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

Gaozheng Pei, Ke Ma, Yingfei Sun, Qianqian Xu, Qingming Huang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:48679-48698, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-pei25b, title = {Diffusion-based Adversarial Purification from the Perspective of the Frequency Domain}, author = {Pei, Gaozheng and Ma, Ke and Sun, Yingfei and Xu, Qianqian and Huang, Qingming}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {48679--48698}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/pei25b/pei25b.pdf}, url = {https://proceedings.mlr.press/v267/pei25b.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Diffusion-based Adversarial Purification from the Perspective of the Frequency Domain %A Gaozheng Pei %A Ke Ma %A Yingfei Sun %A Qianqian Xu %A Qingming Huang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-pei25b %I PMLR %P 48679--48698 %U https://proceedings.mlr.press/v267/pei25b.html %V 267 %X 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.
APA
Pei, G., Ma, K., Sun, Y., Xu, Q. & Huang, Q.. (2025). Diffusion-based Adversarial Purification from the Perspective of the Frequency Domain. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:48679-48698 Available from https://proceedings.mlr.press/v267/pei25b.html.

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