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 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.

Image-generating diffusion models, such as Stable Diffusion, create pictures by gradually turning Gaussian noise into a structured image. However, it is still unclear when, during this process, the model actually settles on the semantic structures that finally show in the generated image. We study this question by measuring how uncertain the model remains about a chosen semantic distinction at each noise level. When this uncertainty drops quickly, it marks the moment when the model has effectively committed to that structure of the image. Our method can look at broad decisions, such as an ImageNet class (e.g. "tiger shark"), or narrower decisions, such as adding a specific attribute to a text prompt. We show mathematically why this signal identifies the critical transition from ambiguity to commitment, and we test it on synthetic examples, EDM2-XS, and Stable Diffusion 1.5. We also use it to analyze guidance, the mechanism that pushes diffusion models toward a requested semantic descriptor, showing how guidance changes when semantic information is recovered. This provides a practical diagnostic for understanding and controlling generative models at the specific stages where semantic decisions are actually made.