发表机构
CREST; ENSAE Paris; Institut Polytechnique de Paris（Crest 研究中心; 巴黎国立统计与经济管理学院; 巴黎理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分析一阶EDM扩散采样器的误差，分离局部离散化误差及其放大，证明通用局部界并给出全局误差$O(e^{\Lambda_K}/K)$，实验验证了放大对误差衰减的影响。
AI 中文摘要
我们分析Karras等人（2022）提出的确定性一阶扩散采样器（简称EDM）在2-Wasserstein距离下的误差，通过分离两个误差来源：局部离散化误差及其随后学习步骤的放大。我们证明局部误差具有通用界：对于任何具有有限二阶矩的数据分布，单步离散化误差关于步长呈二次增长，且显式常数不依赖于数据分布。相比之下，误差传播依赖于学习到的网络。在高噪声水平下，我们利用EDM的网络参数化推导出显式收缩准则。在低噪声水平下，我们通过采样器传输的分布上实现的放大来测量传播；这种实现放大可以任意小于最坏情况的Lipschitz常数。该分析得出K个采样步骤的全局离散化误差为$O(e^{\Lambda_K}/K)$，其中$\Lambda_K$是低噪声对数放大。在一维高斯混合模型上的实验表明，测量的放大解释了有限采样网格上较慢的误差衰减。在预训练的CIFAR-10模型上的诊断说明了相关的稳定性机制，但未证明全局假设。
英文摘要
We analyze the first-order deterministic diffusion sampler of Karras et al. (2022), termed EDM, in 2-Wasserstein distance by separating two sources of error: local discretization error and its amplification by subsequent learned steps. We prove that local error admits a universal bound: for any data distribution with finite second moment, the one-step discretization error is quadratic in the step size, with an explicit constant that does not depend on the data distribution. Error propagation, in contrast, depends on the learned network. At high noise levels, we exploit the network parametrization of EDM to derive an explicit contraction criterion. At low noise levels, we measure propagation through the amplification realized on the distributions transported by the sampler; this realized amplification can be arbitrarily smaller than the worst-case Lipschitz constant. This analysis yields an $O(e^{Λ_K}/K)$ global discretization error for $K$ sampling steps, where $Λ_K$ is the low-noise log-amplification. Experiments on a one-dimensional Gaussian mixture show how measured amplification accounts for slower error decay on finite sampling grids. Diagnostics on a pretrained CIFAR-10 model illustrate related stability mechanisms without certifying the global assumptions.
Comments71 pages; code: https://github.com/nbrosse/edm-error-propagation-code
