Inconsistencies In Consistency Models: Better ODE Solving Does Not Imply Better Samples

TL;DR

This paper investigates the relationship between the accuracy of consistency models in solving the probability flow ODE and the quality of generated samples, revealing that better ODE solving does not necessarily lead to better samples.

Contribution

The authors introduce Direct CMs that directly minimize ODE solving error, providing insights into the disconnect between ODE accuracy and sample quality in consistency models.

Findings

Direct CMs reduce ODE solving error compared to standard CMs.

Improved ODE solving accuracy does not improve sample quality.

Questions the underlying reasons for the effectiveness of CMs in sample generation.

Abstract

Although diffusion models can generate remarkably high-quality samples, they are intrinsically bottlenecked by their expensive iterative sampling procedure. Consistency models (CMs) have recently emerged as a promising diffusion model distillation method, reducing the cost of sampling by generating high-fidelity samples in just a few iterations. Consistency model distillation aims to solve the probability flow ordinary differential equation (ODE) defined by an existing diffusion model. CMs are not directly trained to minimize error against an ODE solver, rather they use a more computationally tractable objective. As a way to study how effectively CMs solve the probability flow ODE, and the effect that any induced error has on the quality of generated samples, we introduce Direct CMs, which \textit{directly} minimize this error. Intriguingly, we find that Direct CMs reduce the ODE solving error compared to CMs but also result in significantly worse sample quality, calling into question why exactly CMs work well in the first place. Full code is available at: https://github.com/layer6ai-labs/direct-cms.