We propose a method for learning non-linear face geometry representations using deep generative models. Our model is a variational autoencoder with multiple levels of hidden variables where lower layers capture global geometry and higher ones encode more local deformations. Based on that, we propose a new parameterization of facial geometry that naturally decomposes the structure of the human face into a set of semantically meaningful levels of detail. This parameterization enables us to do model fitting while capturing varying level of detail under different types of geometrical constraints.​