DENSEPURE: UNDERSTANDING DIFFUSION MODELS FOR ADVERSARIAL ROBUSTNESS

ABSTRACT

Diffusion models have been recently employed to improve certified robustness through the process of denoising. However, the theoretical understanding of why diffusion models are able to improve the certified robustness is still lacking, preventing from further improvement. In this study, we close this gap by analyzing the fundamental properties of diffusion models and establishing the conditions under which they can enhance certified robustness. This deeper understanding allows us to propose a new method DensePure, designed to improve the certified robustness of a pretrained model (i.e. classifier). Given an (adversarial) input, DensePure consists of multiple runs of denoising via the reverse process of the diffusion model (with different random seeds) to get multiple reversed samples, which are then passed through the classifier, followed by majority voting of inferred labels to make the final prediction. This design of using multiple runs of denoising is informed by our theoretical analysis of the conditional distribution of the reversed sample. Specifically, when the data density of a clean sample is high, its conditional density under the reverse process in a diffusion model is also high; thus sampling from the latter conditional distribution can purify the adversarial example and return the corresponding clean sample with a high probability. By using the highest density point in the conditional distribution as the reversed sample, we identify the robust region of a given instance under the diffusion model's reverse process. We show that this robust region is a union of multiple convex sets, and is potentially much larger than the robust regions identified in previous works. In practice, DensePure can approximate the label of the high density region in the conditional distribution so that it can enhance certified robustness. We conduct extensive experiments to demonstrate the effectiveness of DensePure by evaluating its certified robustness given a standard model via randomized smoothing. We show that DensePure is consistently better than existing methods on ImageNet, with 7% improvement on average. Project page:https://densepure.github.io/.

1. INTRODUCTION

Diffusion models have been shown to be a powerful image generation tool (Ho et al., 2020; Song et al., 2021b) owing to their iterative diffusion and denoising processes. These models have achieved state-of-the-art performance on sample quality (Dhariwal & Nichol, 2021; Vahdat et al., 2021) as well as effective mode coverage (Song et al., 2021a) . A diffusion model usually consists of two processes: (i) a forward diffusion process that converts data to noise by gradually adding noise to the input, and (ii) a reverse generative process that starts from noise and generates data by denoising one step at a time (Song et al., 2021b) . Given the natural denoising property of diffusion models, empirical studies have leveraged them for adversarial purification (Nie et al., 2022; Wu et al., 2022; Carlini et al., 2022) . For instance, Nie et al. (2022) employed diffusion models for model purification, DiffPure. They empirically show that by carefully choosing the amount of Gaussian noises added during the diffusion process, adversarial * the first four authors contributed equally 1

