This paper proposes a tractable model of Bayesian learning on large random networks where agents choose whether to adopt an innovation. We study the impact of the network structure on learning dynamics and product diffusion. In directed networks, all direct and indirect links contribute to agents' learning. In comparison, learning and welfare are lower in undirected networks and networks with cliques. In a rich class of networks, behavior is described by a small number of differential equations, making the model useful for empirical work.