[2508.19897] The Information Dynamics of Generative Diffusion

Statistics > Machine Learning arXiv:2508.19897 (stat) [Submitted on 27 Aug 2025 (v1), last revised 26 Mar 2026 (this version, v4)] Title:The Information Dynamics of Generative Diffusion Authors:Dejan Stancevic, Luca Ambrogioni View a PDF of the paper titled The Information Dynamics of Generative Diffusion, by Dejan Stancevic and 1 other authors View PDF HTML (experimental) Abstract:Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This paper provides an integrated perspective on generative diffusion by connecting the information-theoretic, dynamical, and thermodynamic aspects. We demonstrate that the rate of conditional entropy production during generation (i.e., the generative bandwidth) is directly governed by the expected divergence of the score function's vector field. This divergence, in turn, is linked to the branching of trajectories and generative bifurcations, which we characterize as symmetry-breaking phase transitions in the energy landscape. Beyond ensemble averages, we demonstrate that symmetry-breaking decisions are revealed by peaks in the variance of pathwise conditional entropy, capturing heterogeneity in how individual trajectories resolve uncertainty. Together, these results establish generative diffusion as a process of controlled, noise-induced symmetry breaking, in which the score function acts as a dynamic nonlinear filter that re...