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

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.

Figures (5)

• Figure 1: CMs (left) are weakly supervised ODE solvers, only learning to map points along a trajectory that are near the trajectory's origin back to the origin itself; points that are far from the origin instead enforce a self-consistency property, relying on weak self-supervision to solve the PF ODE. Direct CMs (right) are strongly supervised ODE solvers, instead learning to directly map all points along a trajectory back to the origin.
• Figure 2: Samples generated by both CMs and Direct CMs. The samples produced by CMs are clearly of higher quality. All corresponding images are generated from the same initial noise.
• Figure 3: Effect of the teacher's number of discretization intervals $N$. In all cases, we observe that Direct CMs are better at solving the PF ODE, but CMs produce higher quality images.
• Figure 4: Effect of the teacher's guidance scale $\omega$. We use $N=50$ here for faster experimentation. In all cases, we observe that Direct CMs are better at solving the PF ODE, but CMs produce higher quality images.
• Figure 5: Additional images generated by both CMs and Direct CMs, further highlighting the sample quality difference between the two models. All corresponding images are generated from the same initial noise.