[Deep Learning Theory Team Seminar] SymmetricDiffusers: Learning Discrete Diffusion on Finite Symmetric Groups

Title: SymmetricDiffusers: Learning Discrete Diffusion on Finite Symmetric Groups

Speaker: Prof. Renjie Liao (University of British Columbia, Vector Institute, CIFAR AI Chair)

Date &Time: October 20, 2025 (Monday) 11:00 – 12:00 (JST)

Venue: Hybrid (Zoom / RIKEN AIP Nihonbashi Office)
*RIKEN AIP Nihonbashi office is only for AIP members

Abstract:
In this talk, I will present our ICLR 2025 oral paper, SymmetricDiffusers. Finite symmetric groups Sn are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over Sn poses significant challenges due to its intractable size and discrete nature. We introduce SymmetricDiffusers, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over Sn by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performances on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems.

Bio:
Renjie Liao is an Assistant Professor in the Department of Electrical and Computer Engineering and an Associate Member of the Department of Computer Science at the University of British Columbia (UBC). He is also a faculty member at the Vector Institute and holds a Canada CIFAR AI Chair. Prior to joining UBC, he was a Visiting Faculty Researcher at Google Brain, working with Geoffrey Hinton and David Fleet. He received his Ph.D. in Computer Science from the University of Toronto in 2021, under the supervision of Richard Zemel and Raquel Urtasun. During his Ph.D., he also worked as a Senior Research Scientist at Uber Advanced Technologies Group. He holds an M.Phil. in Computer Science from the Chinese University of Hong Kong (2015) and a B.Eng. in Automation from Beihang University (2011). His research interests span machine learning and its intersection with computer vision, self-driving, and beyond, with a particular focus on probabilistic and geometric deep learning.