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This research establishes a novel Wasserstein-2 convergence guarantee for decentralized diffusion models utilizing ODE-based sampling schemes. By decomposing velocity fields into local experts with stochastic switching, the study provides theoretical bounds that address privacy-driven architectural shifts outside standard global frameworks. This work is significant for advancing the mathematical rigor of scalable generative AI systems where traditional convergence analyses do not apply.
Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition
arXiv:2606.15835v1 Announce Type: new 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 $\mathcal{O}(N^{-1/2}+\varepsilon)$ 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.
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 $\mathcal{O}(N^{-1/2}+\varepsilon)$ 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.
50 pages, 9 figures. Preprint under review
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.15835 [cs.LG]
(or arXiv:2606.15835v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.15835 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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