AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-22
Improved Training of Strong Stochastic Flow Maps
Stochastic flow maps promise few-step sampling of stochastic differential equations by learning to jump directly between times along the solution path, but training them is difficult because the Brownian path is an infinite-dimensional, nowhere differentiable object that keeps derivative-based losses out of reach. The authors represent the Brownian path with a shifted Legendre polynomial expansion and train with a Wong-Zakai styled objective to unlock derivative-based losses, and propose a recipe for fine-tuning large pre-trained flow models into strong stochastic flow maps. On ImageNet this yields roughly a three-fold improvement in FD-DINOv2 over SSFM at four NFE.