Images of objects and visual scenes decompose into a hierarchy of parts and subparts with particular appearances and constrained spatial arrangements. The most natural formulation of probabilistic generative models of natural images therefore seems to be a hierarchical one. Such hierarchical representations are conceptually desirable for various reasons, yet, in practice they can pose difficulties in particular with respect to learning and inference. Here we propose to investigate hierarchical part-based generative image models and strategies to learn such models in an unsupervised manner. We currently foresee a model that provides a dense explanation of images, whose part-hierarchy has an AND-OR structure (similar to probabilistic context free grammars), and that explicitly incorporates certain invariances, e.g. with respect to simple geometrical transformations. One of the major major challenges of the project will be the unsupervised learning of AND-OR structured hierarchies.