Critically Damped Third-Order Langevin Dynamics

TL;DR

This paper introduces TOLD++, an improved third-order Langevin dynamics method that uses critical damping to accelerate convergence in diffusion models, verified on toy and real datasets.

Contribution

It proposes a novel critical damping technique for TOLD, enhancing convergence speed through eigen-analysis, a new approach in diffusion model optimization.

Findings

TOLD++ converges faster than TOLD.

Faster convergence verified on Swiss Roll and CIFAR-10 datasets.

Improved diffusion method with theoretical guarantees.

Abstract

While systems analysis has been studied for decades in the context of control theory, it has only been recently used to improve the convergence of Denoising Diffusion Probabilistic Models. This work describes a novel improvement to Third- Order Langevin Dynamics (TOLD), a recent diffusion method that performs better than its predecessors. This improvement, abbreviated TOLD++, is carried out by critically damping the TOLD forward transition matrix similarly to Dockhorn's Critically-Damped Langevin Dynamics (CLD). Specifically, it exploits eigen-analysis of the forward transition matrix to derive the optimal set of dynamics under the original TOLD scheme. TOLD++ is theoretically guaranteed to converge faster than TOLD, and its faster convergence is verified on the Swiss Roll toy dataset and CIFAR-10 dataset according to the FID metric.