%AXingchao Liu%AChengyue Gong%AQiang Liu%D2023%I
%K
%MOSTI ID: 10440561
%PMedium: X
%TFlow Straight and Fast:
Learning to Generate and Transfer Data with Rectified Flow
%XWe present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential
equation (ODE) models to transport between two empirically observed distributions π0 and π1, hence
providing a unified solution to generative modeling and domain transfer, among various other tasks
involving distribution transport. The idea of rectified flow is to learn the ODE to follow the straight
paths connecting the points drawn from π0 and π1 as much as possible. This is achieved by solving a
straightforward nonlinear least squares optimization problem, which can be easily scaled to large models
without introducing extra parameters beyond standard supervised learning. The straight paths are special
and preferred because they are the shortest paths between two points, and can be simulated exactly without time discretization and hence yield computationally efficient models. We show that the procedure
of learning a rectified flow from data, called rectification, turns an arbitrary coupling of π0 and π1 to a
new deterministic coupling with provably non-increasing convex transport costs. In addition, recursively
applying rectification allows us to obtain a sequence of flows with increasingly straight paths, which can
be simulated accurately with coarse time discretization in the inference phase. In empirical studies, we
show that rectified flow performs superbly on image generation, image-to-image translation, and domain
adaptation. In particular, on image generation and translation, our method yields nearly straight flows
that give high quality results even with a single Euler discretization step.
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