Abstract: In recent years, diffusion-based deep generative models have achieved remarkable success in various applications. In this talk, we present statistical theories for diffusion models within the framework of nonparametric structured density estimation. To address the curse of dimensionality in nonparametric density estimation, we assume that the underlying density function factorizes into several low-dimensional components. Such factorizable densities are common in important examples, such as Bayesian networks and Markov random fields. We prove that an implicit density estimator constructed from diffusion models achieves the minimax optimal convergence rate with respect to total variation. Technically, we design a novel network architecture, which includes convolutional neural networks as a special case, to construct a minimax optimal estimator.