Generative models have proved to be useful tools to represent 3D human faces and their statistical variations. With the increase of 3D scan databases available for training, a growing challenge lies in the ability to learn generative face models that effectively encode shape variations with respect to desired attributes, such as identity and expression, given datasets that can be diverse. This paper addresses this challenge by proposing a framework that learns a generative 3D face model using an autoencoder architecture, allowing hence for weakly supervised training. The main contribution is to combine a convolutional neural network-based en-coder with a multilinear model-based decoder, taking therefore advantage of both the convolutional network robust-ness to corrupted and incomplete data, and of the multilin-ear model capacity to effectively model and decouple shape variations. Given a set of 3D face scans with annotation labels for the desired attributes, e.g. identities and expressions, our method learns an expressive multilinear model that decouples shape changes due to the different factors. Experimental results demonstrate that the proposed method outperforms recent approaches when learning multilinear face models from incomplete training data, particularly in terms of space decoupling, and that it is capable of learning from an order of magnitude more data than previous methods.