We investigate the multi-loop correlation functions in a theory of strings embedded in a one-dimensional discrete manifold. Such a theory provides a microscopic definition of 2D quantum gravity coupled to unitary matter. (The conformal anomaly of the matter field depends on the choice of the embedding manifold.) The tree-level loop amplitudes are evaluated by means of a set of Feynman rules with clear geometrical meaning: the propagator is the two-loop correlator of the closed string and the vertices are the multi-loop amplitudes in pure gravity.