Identify additional problems where diffusion models plus low-degree approximations yield improved guarantees

Identify further unsupervised learning problems or distribution families for which combining diffusion-model reductions to score matching with piecewise polynomial (low-degree) approximation techniques leads to improved theoretical guarantees over existing approaches, analogous to the gains demonstrated for Gaussian mixture learning in this work.

Background

This work provides what the authors believe is the first example where diffusion models, via an efficient score-matching algorithm using piecewise polynomial approximation, achieve state-of-the-art theoretical guarantees for an unsupervised learning task (learning Gaussian mixtures).

They explicitly pose the broader open direction of finding other problems where this synthesis of diffusion models and classic low-degree approximation methods can deliver comparable or superior guarantees.