The Pseudo Adiabatic Regime

Abstract

Score-Based Generative Models (SGMs) generate data by evolving samples under a Stochastic Differential Equation (SDE) that may include an auxiliary momentum variable. In this thesis, we investigate the probability density functions describing the evolution of such systems with momentum when the governing SDE slowly changes. For a simple moving Gaussian potential, we show the existence of an intermediate Pseudo-Adiabatic Regime (PAR) in which the momentum variables equilibrate while the position variables continue to evolve. In this regime, we show that the forward and reverse-time SDEs are the same, potentially simplifying the generative process. Using perturbative analysis and numerical experiments, we characterize the conditions under which the PAR emerges, demonstrating that a large damping-to-mass ratio suffices. Our results offer new perspectives on SGMs, and motivate further research into a more efficient generative process for SGMs.