Lipschitz Singularities in Diffusion Models

Fuente: arXiv
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Hauptverfasser: Yang, Zhantao, Feng, Ruili, Zhang, Han, Shen, Yujun, Zhu, Kai, Huang, Lianghua, Zhang, Yifei, Liu, Yu, Zhao, Deli, Zhou, Jingren, Cheng, Fan
Format: Preprint
Veröffentlicht: 2023
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author Yang, Zhantao
Feng, Ruili
Zhang, Han
Shen, Yujun
Zhu, Kai
Huang, Lianghua
Zhang, Yifei
Liu, Yu
Zhao, Deli
Zhou, Jingren
Cheng, Fan
author_facet Yang, Zhantao
Feng, Ruili
Zhang, Han
Shen, Yujun
Zhu, Kai
Huang, Lianghua
Zhang, Yifei
Liu, Yu
Zhao, Deli
Zhou, Jingren
Cheng, Fan
contents Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we explore a perplexing tendency of diffusion models: they often display the infinite Lipschitz property of the network with respect to time variable near the zero point. We provide theoretical proofs to illustrate the presence of infinite Lipschitz constants and empirical results to confirm it. The Lipschitz singularities pose a threat to the stability and accuracy during both the training and inference processes of diffusion models. Therefore, the mitigation of Lipschitz singularities holds great potential for enhancing the performance of diffusion models. To address this challenge, we propose a novel approach, dubbed E-TSDM, which alleviates the Lipschitz singularities of the diffusion model near the zero point of timesteps. Remarkably, our technique yields a substantial improvement in performance. Moreover, as a byproduct of our method, we achieve a dramatic reduction in the Fréchet Inception Distance of acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. Extensive experiments on diverse datasets validate our theory and method. Our work may advance the understanding of the general diffusion process, and also provide insights for the design of diffusion models.
format Preprint
id arxiv_https___arxiv_org_abs_2306_11251
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Lipschitz Singularities in Diffusion Models
Yang, Zhantao
Feng, Ruili
Zhang, Han
Shen, Yujun
Zhu, Kai
Huang, Lianghua
Zhang, Yifei
Liu, Yu
Zhao, Deli
Zhou, Jingren
Cheng, Fan
Computer Vision and Pattern Recognition
Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we explore a perplexing tendency of diffusion models: they often display the infinite Lipschitz property of the network with respect to time variable near the zero point. We provide theoretical proofs to illustrate the presence of infinite Lipschitz constants and empirical results to confirm it. The Lipschitz singularities pose a threat to the stability and accuracy during both the training and inference processes of diffusion models. Therefore, the mitigation of Lipschitz singularities holds great potential for enhancing the performance of diffusion models. To address this challenge, we propose a novel approach, dubbed E-TSDM, which alleviates the Lipschitz singularities of the diffusion model near the zero point of timesteps. Remarkably, our technique yields a substantial improvement in performance. Moreover, as a byproduct of our method, we achieve a dramatic reduction in the Fréchet Inception Distance of acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. Extensive experiments on diverse datasets validate our theory and method. Our work may advance the understanding of the general diffusion process, and also provide insights for the design of diffusion models.
title Lipschitz Singularities in Diffusion Models
topic Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2306.11251