arXiv:2607.23226cs.LGmath.ST2026-07

首次建立扩散模型端到端理论框架,解析生成质量的四大误差来源。

From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models

  • 构建基于残差网络的统一收敛与泛化分析框架
  • 量化样本量、时间步长与优化精度对生成质量的影响
  • 揭示前向截断、反向离散、泛化误差等四类误差机制

尽管基于得分的扩散模型在实践中表现优异,但关于有限样本学习、网络参数化与数值离散化如何共同决定生成质量的完整理论理解仍不充分。现有采样分析通常基于理想得分或预设误差阈值。本文针对实际使用的残差网络结构,建立了一个统一的收敛与泛化分析框架,从有限样本、离散时间的学习问题出发,分析到理想连续时间、总体水平目标的全过程。基于得分函数学习的泛化结果,进一步分析由学习得分函数诱导的采样过程,给出了生成终态分布的端到端总变差距离估计。该估计将整体生成误差明确分解为四个可解释成分:前向过程截断误差、反向时间离散误差、包含有限数据与前向离散化的泛化误差,以及训练优化差距。结果定量刻画了训练样本量、时间离散网格与优化精度如何共同控制扩散模型生成样本的最终保真度。

原文摘要 · Abstract (English)

Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped. Existing sampling analyses often evaluate the generative performance conditional on an oracle score or a pre-specified error threshold. In this work, we establish a unified convergence and generalization framework for score-based diffusion models parameterized by practical ResNet-type architectures. We analyze the generalization and convergence properties from the practical finite-sample, discrete-time learning problem of the score function to the ideal continuous-time, population-level objective. Based on the generalization result of the learning problem of score function, we analyze the sampling process induced by the learned score function and provide an end-to-end total variation distance estimate for the generated terminal distribution. This estimate explicitly decomposes the overall generative error into four interpretable components: the truncation error of the forward process, the reverse-time discretization error, the generalization error incorporating both finite data and forward-time discretization, and the training optimization gap. Our results quantitatively characterize how the training sample size, temporal discretization grids, and optimization accuracy jointly control the final fidelity of samples generated by diffusion models.

扩散模型理论分析生成质量

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。