首次证明去中心化扩散模型的欧拉采样收敛性，为隐私保护生成提供理论支撑。
Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition
- 通过速度场分解构建去中心化采样框架，实现局部专家协作。
- 在Wasserstein-2距离下达到$\mathcal{O}(N^{-1/2}+\varepsilon)$的收敛速率。
- 适合关注分布式生成模型理论分析的研究者与隐私计算从业者。
扩散模型在生成任务中取得显著成功，其收敛理论也日趋成熟。为兼顾隐私与可扩展性，近期的去中心化扩散架构将单一全局速度场替换为多个局部专家与路由机制，导致采样动态出现随机专家切换，超出传统扩散收敛分析范畴。本文研究具有随机速度场的去中心化扩散框架及基于常微分方程（ODE）的采样方法。建立了在Wasserstein-2距离下的收敛保证，表明N步离散化分布以$\mathcal{O}(N^{-1/2}+\varepsilon)$的速率收敛至解析解，其中$\varepsilon$表示神经网络近似误差。据我们所知，这是首个针对基于ODE的去中心化扩散模型的W_2收敛结果。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。