Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow

Rectified flow is a surprisingly simple approach to learning neural ordinary differential equation (ODE) models that transport between two empirically observed distributions, thereby providing a unified solution to generative modeling, domain transfer, and other distribution-transport tasks. The core idea is to learn the ODE to follow the straight paths connecting points drawn from the two distributions as much as possible, achieved by solving a straightforward nonlinear least squares optimization problem that scales easily to large models without introducing extra parameters beyond standard supervised learning. Straight paths are preferred because they are the shortest between two points and can be simulated exactly without time discretization, yielding computationally efficient models.

The authors show that the rectification procedure turns an arbitrary coupling of the two distributions into a new deterministic coupling with provably non-increasing convex transport costs, and that recursively applying rectification produces a sequence of flows with increasingly straight paths that can be simulated accurately with coarse time discretization at inference. Empirically, rectified flow performs superbly on image generation, image-to-image translation, and domain adaptation, with the near-straight flows yielding high-quality results even using a single Euler discretization step, which mattered for fast generative sampling.