# Provably Reliable Classifier Guidance via Cross-Entropy Control

arXiv: https://arxiv.org/abs/2601.21200 · HTML: https://mlsanity.com/paper/2601.21200/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 44 of its 59 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 44)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [Diffusion Models are Minimax Optimal Distribution Estimators](https://mlsanity.com/paper/2303.01861/) (2023)
- [End-to-End Diffusion Latent Optimization Improves Classifier Guidance](https://mlsanity.com/paper/2303.13703/) (2023)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Statistical Efficiency of Score Matching: The View from Isoperimetry](https://mlsanity.com/paper/2210.00726/) (2022)
- [Optimal score estimation via empirical Bayes smoothing](https://mlsanity.com/paper/2402.07747/) (2024)
- [Gradient Guidance for Diffusion Models: An Optimization Perspective](https://mlsanity.com/paper/2404.14743/) (2024)
- [Convergence Analysis of Probability Flow ODE for Score-based Generative Models](https://mlsanity.com/paper/2404.09730/) (2024)
- [O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions](https://mlsanity.com/paper/2409.18959/) (2024)
- [Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization](https://mlsanity.com/paper/2203.05093/) (2022)
- [What does guidance do? A fine-grained analysis in a simple setting](https://mlsanity.com/paper/2409.13074/) (2024)
- [Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions](https://mlsanity.com/paper/2402.15602/) (2024)
- [Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models](https://mlsanity.com/paper/2403.01639/) (2024)
- [Density Estimation in Infinite Dimensional Exponential Families](https://mlsanity.com/paper/1312.3516/) (2013)
- [Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models](https://mlsanity.com/paper/2309.11420/) (2023)
- [Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Models](https://mlsanity.com/paper/2410.04760/) (2024)

## Built on by (most cited first, 1 of 1)

- [On the Robustness of Distribution Support under Diffusion Guidance](https://mlsanity.com/paper/2605.07220/) (2026)

## Abstract (arXiv)

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 varepsilon2 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.