Minimizing Trajectory Curvature of ODE-based Generative Models

TL;DR

This paper introduces a training method for ODE-based generative models that reduces the curvature of generative trajectories, leading to faster sampling without sacrificing performance.

Contribution

It proposes a novel training approach to minimize trajectory curvature in ODE-based generative models, reducing sampling time without needing ODE/SDE simulation.

Findings

Lower trajectory curvature compared to previous models

Reduced sampling costs while maintaining performance

Code available for implementation

Abstract

Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.