DDPM Score Matching and Distribution Learning

Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key result in this area shows that with accurate score estimates, SGMs can efficiently generate samples from any realistic data distribution (Chen et al., ICLR '23; Lee et al., ALT '23). However, this distribution learning result, where the learned distribution is implicitly that of the sampler's output, does not explain how score estimation relates to classical tasks of parameter and density estimation. In this talk, we will discuss a framework that reduces score estimation to these two tasks, with various implications for statistical and computational learning theory.

This is based on joint work with Sinho Chewi, Anay Mehrotra, and Omar Montasser.