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The field of face anti-spoofing (FAS) has witnessed great progress with the surge of deep learning. Due to its data-driven nature, existing FAS methods are sensitive to the noise in the dataset, which will hurdle the learning process. However, very few works consider noise modeling in FAS. In this work, we attempt to fill this gap by automatically addressing the noise problem from both label and data perspectives in a probabilistic manner. Specifically, we propose a unified framework called Dual Probabilistic Modeling (DPM), with two dedicated modules, DPM-LQ (Label Quality aware learning) and DPM-DQ (Data Quality aware learning). Both modules are designed based on the assumption that data and label should form coherent probabilistic distributions. DPM-LQ is able to produce robust feature representations without overfitting to the distribution of noisy semantic labels. DPM-DQ can eliminate data noise from `False Reject' and `False Accept' during inference by correcting the prediction confidence of noisy data based on its quality distribution. Both modules can be incorporated into existing deep networks seamlessly and efficiently. Furthermore, we propose the generalized DPM to address the noise problem in practical usage without the need of semantic annotations. Extensive experiments demonstrate that this probabilistic modeling can 1) significantly improve the accuracy, and 2) make the model robust to the noise in real-world datasets. Without bells and whistles, our proposed DPM achieves state-of-the-art performance on multiple standard FAS benchmarks.