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DDPM Score Matching and Distribution Learning by Chewi, Sinho; Kalavasis, Alkis; Mehrotra, Anay; Montasser, Omar is a scholarly article available to read on EtoBox.

What is DDPM Score Matching and Distribution Learning about?

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). 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. This paper introduces a framework that reduces score estimation to these two tasks, with various implications for statistical and computational learning theory: Parameter Estimation: Koehler et al. (ICLR'23) demonstrate that a score-matching variant is statistically inefficient for the parametric estimation of multimodal densities common in practice. In contrast, we show that under mild conditions, denoising score-matching in DDPMs is asymptotically efficient. Density Estimation: By linking generation to score estimation, we lift existing score estimation guarantees to $(\epsilon,\delta)$-PAC density estimation, i.e., a function approximating the target log-

Author

Chewi, Sinho; Kalavasis, Alkis; Mehrotra, Anay; Montasser, Omar

Published

2025

Language

EN