Coarse-Grained Kullback--Leibler Control of Diffusion-Based Generative AI

Diffusion models and score-based generative models provide a powerful framework for synthesizing high-quality images from noise. However, there is still no satisfactory theory that describes how coarse-grained quantities, such as blockwise intensity or class proportions after partitioning an image into spatial blocks, are preserved and evolve along the reverse diffusion dynamics. In previous work, the author introduced an information-theoretic Lyapunov function V for non-ergodic Markov processes on a state space partitioned into blocks, defined as the minimal Kullback-Leibler divergence to the set of stationary distributions reachable from a given initial condition, and showed that a leak-tolerant potential V-delta with a prescribed tolerance for block masses admits a closed-form expression as a scaling-and-clipping operation on block masses.