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

**Authors:** Noël Vouitsis, Rasa Hosseinzadeh, Brendan Leigh Ross, Valentin Villecroze, Satya Krishna Gorti, Jesse C. Cresswell, Gabriel Loaiza-Ganem  
**arXiv:** [2411.08954](https://arxiv.org/abs/2411.08954)  
**Date:** 2024-11-13  
**Summary page:** https://www.summarizepaper.com/en/paper/2411.08954v1/

## Key points

- Diffusion models (DMs) are popular generative models for various types of perceptual data such as images, video, and audio.
- The iterative sampling process of DMs poses a significant bottleneck in terms of efficiency.
- Researchers have explored distillation methods to create models capable of generating high-fidelity samples quickly, with consistency models (CMs) being one promising approach.
- CMs aim to solve the probability flow ordinary differential equation (ODE) defined by existing diffusion models.
- While CMs have shown potential in reducing sampling costs compared to traditional diffusion models, there are concerns about how effectively they solve the ODE and the impact of any induced error on sample quality.
- Direct CMs were introduced as a method that directly minimizes ODE solving error but surprisingly result in significantly worse sample quality compared to CMs.
- This study sheds light on the trade-offs between ODE solving accuracy and sample quality in consistency models.

## Summary

In recent years, diffusion models (DMs) have emerged as the go-to generative models for various perceptual data modalities like images, video, and audio. However, their iterative sampling process poses a significant bottleneck in terms of efficiency. To address this limitation, researchers have explored distillation methods to create models capable of generating high-fidelity samples in just a few iterations. One such promising approach is consistency models (CMs), which aim to solve the probability flow ordinary differential equation (ODE) defined by an existing diffusion model. While CMs have shown potential in reducing the cost of sampling compared to traditional diffusion models, there remains a question about how effectively they solve the probability flow ODE and the impact of any induced error on sample quality. are popular generative models for various types of perceptual data such as images, video, and audio. However, can be an issue due to their iterative sampling process. To overcome this challenge, have been explored to create efficient models that can generate high-quality samples quickly. One promising approach is , which aim to solve the  defined by existing diffusion models. While CMs have shown potential in reducing sampling costs compared to traditional diffusion models,

To address these concerns, were introduced as a method that directly minimizes ODE solving error. Surprisingly,< kd > while Direct CMs reduce ODE solving error compared to CMs,</ kd > they also result in significantly worse sample quality. This raises questions about why CMs perform well in practice despite potentially inducing errors in the ODE solving process. This study sheds light on the trade-offs between ODE solving accuracy and sample quality in consistency models. The full code for Direct CMs is available at https://github.com/layer6ai-labs/direct-cms. Authors of this research include Noël Vouitsis, Rasa Hosseinzadeh, Brendan Leigh Ross, Valentin Villecroze, Satya Krishna Gorti, Jesse C. Cresswell, and Gabriel Loaiza-Ganem. This work was presented at NeurIPS 2024 ATTRIB Workshop and falls under primary categories of cs.LG and cs.AI according to arXiv classification.