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

• URL: http://arxiv.org/abs/2606.15835v1
• Date: Sun, 14 Jun 2026 14:28:07 GMT
• Title: Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition
• Abstract summary: We study a decentralized diffusion framework with velocity fields and ODE-based sampling.<n>To our knowledge, this is the first convergence result for decentralized diffusion models with an ODE-based sampling scheme.
• Score: 7.646780142293
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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