We demonstrate the nucleation of self-assembled, epitaxial GaN nanowires (NWs) on (111) single-crystalline diamond without using a catalyst or buffer layer. The NWs show an excellent crystalline quality of the wurtzite crystal structure with m-plane faceting, a low defect density, and axial growth along the c-axis with N-face polarity, as shown by aberration corrected annular bright-field scanning transmission electron microscopy. X-ray diffraction confirms single domain growth with an in-plane epitaxial relationship of (10 ̅10)(GaN) [parallel] (01 ̅1)(Diamond) as well as some biaxial tensile strain induced by thermal expansion mismatch. In photoluminescence, a strong and sharp excitonic emission reveals excellent optical properties superior to state-of-the-art GaN NWs on silicon substrates. In combination with the high-quality diamond/NW interface, confirmed by high-resolution transmission electron microscopy measurements, these results underline the potential of p-type diamond/n-type nitride heterojunctions for efficient UV optoelectronic devices.