# Diffusion-based Adversarial Purification from the Perspective of the Frequency Domain

arXiv: https://arxiv.org/abs/2505.01267 · HTML: https://mlsanity.com/paper/2505.01267/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 54 references that are in the map.
- First posted on arXiv 2 May 2025.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Do Adversarially Robust ImageNet Models Transfer Better?](https://mlsanity.com/paper/2007.08489/) (2020)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examples](https://mlsanity.com/paper/1710.10766/) (2017)
- [Improving Robustness using Generated Data](https://mlsanity.com/paper/2110.09468/) (2021)
- [Fixing Data Augmentation to Improve Adversarial Robustness](https://mlsanity.com/paper/2103.01946/) (2021)
- [Data Augmentation Can Improve Robustness](https://mlsanity.com/paper/2111.05328/) (2021)
- [A Self-supervised Approach for Adversarial Robustness](https://mlsanity.com/paper/2006.04924/) (2020)
- [Adversarial purification with Score-based generative models](https://mlsanity.com/paper/2106.06041/) (2021)
- [Robustness and Accuracy Could Be Reconcilable by (Proper) Definition](https://mlsanity.com/paper/2202.10103/) (2022)

## Built on by (most cited first, 8 of 8)

- [Adversarial-Guided Diffusion for Multimodal LLM Attacks](https://mlsanity.com/paper/2507.23202/) (2025)
- [DBLP: Noise Bridge Consistency Distillation For Efficient And Reliable Adversarial Purification](https://mlsanity.com/paper/2508.00552/) (2025)
- [MANI-Pure: Magnitude-Adaptive Noise Injection for Adversarial Purification](https://mlsanity.com/paper/2509.25082/) (2025)
- [Efficient and Robust Video Defense Framework against 3D-field Personalized Talking Face](https://mlsanity.com/paper/2512.21019/) (2025)
- [Do Protective Perturbations Really Protect Portrait Privacy under Real-world Image Transformations?](https://mlsanity.com/paper/2604.23688/) (2026)
- [Fast Preemptive Robustification: High-Frequency Response Anti-Aligns Shared Vulnerability](https://mlsanity.com/paper/2603.25244/) (2026)
- [Localize and Neutralize: Gradient-guided Token Suppression against Visual Prompt Injection Attack](https://mlsanity.com/paper/2605.25194/) (2026)
- [VCR-Bench: A Modular Open-Source Benchmark for Video Classification Robustness](https://mlsanity.com/paper/2610.08936/) (2026)

## Abstract (arXiv)

The diffusion-based adversarial purification methods attempt to drown adversarial perturbations into a part of isotropic noise through the forward process, and then recover the clean images through the reverse process. Due to the lack of distribution information about adversarial perturbations in the pixel domain, it is often unavoidable to damage normal semantics. We turn to the frequency domain perspective, decomposing the image into amplitude spectrum and phase spectrum. We find that for both spectra, the damage caused by adversarial perturbations tends to increase monotonically with frequency. This means that we can extract the content and structural information of the original clean sample from the frequency components that are less damaged. Meanwhile, theoretical analysis indicates that existing purification methods indiscriminately damage all frequency components, leading to excessive damage to the image. Therefore, we propose a purification method that can eliminate adversarial perturbations while maximizing the preservation of the content and structure of the original image. Specifically, at each time step during the reverse process, for the amplitude spectrum, we replace the low-frequency components of the estimated image's amplitude spectrum with the corresponding parts of the adversarial image. For the phase spectrum, we project the phase of the estimated image into a designated range of the adversarial image's phase spectrum, focusing on the low frequencies. Empirical evidence from extensive experiments demonstrates that our method significantly outperforms most current defense methods.