Harnessing Low Dimensionality in Diffusion Models: From Theory to Practice: Lecture I: The Generalizability of Diffusion Models

Qing Qu, Yuxin Chen, Liyue Shen

International Conference on Machine Learning 2025 · Tutorial

This article delves into the foundational mathematical aspects of **diffusion models**, specifically focusing on their remarkable **generalization** capabilities. Presented as the first lecture in a tutorial series titled "Harnessing Low Dimensionality in Diffusion Models," this talk by Professor Qing Qu from the University of Michigan, alongside Professors Yuxin Chen and Liyue Shen, shifts the common narrative around diffusion models from their diverse applications to their underlying theoretical principles. While many past tutorials have focused on introducing different diffusion methods and their practical uses, this series aims to unpack *how* these models work by understanding the low-dimensional structures inherent in data and the models themselves.

AI review

A technically substantive tutorial lecture that makes a genuine theoretical contribution: the equivalence between DAE training on mixture-of-low-rank-Gaussian data and PCA/subspace clustering, yielding a sample complexity bound that scales linearly in intrinsic dimension. The reproducibility-generalizability correlation is a well-motivated empirical finding given rigorous measurement scaffolding, and the low-rank Jacobian analysis connects the model's inductive bias directly to the data geometry. The work is honest about its simplifying assumptions and the gap to full-scale models. Rating…