SCIENCE@home

Provably Reliable Classifier Guidance via Cross-Entropy Control

Sharan Sahu,Arisina Banerjee,Yuchen Wu

Published 2026 in Unknown venue

ABSTRACT

Classifier-guided diffusion models generate conditional samples by augmenting the reverse-time score with the gradient of the log-probability predicted by a probabilistic classifier. In practice, this classifier is usually obtained by minimizing an empirical loss function. While existing statistical theory guarantees good generalization performance when the sample size is sufficiently large, it remains unclear whether such training yields an effective guidance mechanism. We study this question in the context of cross-entropy loss, which is widely used for classifier training. Under mild smoothness assumptions on the classifier, we show that controlling the cross-entropy at each diffusion model step is sufficient to control the corresponding guidance error. In particular, probabilistic classifiers achieving conditional KL divergence $\varepsilon^2$ induce guidance vectors with mean squared error $\widetilde O(d \varepsilon )$, up to constant and logarithmic factors. Our result yields an upper bound on the sampling error of classifier-guided diffusion models and bears resemblance to a reverse log-Sobolev--type inequality. To the best of our knowledge, this is the first result that quantitatively links classifier training to guidance alignment in diffusion models, providing both a theoretical explanation for the empirical success of classifier guidance, and principled guidelines for selecting classifiers that induce effective guidance.

PUBLICATION RECORD

  • Publication year

    2026

  • Venue

    Unknown venue

  • Publication date

    2026-01-29

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 2601.21200
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-59 of 59 references · Page 1 of 1

CITED BY

  • No citing papers are available for this paper.

Showing 0-0 of 0 citing papers · Page 1 of 1