Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization

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.