Alzheimer’s disease (AD) is a neurodegenerative brain disorder of unknown etiology that has a significant impact on the lives of patients and their families. Currently, there are no drugs or treatments that can cure AD, but early diagnosis and intervention can mitigate the effects of the disease on patients. Of various brain imaging tools, structural magnetic resonance imaging (sMRI) has been most intensively studied for AD diagnosis as it provides imaging biomarkers of neuronal loss. However, the accuracy of visual inspection by doctors is limited. Therefore, computer-aided diagnosis (CAD) based on sMRI has important clinical significance. Previous research has employed traditional machine learning and deep learning methods for AD image classification. However, these methods face challenges due to the scarcity, high noise, and high redundancy of medical data. Recent studies demonstrate the effectiveness of self-distillation in enhancing the model robustness, but the lack of additional knowledge limits such improvement. To address the issues of high redundancy in medical data and the lack of additional knowledge in self-distillation architectures, we propose the Self-Distillation Adversarial Training Network (SDATNet), which integrates self-distillation and adversarial training into a single framework. We utilize adversarial training methods to simulate noise on medical images, thereby supplementing additional information. Through self-distillation, we achieve cross-scale information interaction, enabling the extraction of discriminative features and effectively improving model performance. Experimental validation on the ADNI dataset demonstrates that our model outperforms other methods on publicly available datasets, achieving an accuracy of 92.77% and specificity of 92.19%. Our ablation experiments and visualization results further validate the reliability and superiority of the model.