Please note: This master’s thesis presentation will take place online.
Spencer Szabados, Master’s candidate
David R. Cheriton School of Computer Science
Supervisor: Professor Yaoliang Yu
This thesis investigates the theoretical foundations and extensions of generative diffusion models, starting with continuous diffusion processes and discrete variations, and expanding to include Riemannian manifolds and reflected boundary constraints. A key focus is on structure-preserving diffusion models, which are designed to maintain inherent symmetries such as affine group invariances.
The thesis provides a summary characterization of the drift and diffusion terms required for these invariances and extends these results to reflected and Riemannian manifold diffusion processes. Several techniques for constructing invariant diffusion models are proposed and evaluated against baselines using medical imaging and synthetic datasets, achieving comparable or superior performance while rigorously preserving invariance. Building on this, a proof-of-concept application demonstrates the utility of reflected (manifold) diffusion models in generating collision-free paths for robotic motion planning, highlighting the utility of these constrained diffusion frameworks.