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

Diffusion-Based Purification (DBP) has emerged as an effective defense mechanism against adversarial attacks. The efficacy of DBP has been attributed to the forward diffusion process, which narrows the distribution gap between clean and adversarial images through the addition of Gaussian noise. Although this explanation has some theoretical support, the significance of its contribution to robustness remains unclear. In this paper, we argue that the inherent stochasticity in the DBP process is the primary driver of its robustness. To explore this, we introduce a novel Deterministic White-Box (DW-box) evaluation protocol to assess robustness in the absence of stochasticity and to analyze the attack trajectories and loss landscapes. Our findings suggest that DBP models primarily leverage stochasticity to evade effective attack directions, and their ability to purify adversarial perturbations can be weak. To further enhance the robustness of DBP models, we introduce Adversarial Denoising Diffusion Training (ADDT), which incorporates classifier-guided adversarial perturbations into diffusion training, thereby strengthening the DBP models' ability to purify adversarial perturbations. Additionally, we propose Rank-Based Gaussian Mapping (RBGM) to make perturbations more compatible 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 the stochasticity-based and purification-based robustness.