People reason with incomplete models. How do people hampered by different, incomplete views learn from each other? We introduce a model of ``model-based inference.'' Model-based reasoners partition an otherwise hopelessly complex state space into a manageable model. Unless the differences in agents' models are trivial, interactions will often not lead agents to common beliefs, and the correct-model belief will typically lie outside the convex hull of the agents' beliefs. However, if the agents' models have enough in common, then interacting will lead agents to similar beliefs, even if their models also exhibit bizarre idiosyncrasies and their information is widely dispersed.