Dejan Dejan Stančević

Florian Handke, Dejan Stančević, Felix Koulischer et al.

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.

Gabriel Raya, Bac Nguyen, Georgios Batzolis et al.

We introduce InfoNoise, an online adaptive noise schedule for diffusion training that reallocates optimization effort toward noise levels where denoising is most informative. Together with loss weighting, a noise schedule induces an effective allocation across denoising problems, often fixed before informative noise levels are known. InfoNoise makes this allocation data-adaptive by estimating a conditional-entropy-rate profile from denoising losses during training, without auxiliary models or offline search. Through I--MMSE, this profile identifies where noisy observations rapidly reduce uncertainty about the clean sample and guides adaptation of the training noise distribution. It changes only this distribution, keeping the objective, weighting, and parameterization fixed. On image benchmarks, where schedules have been extensively tuned, InfoNoise matches or slightly exceeds strong baselines and can reach the same quality with fewer updates. On representation, sequence, and modality shifts, including DNA and language generation, InfoNoise improves over fixed and adaptive baselines and reaches target quality with up to $3\times$ less training compute. These results establish the conditional-entropy-rate profile as the data-dependent target for noise schedule design and make online adaptation a practical alternative to manual schedule search.

Luca Ambrogioni

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 their dynamic, information-theoretic, and thermodynamic properties under a unified mathematical framework. 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. This synthesis offers a powerful insight: the process of generation is fundamentally driven by the controlled, noise-induced breaking of (approximate) symmetries, where peaks in information transfer correspond to critical transitions between possible outcomes. The score function acts as a dynamic non-linear filter that regulates the bandwidth of the noise by suppressing fluctuations that are incompatible with the data.