We study random knotting by considering knot diagrams as decorated, (rooted) topological maps on spheres and sampling them uniformly from among sets of a fixed number of vertices. This model of random knotting is similar to those studied by Diao et al., and Dunfield et al., although we are careful to preserve the uniform distribution. The knot diagram model captures both the random geometry of space curve models of knotting as well as the ease of computing invariants from diagrams. We prove that unknot diagrams are asymptotically exponentially rare, an analogue of Sumners-Whittington and Pippenger’s landmark result for self-avoiding polygons. Our proof uses the same key idea: We first show that knot diagrams obey a pattern theorem describing their fractal structure, from which the result follows.