Critically-Damped Higher-Order Langevin Dynamics

Abstract: Denoising Diffusion Probabilistic Models represent an entirely new class of generative AI methods that have yet to be fully explored. Critical damping has been successfully introduced in Critically-Damped Langevin Dynamics (CLD) and Critically-Damped Third-Order Langevin Dynamics (TOLD++), but has not yet been applied to dynamics of arbitrary order. The proposed line of work generalizes Higher-Order Langevin Dynamics (HOLD), a recent state-of-the-art diffusion method, by introducing the concept of critical damping from systems analysis.