Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition

This paper presents a convergence guarantee for decentralized diffusion models using ODE-based sampling, demonstrating that the distribution of the N-step discretization converges to the analytical solution in Wasserstein-2 distance at a rate of \(\mathcal{O}(N^{-1/2}+\varepsilon)\), where \(\varepsilon\) accounts for neural approximation errors. This is the first result of its kind for decentralized diffusion models, which utilize multiple local experts and a stochastic routing mechanism, marking a significant advancement in the theoretical understanding of these architectures. The findings are crucial for practitioners as they provide a foundational framework for improving the privacy and scalability of generative models through decentralized approaches.