依赖性调度分解为方差路径和因子化，以优化采样动态及减少回归目标的方差。

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.

Problem

• Flow-matching schedules
• Gaussian distributions
• Variance path
• Factorization
• Regression variance

Innovation

• Gaussian Flow-Matching
• Variance Path
• Factorization
• Regression Variance
• Euler Accuracy