Demystifying the Effectiveness of Diffusion Models: Low-Dimensional Adaptation and Diffusion Guidance

Lunch will be provided at 11:45am. 

Abstract:  Diffusion models have emerged as a cornerstone of modern generative modeling, yet their theoretical and algorithmic foundations remain underexplored. This talk aims to advance our understanding in two directions. First, we investigate how diffusion models leverage (unknown) low-dimensional structure to accelerate sampling. For two prominent samplers --- denoising diffusion implicit model (DDIM) and denoising diffusion probabilistic model (DDPM) --- we prove, assuming accurate scores, that their iteration complexities scale linearly in some intrinsic dimension of the target distribution, as opposed to the ambient dimension. Second, we turn to guided data generation with diffusion models. We prove that classifier-free guidance (CFG) decreases the expected reciprocal of the classifier probability, providing the first theoretical characterization of the specific performance metric that CFG improves for general target distributions. 

Bio: Yuxin Chen is currently a professor of statistics and data science and of electrical and systems engineering at the University of Pennsylvania. Before joining UPenn, he was an assistant professor of electrical and computer engineering at Princeton University. He completed his Ph.D. in Electrical Engineering at Stanford University and was also a postdoc scholar at Stanford Statistics. His current research interests include machine learning theory, high-dimensional statistics, and optimization. He has received the Alfred P. Sloan Research Fellowship, the SIAM Activity Group on Imaging Science Best Paper Prize, the ICCM Best Paper Award (gold medal), and was selected as a finalist for the Best Paper Prize for Young Researchers in Continuous Optimization. He has also received the Princeton Graduate Mentoring Award.