Numerical Gauge Fixing for Generative ODEs

Sampling from generative ordinary differential equations (ODEs) involves numerically integrating learned velocity fields, often requiring many model evaluations. Existing approaches accelerate sampling by improving solvers and time grids for a fixed velocity field, or by distilling pretrained generators into faster samplers. A complementary degree of freedom arises from gauge equivalence: a prescribed marginal probability path can admit multiple velocity fields with different finite-step numerical errors under the same sampler. In this work, we introduce numerical gauge fixing, a post-training framework that optimizes the choice of velocity field for a frozen pretrained model's marginal path to improve finite-step integration accuracy. Theoretically, we characterize how the choice among gauge-equivalent velocity fields affects finite-step integration error relative to the exact flow of the corrected velocity field. Building on this formulation, we develop a practical compiler that optimizes parameterized corrections by minimizing the discrepancy between coarse and refined rollouts of the same corrected field. Experiments on Gaussian-mixture flows and pretrained image generators show that gauge optimization can reduce finite-step integration error and improve generation quality with the base model, solver, and time grid held fixed. Our work identifies gauge selection as a complementary numerical optimization axis for few-step generative sampling.