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 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. While this explanation is theoretically sound, the exact role of this mechanism in enhancing robustness remains unclear. In this paper, through empirical analysis, we propose that the intrinsic stochasticity in the DBP process is the primary factor driving robustness. To test this hypothesis, we introduce a novel Deterministic White-Box (DW-box) setting to assess robustness in the absence of stochasticity, and we analyze attack trajectories and loss landscapes. Our results suggest that DBP models primarily rely on stochasticity to avoid effective attack directions, while their ability to purify adversarial perturbations may be limited. To further enhance the robustness of DBP models, we propose Adversarial Denoising Diffusion Training (ADDT), which incorporates classifier-guided adversarial perturbations into the diffusion training process, 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 a clearer distinction between stochasticity-driven and purification-driven robustness.