Techniques are disclosed for training and applying nonlinear face models. In embodiments, a nonlinear face model includes an identity encoder, an expression encoder, and a decoder. The identity encoder takes as input a representation of a facial identity, such as a neutral face mesh minus a reference mesh, and outputs a code associated with the facial identity. The expression encoder takes as input a representation of a target expression, such as a set of blendweight values, and outputs a code associated with the target expression. The codes associated with the facial identity and the facial expression can be concatenated and input into the decoder, which outputs a representation of a face having the facial identity and expression. The representation of the face can include vertex displacements for deforming the reference mesh.