2024/09/12 by Benjamin Sterling, Sterling, Benjamin, Mónica F. Bugallo +1 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Reservoir Computing #Quantum chaos and dynamical systems #Signal Processing (eess.SP) #Systems and Control (eess.SY) #electronic engineering #information engineering #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2409.07697
openalex publication_date 2024/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.