A Gaussian Perspective on Generative Discrepancy in Diffusion Models

Release Time：2026-05-14Number of visits：10

Speaker:             Wenyi Zhang

Time:                  14:00, May. 15th.

Location:            SIST 2-215

Host:                   Prof. Youlong Wu

Abstract:

We introduce an analytical approach to quantifying and optimizing the reverse sampling discretization error in generative diffusion models. We explicitly derive the closed-form evolution trajectory and the resulting Kullback-Leibler (KL) divergence for the reverse sampling process under a multivariate Gaussian formulation. Asymptotic analysis via the Euler-Maclaurin expansion characterizes the convergence behavior of this KL divergence, extracting its leading order term as an explicit functional of the noise schedule. Minimizing this error functional via the calculus of variations yields a noise schedule governed by a tangent law, inherently determined by the source covariance spectrum. We mathematically prove that this Gaussian-based analysis is not merely a special case, but acts as a global theoretical lower bound for the KL divergence of arbitrary distributions under given covariance constraints. Furthermore, we utilize the analytical KL divergence as a principled metric to identify improved time discretization strategies for pre-trained models. Experiments across diverse datasets demonstrate that the strategies identified by our framework consistently outperform established baselines, particularly under restricted function evaluation budgets. (Joint work with Qiang Sun and H. Vincent Poor)

Bio:

Wenyi Zhang received the bachelor's degree from the Department of Automation, Tsinghua University, in 2001, and the master's and Ph.D. degrees from the Department of Electrical Engineering, University of Notre Dame, in 2003 and 2006, respectively. Since January 2010, he has been a Faculty Member with the Department of Electronic Engineering and Information Science, University of Science and Technology of China, where he is currently a professor. Prior to that, he was with the Communications Science Institute, University of Southern California, and Qualcomm Inc., Corporate Research and Development. His research interests lie at the intersection of communications, information theory, and statistical inference. He is an Editor of IEEE Transactions on Information Theory and IEEE Transactions on Communications. He is a Distinguished Lecturer of the IEEE Information Theory Society from 2026 to 2027.