Diffusion models are becoming widely used in state-of-the-art image, video
and audio generation. Score-based diffusion models stand out among these
methods, necessitating the estimation of score function of the input data
distribution. In this study, we present a theoretical framework to analyze
two-layer neural network-based diffusion models by reframing score matching and
denoising score matching as convex optimization. Though existing diffusion
theory is mainly asymptotic, we characterize the exact predicted score function
and establish the convergence result for neural network-based diffusion models
with finite data. This work contributes to understanding what neural
network-based diffusion model learns in non-asymptotic settings.

本研究提出了一个理论框架，通过将评分匹配和去噪评分匹配视为凸优化问题，对基于两层神经网络的扩散模型进行了分析。尽管现有的扩散理论主要是渐近的，但我们对有限数据的神经网络扩散模型进行了确切的预测评分函数表征，并建立了收敛结果，从而有助于理解非渐近设置中神经网络扩散模型的学习过程。