`Capsule' models try to explicitly represent the poses of objects, enforcing a linear relationship between an objects pose and those of its constituent parts. This modelling assumption should lead to robustness to viewpoint changes since the object-component relationships are invariant to the poses of the object. We describe a probabilistic generative model that encodes these assumptions. Our probabilistic formulation separates the generative assumptions of the model from the inference scheme, which we derive from a variational bound. We experimentally demonstrate the applicability of our unified objective, and the use of test time optimisation to solve problems inherent to amortised inference.