The Entropic Signature of Class Speciation in Diffusion Models

Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical instabilities along class-separating directions, but practical methods to detect and exploit these windows in trained models are still limited. We show that tracking the class-conditional entropy of a latent semantic variable given the noisy state provides a reliable signature of these transition regimes. By restricting the entropy to semantic partitions, the entropy can furthermore resolve semantic decisions at different levels of abstraction. We analyze this behavior in high-dimensional Gaussian mixture models and show that the entropy rate concentrates on the same logarithmic time scale as the speciation symmetry-breaking instability previously identified in variance-preserving diffusion. We validate our method on EDM2-XS and Stable Diffusion 1.5, where class-conditional entropy consistently isolates the noise regimes critical for semantic structure formation. Finally, we use our framework to quantify how guidance redistributes semantic information over time. Together, these results connect information-theoretic and statistical physics perspectives on diffusion and provide a principled basis for time-localized control.

💡 Research Summary

This paper tackles the long‑standing question of when and how semantic structure emerges during the reverse diffusion process of modern generative models. While diffusion models have achieved state‑of‑the‑art results across image, audio, video, and multimodal domains, the dynamics of class or prompt commitment along the denoising trajectory remain poorly understood. Recent theoretical work from statistical physics has identified a sharp “speciation” transition—an instability that breaks symmetry among class‑separating directions—but it has not yielded an operational diagnostic that can be measured in trained networks.

The authors propose to monitor the class‑conditional entropy (H