[Deep Learning Theory Team Seminar] Talk by Prof. Qing Qu (UMich) on the Emergence of Generalizability and Semantic Low-Dim Subspaces in Diffusion Models

Venue: Online and the Open Space at the RIKEN AIP Nihonbashi office

Language: English

Title: The Emergence of Generalizability and Semantic Low-Dim Subspaces in Diffusion Models

Abstract: Recent empirical studies have shown that diffusion models possess a unique reproducibility property, transiting from memorization to generalization as the number of training samples increases. This demonstrates that diffusion models can effectively learn image distributions and generate new samples. Remarkably, these models achieve this even with a small number of training samples, despite the challenge of large image dimensions, effectively circumventing the curse of dimensionality. In this work, we provide theoretical insights into this phenomenon by leveraging two key empirical observations: (i) the low intrinsic dimensionality of image datasets and (ii) the low-rank property of the denoising autoencoder in trained diffusion models. With these setups, we rigorously demonstrate that optimizing the training loss of diffusion models is equivalent to solving the canonical subspace clustering problem across the training samples. This insight has practical implications for training and controlling diffusion models. Specifically, it enables us to precisely characterize the minimal number of samples necessary for accurately learning the low-rank data support, shedding light on the phase transition from memorization to generalization. Additionally, we empirically establish a correspondence between the subspaces and the semantic representations of image data, which enables one-step, transferrable, efficient image editing. Moreover, our results have profound practical implications for training efficiency and model safety, and they also open up numerous intriguing theoretical questions for future research.

Speaker Bio: Qing Qu is an assistant professor in the EECS department at the University of Michigan. Before that, he was a Moore-Sloan data science fellow at the Center for Data Science, New York University, from 2018 to 2020. He received his Ph.D from Columbia University in Electrical Engineering in Oct. 2018. He received his B.Eng. from Tsinghua University in Jul. 2011, and a M.Sc. from Johns Hopkins University in Dec. 2012, both in Electrical and Computer Engineering. His research interest lies at the intersection of the foundation of data science, machine learning, numerical optimization, and signal/image processing. His current research interests focus on deep representation learning and diffusion models. He is the recipient of the Best Student Paper Award at SPARS’15, the recipient of the Microsoft PhD Fellowship in machine learning in 2016, and the Best Paper Award in the NeurIPS Diffusion Model Workshop in 2023. He received the NSF Career Award in 2022, and Amazon Research Award (AWS AI) in 2023. He was the program chair of the new Conference on Parsimony & Learning (CPAL’24), area chair of NeurIPS, ICML, and ICLR, and action editor of TMLR.