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

2026-06-14

AI Summary

This work addresses the lack of theoretical convergence guarantees for ODE samplers in decentralized diffusion models, which arises from stochastic expert switching. To resolve this issue, the paper proposes a decentralized ODE sampling framework based on velocity field decomposition. By integrating stochastic velocity field modeling, ODE discretization analysis, and Wasserstein-2 metric theory, the authors establish the first rigorous convergence guarantee for such models. The theoretical analysis demonstrates that the distribution obtained via N-step discretization converges to the analytical solution of the continuous ODE in Wasserstein-2 distance at a rate of \(O(N^{-1/2} + \varepsilon)\), where \(\varepsilon\) denotes the neural network approximation error.

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.

Problem

• decentralized diffusion models
• Wasserstein convergence
• ODE-based sampling
• stochastic velocity fields
• convergence analysis

Innovation

• decentralized diffusion
• ODE-based sampling
• Wasserstein convergence
• velocity field decomposition
• stochastic expert switching