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

arXiv:2606.15835v2 Announce Type: replace Abstract: 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 O(N^{-1/2}+arepsilon) in W_2, where arepsilon 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.

Source: arXiv cs.LG | 2026-09-29