U-Turn Diffusion
Hamidreza Behjoo Michael Chertkov
We present a comprehensive examination of score-based diffusion models of AI
for generating synthetic images. These models hinge upon a dynamic auxiliary
time mechanism driven by stochastic differential equations, wherein the score
function is acquired from input images. Our investigation unveils a criterion
for evaluating efficiency of the score-based diffusion models: the power of the
generative process depends on the ability to de-construct fast correlations
during the reverse/de-noising phase. To improve the quality of the produced
synthetic images, we introduce an approach coined "U-Turn Diffusion". The
U-Turn Diffusion technique starts with the standard forward diffusion process,
albeit with a condensed duration compared to conventional settings.
Subsequently, we execute the standard reverse dynamics, initialized with the
concluding configuration from the forward process. This U-Turn Diffusion
procedure, combining forward, U-turn, and reverse processes, creates a
synthetic image approximating an independent and identically distributed
(i.i.d.) sample from the probability distribution implicitly described via
input samples. To analyze relevant time scales we employ various analytical
tools, including auto-correlation analysis, weighted norm of the score-function
analysis, and Kolmogorov-Smirnov Gaussianity test. The tools guide us to
establishing that the Kernel Intersection Distance, a metric comparing the
quality of synthetic samples with real data samples, is minimized at the
optimal U-turn time.