# One Stone, Two Birds: Enhancing Adversarial Defense Through the Lens of Distributional Discrepancy

arXiv: https://arxiv.org/abs/2503.02169 · HTML: https://mlsanity.com/paper/2503.02169/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 79 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 30 of 60)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [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)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [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)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Defense against Adversarial Attacks Using High-Level Representation Guided Denoiser](https://mlsanity.com/paper/1712.02976/) (2017)
- [Do Adversarially Robust ImageNet Models Transfer Better?](https://mlsanity.com/paper/2007.08489/) (2020)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [MagNet: a Two-Pronged Defense against Adversarial Examples](https://mlsanity.com/paper/1705.09064/) (2017)
- [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)
- [Bag of Tricks for Adversarial Training](https://mlsanity.com/paper/2010.00467/) (2020)

## Built on by (most cited first, 3 of 3)

- [Neural Network Reprogrammability: A Unified Theme on Model Reprogramming, Prompt Tuning, and Prompt Instruction](https://mlsanity.com/paper/2506.04650/) (2025)
- [Sample-Specific Noise Injection For Diffusion-Based Adversarial Purification](https://mlsanity.com/paper/2506.06027/) (2025)
- [USAD: Uncertainty-aware Statistical Adversarial Detection](https://mlsanity.com/paper/2606.27832/) (2026)

## Abstract (arXiv)

Statistical adversarial data detection (SADD) detects whether an upcoming batch contains adversarial examples (AEs) by measuring the distributional discrepancies between clean examples (CEs) and AEs. In this paper, we explore the strength of SADD-based methods by theoretically showing that minimizing distributional discrepancy can help reduce the expected loss on AEs. Despite these advantages, SADD-based methods have a potential limitation: they discard inputs that are detected as AEs, leading to the loss of useful information within those inputs. To address this limitation, we propose a two-pronged adversarial defense method, named Distributional-discrepancy-based Adversarial Defense (DAD). In the training phase, DAD first optimizes the test power of the maximum mean discrepancy (MMD) to derive MMD-OPT, which is a stone that kills two birds. MMD-OPT first serves as a guiding signal to minimize the distributional discrepancy between CEs and AEs to train a denoiser. Then, it serves as a discriminator to differentiate CEs and AEs during inference. Overall, in the inference stage, DAD consists of a two-pronged process: (1) directly feeding the detected CEs into the classifier, and (2) removing noise from the detected AEs by the distributional-discrepancy-based denoiser. Extensive experiments show that DAD outperforms current state-of-the-art (SOTA) defense methods by simultaneously improving clean and robust accuracy on CIFAR-10 and ImageNet-1K against adaptive white-box attacks. Codes are publicly available at: https://github.com/tmlr-group/DAD.