  Images are composed as a hierarchy of object parts. We use this insight to
create a generative graphical model that defines a hierarchical distribution
over image parts. Typically, this leads to intractable inference due to loops
in the graph. We propose an alternative model structure, the Dense Latent Tree
(DLT), which avoids loops and allows for efficient exact inference, while
maintaining a dense connectivity between parts of the hierarchy. The usefulness
of DLTs is shown for the example task of image completion on partially observed
MNIST and Fashion-MNIST data. We verify having successfully learned a
hierarchical model of images by visualising its latent states.
