LoRID: Low-Rank Iterative Diffusion for Adversarial Purification

TL;DR

LoRID introduces a low-rank iterative diffusion method that enhances adversarial purification by reducing errors and leveraging multi-stage diffusion and Tucker decomposition, resulting in improved robustness across multiple datasets.

Contribution

It proposes LoRID, a novel low-rank iterative diffusion approach combining multi-stage purification and Tucker decomposition to effectively remove adversarial noise with low errors.

Findings

Achieves superior robustness on CIFAR-10/100, CelebA-HQ, and ImageNet.

Effectively overcomes strong adversarial attacks in white-box and black-box settings.

Reduces purification errors compared to existing diffusion-based defenses.

Abstract

This work presents an information-theoretic examination of diffusion-based purification methods, the state-of-the-art adversarial defenses that utilize diffusion models to remove malicious perturbations in adversarial examples. By theoretically characterizing the inherent purification errors associated with the Markov-based diffusion purifications, we introduce LoRID, a novel Low-Rank Iterative Diffusion purification method designed to remove adversarial perturbation with low intrinsic purification errors. LoRID centers around a multi-stage purification process that leverages multiple rounds of diffusion-denoising loops at the early time-steps of the diffusion models, and the integration of Tucker decomposition, an extension of matrix factorization, to remove adversarial noise at high-noise regimes. Consequently, LoRID increases the effective diffusion time-steps and overcomes strong adversarial attacks, achieving superior robustness performance in CIFAR-10/100, CelebA-HQ, and ImageNet datasets under both white-box and black-box settings.