Diffusion models have achieved impressive empirical success in generative tasks, and their convergence theory is now relatively well understood. Motivated by privacy and scalability, recent decentralized diffusion architectures replace a single global velocity field with multiple local experts and a routing mechanism, yielding a sampling dynamics with stochastic expert switching that falls outside standard diffusion convergence analyses. In this work, We study a decentralized diffusion framework with stochastic velocity fields and ODE-based sampling. We establish a convergence guarantee in Wasserstein-2 distance, showing that the distribution of the $N$-step discretization converges to the analytical solution at rate $\mathcal{O}(N^{-1/2}+\varepsilon)$ in $W_2$, where $\varepsilon$ captures the neural approximation errors. To our knowledge, this is the first $W_2$ convergence result for decentralized diffusion models with an ODE-based sampling scheme.

翻译：扩散模型在生成任务中取得了令人瞩目的经验成功，其收敛理论目前已相对完善。然而，受隐私性和可扩展性的驱动，近期分散式扩散架构将单一的全局速度场替换为多个局部专家与路由机制的结合，由此产生的采样动力学涉及随机专家切换，这超出了标准扩散收敛分析的范围。本研究针对具有随机速度场和基于ODE采样的分散扩散框架进行探究。我们在Wasserstein-2距离下建立了收敛保证，表明$N$步离散化分布以$\mathcal{O}(N^{-1/2}+\varepsilon)$的速率在$W_2$度量下收敛至解析解，其中$\varepsilon$表征神经网络近似误差。据我们所知，这是针对采用ODE采样方案的分散扩散模型所提出的首个$W_2$收敛性结果。