Diffusion Models are Certifiably Robust Classifiers

Generative learning, recognized for its effective modeling of data distributions, offers inherent advantages in handling out-of-distribution instances, especially for enhancing robustness to adversarial attacks. Among these, diffusion classifiers, utilizing powerful diffusion models, have demonstrated superior empirical robustness. However, a comprehensive theoretical understanding of their robustness is still lacking, raising concerns about their vulnerability to stronger future attacks. In this study, we prove that diffusion classifiers possess $O(1)$ Lipschitzness, and establish their certified robustness, demonstrating their inherent resilience. To achieve non-constant Lipschitzness, thereby obtaining much tighter certified robustness, we generalize diffusion classifiers to classify Gaussian-corrupted data. This involves deriving the evidence lower bounds (ELBOs) for these distributions, approximating the likelihood using the ELBO, and calculating classification probabilities via Bayes' theorem. Experimental results show the superior certified robustness of these Noised Diffusion Classifiers (NDCs). Notably, we achieve over 80\% and 70\% certified robustness on CIFAR-10 under adversarial perturbations with \(\ell_2\) norms less than 0. 25 and 0. 5, respectively, using a single off-the-shelf diffusion model without any additional data.

Authors

• Huanran Chen
• Yinpeng Dong
• Shitong Shao
• Zhongkai Hao Tsinghua University
• Xiao Yang Nanyang Technological University
• Hang Su Dept. of CST, BNRist Center, Inst. for AI, Tsinghua-Bosch Joint Center for ML, Tsinghua University
• Jun Zhu Tsinghua University National Center for Protein Sciences (Beijing) Beijing Institute of Lifeomics

Keywords

No keywords are indexed for this paper.