SCoT: Unifying Consistency Models and Rectified Flows via Straight-Consistent Trajectories

TL;DR

SCoT unifies consistency models and rectified flows to produce fast, accurate, and straight trajectories for diffusion model sampling, combining their advantages and improving efficiency.

Contribution

The paper introduces SCoT, a novel model that unifies consistency and rectified flow methods to enhance sampling speed and accuracy in diffusion models.

Findings

SCoT achieves faster sampling with high-quality results.

SCoT maintains trajectory consistency and straightness.

Experimental results validate SCoT's effectiveness and efficiency.

Abstract

Pre-trained diffusion models are commonly used to generate clean data (e.g., images) from random noises, effectively forming pairs of noises and corresponding clean images. Distillation on these pre-trained models can be viewed as the process of constructing advanced trajectories within the pair to accelerate sampling. For instance, consistency model distillation develops consistent projection functions to regulate trajectories, although sampling efficiency remains a concern. Rectified flow method enforces straight trajectories to enable faster sampling, yet relies on numerical ODE solvers, which may introduce approximation errors. In this work, we bridge the gap between the consistency model and the rectified flow method by proposing a Straight Consistent Trajectory~(SCoT) model. SCoT enjoys the benefits of both approaches for fast sampling, producing trajectories with consistent and straight properties simultaneously. These dual properties are strategically balanced by targeting two critical objectives: (1) regulating the gradient of SCoT's mapping to a constant, (2) ensuring trajectory consistency. Extensive experimental results demonstrate the effectiveness and efficiency of SCoT.