By estimating 3D shape and instances from a single view, we can capture information about an environment quickly, without the need for comprehensive scanning and multi-view fusion. Solving this task for composite scenes (such as object stacks) is challenging: occluded areas are not only ambiguous in shape but also in instance segmentation; multiple decompositions could be valid. We observe that physics constrains decomposition as well as shape in occluded regions and hypothesise that a latent space learned from scenes built under physics simulation can serve as a prior to better predict shape and instances in occluded regions. To this end we propose SIMstack, a depth-conditioned Variational Auto-Encoder (VAE), trained on a dataset of objects stacked under physics simulation. We formulate instance segmentation as a centre voting task which allows for class-agnostic detection and doesn’t require setting the maximum number of objects in the scene. At test time, our model can generate 3D shape and instance segmentation from a single depth view, probabilistically sampling proposals for the occluded region from the learned latent space. Our method has practical applications in providing robots some of the ability humans have to make rapid intuitive inferences of partially observed scenes. We demonstrate an application for precise (non-disruptive) object grasping of unknown objects from a single depth view.