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.