The increasing demand for face recognition systems across various domains underscores the critical need for secure and reliable face anti-spoofing systems. Common spoofing attacks include the use of printed photographs, videos, 3D masks, paper masks, partial tattoos/glasses, and makeup. Designing face anti-spoofing or face presentation attack detection (face PAD) systems involves utilizing multiple datasets, where all images that are not real must be considered fake. However, generating a large and diverse presentation attack dataset is costly. To improve model security, we present a novel robust face anti-spoofing system called AdvSpoofGuard, which aims at mitigating presentation attacks generated by deep generative models. Our proposed method leverages adversarial meta-training to enhance overall robustness. We conducted extensive experiments to evaluate the performance of our method on various face anti-spoofing datasets. The results demonstrate that our optimal transport (OT)-driven CycleGAN-based adversarial meta-learning approach improves classification across different domains and types of attacks, outperforming state-of-the-art methods in performance gain and defense against adversarial attacks.