Feature Information Dynamics in Diffusion

Diffusion models generate data through a continuum of denoising problems, and are widely observed to reveal coarse structure before fine detail. Yet, this intuition is mostly empirical and qualitative. We introduce \emph{feature information dynamics}, an information-theoretic framework for localizing when a feature is generated during diffusion. Using the I-MMSE identity, we connect the rate of feature mutual information change to a gap between optimal unconditional and feature-conditional denoising losses, yielding practical estimators for feature information density. We further develop a chained decomposition that separates shared from incremental information in a feature hierarchy. We use this framework first to quantitatively confirm spectral autoregression in pixel diffusion, and then to extend the analysis beyond frequency: under a class$\to$mask$\to$Canny conditioning chain, the per-feature information densities differ across pixel, SDVAE, VAVAE, and RAE, exposing fundamental differences between these representations.