  We present rectified flow, a surprisingly simple approach to learning
(neural) ordinary differential equation (ODE) models to transport between two
empirically observed distributions \pi_0 and \pi_1, 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 \pi_0 and
\pi_1 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 \pi_0 and \pi_1 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.
