Unsupervised anomaly detection in medical images such as chest radiographs is stepping into the spotlight as it mitigates the scarcity of the labor-intensive and costly expert annotation of anomaly data. However, nearly all existing methods are formulated as a one-class classification trained only on representations from the normal class and discard a potentially significant portion of the unlabeled data. This paper focuses on a more practical setting, dual distribution anomaly detection for chest X-rays, using the entire training data, including both normal and unlabeled images. Inspired by a modern self-supervised vision transformer model trained using partial image inputs to reconstruct missing image regions- we propose AMAE, a two-stage algorithm for adaptation of the pre-trained masked autoencoder (MAE). Starting from MAE initialization, AMAE first creates synthetic anomalies from only normal training images and trains a lightweight classifier on frozen transformer features. Subsequently, we propose an adaptation strategy to leverage unlabeled images containing anomalies. The adaptation scheme is accomplished by assigning pseudo-labels to unlabeled images and using two separate MAE based modules to model the normative and anomalous distributions of pseudo-labeled images. The effectiveness of the proposed adaptation strategy is evaluated with different anomaly ratios in an unlabeled training set. AMAE leads to consistent performance gains over competing self-supervised and dual distribution anomaly detection methods, setting the new state-of-the-art on three public chest X-ray benchmarks - RSNA, NIH-CXR, and VinDr-CXR.