Formal characterization of guidance-driven entropy redistribution

Establish a formal characterization of how guidance controls both the magnitude and the timing of entropy redistribution along the diffusion sampling trajectory, specifying the mechanisms by which guidance modifies class-conditional information flow over time.

Background

Empirical results in the paper demonstrate that guidance (including classifier-free guidance applied in limited or full intervals) systematically redistributes entropy production across the sampling trajectory, often shifting semantic commitment toward higher noise regimes and affecting the temporal profile of information recovery.

While the empirical distortions are documented for models such as EDM2-XS on ImageNet, the authors state that a rigorous, formal account of how guidance modulates entropy dynamics—quantifying both magnitude and timing—has not yet been developed, leaving a theoretical gap.

References

Finally, a more formal characterization of how guidance controls the magnitude and timing of entropy redistribution along the sampling trajectory remains an open problem.

— The Entropic Signature of Class Speciation in Diffusion Models  (2602.09651 - Handke et al., 10 Feb 2026) in Section 6 (Limitations and Future Work)

Autoguidance implicitly addresses several issues with CFG -- it is domain agnostic and does not require classes -- but why both methods work is still poorly understood~\citep{bradley2024classifier, li2026towards}.

— How to Guide Your Language Flow  (2609.19356 - Dilip et al., 16 Sep 2026) in Section 5, “Adapting autoguidance to language”

Looking at cosine dynamics during integration was insufficient to explain guidance dynamics. We leave further investigations into guidance dynamics to future work.

— How to Guide Your Language Flow  (2609.19356 - Dilip et al., 16 Sep 2026) in Appendix, Section “Additional ablations and experiments,” paragraph “Cosine similarities”

Extending this characterization to mixed reconstruction losses and the complete guided sampling trajectory remains open.

— FuseReg: Regularizing Layer Fusion Mitigates the Reconstruction-Generation Gap in Representation Autoencoders  (2609.31620 - Du et al., 25 Sep 2026) in Section 6, Limitations