We investigate a novel approach to time-series modeling, inspired by the successes of large pretrained foundation models. We introduce FAE (Foundation Auto-Encoders), a foundation generative-AI model for anomaly detection in time-series data, based on Variational Auto-Encoders (VAEs). By foundation, we mean a model pretrained on massive amounts of time-series data which can learn complex temporal patterns useful for accurate modeling, forecasting, and detection of anomalies on previously unseen datasets. FAE leverages VAEs and Dilated Convolutional Neural Networks (DCNNs) to build a generic model for univariate time-series modeling, which could eventually perform properly in out-of-the-box, zero-shot anomaly detection applications. We introduce the main concepts of FAE, and present preliminary results in different multidimensional time-series datasets from various domains, including a real dataset from an operational mobile ISP, and the well known KDD 2021 Anomaly Detection dataset.