DC-DPM: A Divide-and-Conquer Approach for Diffusion Reverse Process

Yue-Jiang Dong, Hubery Yin, Fangyikang Wang, Yizhe Zhao, Chao Zhang, Chen Li, Song-Hai Zhang

Keywords: Diffusion Model; Reverse Process Transition Kernel; Divide-and-Conquer

TL;DR: We propose a divide-and-conquer approach to approximate the reversed transition kernel for diffusion models to enhance generation quality especially at small denoising timesteps.

Abstract:

Diffusion models have achieved great success in generative tasks\textblue{, with the quality of generated samples guaranteed by their convergence properties, typically derived within the context of stochastic differential equations(SDE) and often involving Kolmogorov equations for proofs. This paper introduces a novel method for proving the convergence of diffusion models, which relies on direct estimation of distributions without the need for SDE tools. This approach inspires a \textbf{D}ivide-and-\textbf{C}onquer strategy for approximating the reversed transition kernel of \textbf{D}iffusion \textbf{P}robabilistic \textbf{M}odels (DC-DPM), which is not derived from SDEs, making previous convergence methods inapplicable. However, our method can be easily extended to accommodate this. As} our DC-DPM learns specific kernels for each partition \textblue{, these kernels require merging. According to the proof of convergence, we} design two merging strategies for these cluster-specific kernels along with corresponding training and sampling methods. Experimental results demonstrate the superior generation quality of our method compared to the traditional single Gaussian kernel. Furthermore, our DC-DPM can synergize with previous kernel optimization methods, enhancing their generation quality, especially with a small number of timesteps.

Primary Area: generative models

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Submission Number: 1473