We present a first-principles study of excitonic self-trapping in diamond. Our calculation provides evidence for self-trapping of the core exciton and gives a coherent interpretation of recent experimental x-ray absorption and emission data. Self-trapping does not occur in the case of a single valence exciton. We predict, however, that self-trapping should occur in the case of a valence biexciton. This process is accompanied by a large local relaxation of the lattice which could be observed experimentally.