Nonparametric Estimation of a Factorizable Density using Diffusion Models

Summary

The paper treats diffusion models as an implicit approach to nonparametric density estimation and analyzes them within a statistical framework. It assumes the underlying density factorizes into low-dimensional components, as in Bayesian networks and Markov random fields. The authors show that a diffusion-based implicit estimator adapts to this factorization and achieves the minimax optimal rate under total variation distance, using a sparse weight-sharing neural network architecture.