In this paper we construct an atlas that captures functional characteristics of a cognitive process from a population of individuals. The functional connectivity is encoded in a low-dimensional embedding space derived from a diffusion process on a graph that represents correlations of fMRI time courses. The atlas is represented by a common prior distribution for the embedded fMRI signals of all subjects. The atlas is not directly coupled to the anatomical space, and can represent functional networks that are variable in their spatial distribution. We derive an algorithm for fitting this generative model to the observed data in a population. Our results in a language fMRI study demonstrate that the method identifies coherent and functionally equivalent regions across subjects.