A0517
Title: Nonparametric estimation of a factorizable density using diffusion models
Authors: Minwoo Chae - Pohang University of Science and Technology (Korea, South) [presenting]
Hyeok Kyu Kwon - (Korea, South)
Dongha Kim - Sungshin Women's University (Korea, South)
Ilsang Ohn - Inha University (Korea, South)
Abstract: In recent years, diffusion-based deep generative models have achieved remarkable success in various applications. Statistical theories are presented for diffusion models within the framework of nonparametric structured density estimation. To address the curse of dimensionality in nonparametric density estimation, it is assumed 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. It is proven that an implicit density estimator constructed from diffusion models achieves the minimax optimal convergence rate with respect to total variation. Technically, a novel network architecture is designed, which includes convolutional neural networks as a special case, to construct a minimax optimal estimator.
