Many computer vision tasks rely on labeled data. Rapid progress in generative modeling has led to the ability to synthesize photorealistic images. However, controlling specific aspects of the generation process such that the data can be used for supervision of downstream tasks remains challenging. In this paper we propose a novel generative model for images of faces, that is capable of producing high-quality images under fine-grained control over eye gaze and head orientation angles. This requires the disentangling of many appearance related factors including gaze and head orientation but also lighting, hue etc. We propose a novel architecture which learns to discover, disentangle and encode these extraneous variations in a self-learned manner. We further show that explicitly disentangling task-irrelevant factors results in more accurate modelling of gaze and head orientation. A novel evaluation scheme shows that our method improves upon the state-of-the-art in redirection accuracy and disentanglement between gaze direction and head orientation changes. Furthermore, we show that in the presence of limited amounts of real-world training data, our method allows for improvements in the downstream task of semi-supervised cross-dataset gaze estimation. Please check our project page at: https://ait.ethz.ch/projects/2020/STED-gaze/