# LoRID: Low-Rank Iterative Diffusion for Adversarial Purification

arXiv: https://arxiv.org/abs/2409.08255 · HTML: https://mlsanity.com/paper/2409.08255/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 28 of its 45 references that are in the map.
- First posted on arXiv 12 Sep 2024.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [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)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Fixing Data Augmentation to Improve Adversarial Robustness](https://mlsanity.com/paper/2103.01946/) (2021)
- [Geometry-aware Instance-reweighted Adversarial Training](https://mlsanity.com/paper/2010.01736/) (2020)
- [Torchattacks: A PyTorch Repository for Adversarial Attacks](https://mlsanity.com/paper/2010.01950/) (2020)
- [Guided Diffusion Model for Adversarial Purification](https://mlsanity.com/paper/2205.14969/) (2022)
- [Robust Evaluation of Diffusion-Based Adversarial Purification](https://mlsanity.com/paper/2303.09051/) (2023)
- [Stochastic Security: Adversarial Defense Using Long-Run Dynamics of Energy-Based Models](https://mlsanity.com/paper/2005.13525/) (2020)
- [Ensembling with Deep Generative Views](https://mlsanity.com/paper/2104.14551/) (2021)
- [DiffAttack: Evasion Attacks Against Diffusion-Based Adversarial Purification](https://mlsanity.com/paper/2311.16124/) (2023)
- [Comment on "Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network"](https://mlsanity.com/paper/1907.00895/) (2019)
- [Robust Adversarial Defense by Tensor Factorization](https://mlsanity.com/paper/2309.01077/) (2023)

## Built on by (most cited first, 7 of 7)

- [Safety at Scale: A Comprehensive Survey of Large Model and Agent Safety](https://mlsanity.com/paper/2502.05206/) (2025)
- [Diffusion-based Adversarial Purification from the Perspective of the Frequency Domain](https://mlsanity.com/paper/2505.01267/) (2025)
- [World Model Robustness via Surprise Recognition](https://mlsanity.com/paper/2512.01119/) (2025)
- [DBLP: Noise Bridge Consistency Distillation For Efficient And Reliable Adversarial Purification](https://mlsanity.com/paper/2508.00552/) (2025)
- [Keep It Real: Challenges in Attacking Compression-Based Adversarial Purification](https://mlsanity.com/paper/2508.05489/) (2025)
- [Universal Adversarial Purification with DDIM Metric Loss for Stable Diffusion](https://mlsanity.com/paper/2601.07253/) (2026)
- [Feature-Space Smoothing: Certified Robustness of Deep Representations](https://mlsanity.com/paper/2601.16200/) (2026)

## Abstract (arXiv)

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.