Year: 2024
Type: preprint
Abstract: Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into the training phase, consistency models attempt to train a sequence of consistency functions capable of mapping any point at any time step of the diffusion process to its starting point. Despite the empirical success, a comprehensive theoretical understanding of consistency training remains elusive. This paper takes a first step towards establishing theoretical underpinnings for consistency models. We demonstrate that, in order to generate samples within $\varepsilon$ proximity to the target in distribution (measured by some Wasserstein metric), it suffices for the number of steps in consistency learning to exceed the order of $d^{5/2}/\varepsilon$, with $d$ the data dimension. Our theory offers rigorous insights into the validity and efficacy of consistency models, illuminating their utility in downstream inference tasks.
Source: arXiv (Cornell University)
Authors: Li, Gen, Huang, Zhihan, Wei, Yuting
Institutions: Chinese University of Hong Kong, University of Pennsylvania
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: Collaborative Research: Fine-Grained Statistical Inference in High Dimension: Actionable Information, Bias Reduction, and Optimality, CAREER: Statistical Learning from a Modern Perspective: Over-parameterization, Regularization, and Generalization, Collaborative Research: CIF: Medium: Statistical and Algorithmic Foundations of Efficient Reinforcement Learning, G6671297155, Collaborative Research: Fine-Grained Statistical Inference in High Dimension: Actionable Information, Bias Reduction, and Optimality
OpenAlex ID: W4391801159