We introduce a hierarchical probabilistic approach to go from a 2D image to multiview 3D: a diffusion "prior" predicts the unseen 3D geometry, which then conditions a diffusion "decoder" to generate novel views of the subject. We use a pointmap-based geometric representation to coordinate the generation of multiple target views simultaneously. We construct a predictable distribution of geometric features per target view to enable learnability across examples, and generalization to arbitrary inputs images. Our modular, geometry-driven approach to novel-view synthesis (called "unPIC") beats competing baselines such as CAT3D, EscherNet, Free3D, and One-2-3-45 on held-out objects from ObjaverseXL, as well as unseen real-world objects from Google Scanned Objects, Amazon Berkeley Objects, and the Digital Twin Catalog.