  Diffusion models have shown great promise for image and video generation, but
sampling from state-of-the-art models requires expensive numerical integration
of a generative ODE. One approach for tackling this problem is rectified flows,
which iteratively learn smooth ODE paths that are less susceptible to
truncation error. However, rectified flows still require a relatively large
number of function evaluations (NFEs). In this work, we propose improved
techniques for training rectified flows, allowing them to compete with
knowledge distillation methods even in the low NFE setting. Our main insight is
that under realistic settings, a single iteration of the Reflow algorithm for
training rectified flows is sufficient to learn nearly straight trajectories;
hence, the current practice of using multiple Reflow iterations is unnecessary.
We thus propose techniques to improve one-round training of rectified flows,
including a U-shaped timestep distribution and LPIPS-Huber premetric. With
these techniques, we improve the FID of the previous 2-rectified flow by up to
72% in the 1 NFE setting on CIFAR-10. On ImageNet 64$\times$64, our improved
rectified flow outperforms the state-of-the-art distillation methods such as
consistency distillation and progressive distillation in both one-step and
two-step settings and rivals the performance of improved consistency training
(iCT) in FID. Code is available at https://github.com/sangyun884/rfpp.
