Same Flow, Different Paths: Variance Reduction in Flow Matching
The paper argues that path choice alone can change SGD convergence in flow matching, even when the objective is unchanged.
Alexander Tyurin studies paths that produce the same marginal distributions and velocity field, then compares their stochastic-gradient variance. In a simple Gaussian setting, the paper derives a near-tight SGD complexity bound and identifies an optimal linear path under that constraint. It then generalizes the setup into a variance-minimizing path-selection problem and shows why preserving the same flow-matching problem is necessary. Experiments on Gaussian, mixture, and real datasets support the theory. ArXiv · AI/CL/LG's note
Alexander Tyurin studies paths that produce the same marginal distributions and velocity field, then compares their stochastic-gradient variance. In a simple Gaussian setting, the paper derives a near-tight SGD complexity bound and identifies an optimal linear path under that constraint. It then generalizes the setup into a variance-minimizing path-selection problem and shows why preserving the same flow-matching problem is necessary. Experiments on Gaussian, mixture, and real datasets support the theory. ArXiv · AI/CL/LG's note
score 6