Capsule networks are a neural network architecture specialized for visual scene recognition. Features and pose information are extracted from a scene and then dynamically routed through a hierarchy of vector-valued nodes called ‘capsules’ to create an implicit scene graph, with the ultimate aim of learning vision directly as inverse graphics. Despite these intuitions, however, capsule networks are not formulated as explicit probabilistic generative models; moreover, the routing algorithms typically used are ad-hoc and primarily motivated by algorithmic intuition. In this paper, we derive an alternative capsule routing algorithm utilizing iterative inference under sparsity constraints. We then introduce an explicit probabilistic generative model for capsule networks based on the self-attention operation in transformer networks and show how it is related to a variant of predictive coding networks using Von-Mises-Fisher (VMF) circular Gaussian distributions.