Diffusion models and minimax rates: scores, functionals, and tests
Subhodh Kotekal (MIT)
E18-304
Abstract: While score-based diffusion models have achieved remarkable success in high-dimensional generative modeling, some basic theoretical questions have not been precisely resolved. In this talk, we address minimax optimality of density estimation, functional estimation, and hypothesis testing. First, we show diffusion models achieve the optimal density estimation rate over Holder balls. This result is a consequence of our sharp characterization of minimax score estimation across all noising levels. A key contribution is our lower bound argument which involves a slight…
