Face alignment is an active topic in computer vision, consisting in aligning a shape model on the face. To this end, most modern approaches refine the shape in a cascaded manner, starting from an initial guess. Those shape updates can either be applied in the feature point space (i.e. explicit updates) or in a low-dimensional, parametric space. In this paper, we propose a semi-parametric cascade that first aligns a parametric shape, then captures more fine-grained deformations of an explicit shape. For the purpose of learning shape updates at each cascade stage, we introduce a deep greedy neural forest (GNF) model, which is an improved version of deep neural forest (NF). GNF appears as an ideal regressor for face alignment, as it combines differentiability, high expressivity and fast evaluation runtime. The proposed framework is very fast and achieves high accuracies on multiple challenging benchmarks, including small, medium and large pose experiments.