Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow
Authors: name: Fu-Yun Wang, name: Ling Yang, name: Zhaoyang Huang, name: Mengdi Wang, name: Hongsheng Li

Diffusion models have greatly improved visual generation but are hindered by
slow generation speed due to the computationally intensive nature of solving
generative ODEs. Rectified flow, a widely recognized solution, improves
generation speed by straightening the ODE path. Its key components include: 1)
using the diffusion form of flow-matching, 2) employing boldsymbol
v-prediction, and 3) performing rectification (a.k.a. reflow). In this paper,
we argue that the success of rectification primarily lies in using a pretrained
diffusion model to obtain matched pairs of noise and samples, followed by
retraining with these matched noise-sample pairs. Based on this, components 1)
and 2) are unnecessary. Furthermore, we highlight that straightness is not an
essential training target for rectification; rather, it is a specific case of
flow-matching models. The more critical training target is to achieve a
first-order approximate ODE path, which is inherently curved for models like
DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion,
which generalizes the design space and application scope of rectification to
encompass the broader category of diffusion models, rather than being
restricted to flow-matching models. We validate our method on Stable Diffusion
v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the
training procedure of rectified flow-based previous works (e.g., InstaFlow) but
also achieves superior performance with even lower training cost. Our code is
available at https://github.com/G-U-N/Rectified-Diffusion.