Title: Convergence Theory of Decentralized Diffusion Models via Pseudo-Non-Markov Analysis
Primary area: generative models
Keywords: diffuison models

Abstract: Diffusion probabilistic models (DPMs) have demonstrated remarkable success in generative tasks, supported by a solid foundation of convergence analysis. 
  Recently, decentralized DPMs have been proposed to enhance data security and enable cross-institutional collaboration.
  However, their unique decentralized structure renders existing analysis techniques inapplicable, leaving their theoretical convergence properties an open question.
  In this paper, we introduce a novel pseudo-non-Markovian method to analyze the convergence of both standard and decentralized DPMs within the context of the denoising diffusion probabilistic model (DDPM) sampler.
  Our key technical insight is to reframe the analysis of the backward transition. While the transition from $x_t$ to $x_s$ ($s<t$) is Markovian, we analyze its conditional form given the initial data $x_0$. This conditional transition becomes non-Markovian but gains a tractable analytical expression, allowing for a direct analysis of the discretization error on the Cartesian product space of $x_t\times x_s\times x_0$.
 We show that this method is readily extensible to the decentralized setting. To the best of our knowledge, our convergence theory represents the first of its kind applicable to the decentralized scenario.