Towards Understanding the Robustness of Diffusion-Based Purification: A Stochastic Perspective

Yiming Liu, Kezhao Liu, Yao Xiao, ZiYi Dong, Xiaogang Xu, Pengxu Wei, Liang Lin

Keywords: Adversarial Defense, Adversarial Purification, Diffusion Training, Randomized Defense

TL;DR: We identify stochasticity as the primary factor of the adversarial robustness of diffusion-based purification. We further propose a novel method, ADDT, to improve the purification ability of diffusion models.

Abstract:

Diffusion-Based Purification (DBP) has emerged as an effective defense mechanism against adversarial attacks. The success of DBP is often attributed to the forward diffusion process, which reduces the distribution gap between clean and adversarial images by adding Gaussian noise. Although this explanation is theoretically grounded, the precise contribution of this process to robustness remains unclear. In this paper, through a systematic investigation, we propose that the intrinsic stochasticity in the DBP procedure is the primary factor driving robustness. To explore this hypothesis, we introduce a novel Deterministic White-Box (DW-box) evaluation protocol to assess robustness in the absence of stochasticity, and analyze attack trajectories and loss landscapes. Our results suggest that DBP models primarily leverage stochasticity to evade effective attack directions, and that their ability to purify adversarial perturbations can be weak. To further enhance the robustness of DBP models, we propose Adversarial Denoising Diffusion Training (ADDT), which incorporates classifier-guided adversarial perturbations into diffusion training, thereby strengthening the models' ability to purify adversarial perturbations. Additionally, we propose Rank-Based Gaussian Mapping (RBGM) to improve the compatibility of perturbations with diffusion models. Experimental results validate the effectiveness of ADDT. In conclusion, our study suggests that future research on DBP can benefit from the perspective of decoupling stochasticity-based and purification-based robustness.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 3896