Recent studies in deepfake detection have shown promising results when detecting deepfakes of the same type as those present in training. However, their ability to generalize to unseen deepfakes remains limited. This work improves the generalizable deepfake detection from a simple principle: an ideal detector classifies any face that contains anomalies not found in real faces as fake. Namely, detectors should learn consistent real appearances rather than fake patterns in the training set that may not apply to unseen deepfakes. Guided by this principle, we propose a learning task named Real Appearance Modeling (RAM) that guides the model to learn real appearances by recovering original faces from slightly disturbed faces. We further propose Face Disturbance to produce disturbed faces while preserving original information that enables recovery, which aids the model in learning the fine-grained appearance of real faces. Extensive experiments demonstrate the effectiveness of modeling real appearances to spot richer deepfakes. Our method surpasses existing state-of-the-art methods by a large margin on multiple popular deepfake datasets.