统一分析扩散模型采样器收敛性，首次给出Heun方法的理论保证。
Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
- 构建统一框架分析随机与确定性采样器的误差来源。
- 首次获得Heun采样器在Wasserstein距离下的收敛界，改进欧拉法结果。
- 强调得分函数空间正则性重要性，适合研究生成模型理论者阅读。
我们为基于扩散的生成模型提供了新的Wasserstein距离收敛保证，涵盖随机（如DDPM）和确定性（如DDIM）采样方法。提出一个简单框架，用于分析离散化、初始化及得分估计误差。特别地，首次推导出Heun采样器的Wasserstein收敛界，并改进了概率流ODE中欧拉采样器的已有结果。分析强调学习得分函数的空间正则性的重要性，主张以真实反向过程为基准控制得分误差，符合去噪得分匹配原则。同时结合近期关于平滑Wasserstein距离的结果，进一步收紧初始化误差界。
原文摘要 · Abstract (English)
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze discretization, initialization, and score estimation errors. Notably, we derive the first Wasserstein convergence bound for the Heun sampler and improve existing results for the Euler sampler of the probability flow ODE. Our analysis emphasizes the importance of spatial regularity of the learned score function and argues for controlling the score error with respect to the true reverse process, in line with denoising score matching. We also incorporate recent results on smoothed Wasserstein distances to sharpen initialization error bounds.
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