Abstract. In this work we introduce Deforming Autoencoders, a generative model for images that disentangles shape from appearance in an unsupervised manner. As in the deformable template paradigm, shape is represented as a deformation between a canonical coordinate system (‘template’) and an observed image, while appearance is modeled in deformation-invariant, template coordinates. We introduce novel techniques that allow this approach to be deployed in the setting of autoencoders and show that this method can be used for unsupervised group-wise image alignment. We show experiments with expression morphing in humans, hands, and digits, face manipulation, such as shape and appearance interpolation, as well as unsupervised landmark localization. We also achieve a more powerful form of unsupervised disentangling in template coordinates, that successfully decomposes face images into shading and albedo, allowing us to further manipulate face images