提出无需访问最优解的扩散模型训练样本复杂度新理论。
Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access
- 分解得分估计误差为统计、近似和优化三部分，构建新分析框架。
- 证明样本复杂度为ε⁻⁴，避免了参数量指数依赖的缺陷。
- 适合关注生成模型理论基础的研究者，尤其关心训练效率者。
扩散模型在视觉、语言和科学领域均展现出顶尖性能。尽管实证成功，以往的样本复杂度理论分析存在与输入维度呈差劲缩放关系或依赖不切实际假设（如可访问精确的经验风险最小化器）的问题。本文对得分估计进行严谨分析，建立样本复杂度上界为𝒪(ε⁻⁴)。方法通过将得分估计误差结构化分解为统计、近似和优化误差，成功消除了先前分析中由神经网络参数带来的指数依赖。这是首个在不假设可访问得分函数估计损失的经验风险最小化器的前提下，获得样本复杂度上界的成果。
原文摘要 · Abstract (English)
Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data dimension or rely on unrealistic assumptions such as access to exact empirical risk minimizers. In this work, we provide a principled analysis of score estimation, establishing a sample complexity bound of $\mathcal{O}(ε^{-4})$. Our approach leverages a structured decomposition of the score estimation error into statistical, approximation, and optimization errors, enabling us to eliminate the exponential dependence on neural network parameters that arises in prior analyses. It is the first such result that achieves sample complexity bounds without assuming access to the empirical risk minimizer of score function estimation loss.
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