In this work we propose a novel model-based deep convolutional autoencoder that addresses the highly challenging problem of reconstructing a 3D human face from a single in-the-wild color image. To this end, we combine a convolutional encoder network with an expert-designed generative model that serves as decoder. The core innovation is the differentiable parametric decoder that encapsulates image formation analytically based on a generative model. Our decoder takes as input a code vector with exactly defined semantic meaning that encodes detailed face pose, shape, expression, skin reflectance and scene illumination. Due to this new way of combining CNN-based with model-based face reconstruction, the CNN-based encoder learns to extract semantically meaningful parameters from a single monocular input image. For the first time, a CNN encoder and an expert-designed generative model can be trained end-to-end in an unsupervised manner, which renders training on very large (unlabeled) real world datasets feasible. The obtained reconstructions compare favorably to current state-of-the-art approaches in terms of quality and richness of representation. This work is an extended version of the paper "MoFA: Model-based Deep Convolutional Face Autoencoder for Unsupervised Monocular Reconstruction", where we additionally present a stochastic vertex sampling technique for faster training of our networks, and moreover, we propose and evaluate analysis-by-synthesis and shape-from-shading refinement approaches to achieve a high-fidelity reconstruction.