Gaussian flow schedules improve sampling and training control
Gaussian Flow-Matching Schedules: Implications for Sampling and Training
Machine Learning
Summary
When creating models that generate data step-by-step, the way you plan the flow between steps matters a lot. The authors show that for a particular kind of simple data distributions, you can think of this planning in two separate parts: one part decides how the data changes during the process, and the other controls how hard it is for the model to learn. They found methods to reduce learning errors and better understand how close the generated data is to ideal at various steps. This helps make models both easier to train and more accurate when generating data.
What this means in practice
- •For machine learning engineers: Design schedules for generative models that reduce training errors and improve sample quality in stepwise data generation processes.
- •For statistical software developers: Incorporate variance-minimizing factorizations into tools that simulate Gaussian-related stochastic processes with better accuracy.
A theory result. No direct application yet.
Authors
Arsène Claustre, Hugo Negrel, Claire Boyer, Kimia Nadjahi, Eric Vanden-Eijnden
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.