We report on a defect‐related broad emission band at around 2.05 eV in bulk aluminum nitride crystals nominally undoped, but containing high concentrations of carbon, oxygen, and silicon. Time‐resolved photoluminescence spectroscopy yields two different exponential decays of this band: A slower process with 1.5 ms lifetime, and a faster process with a characteristic lifetime below 100 ns, which is activated with around 180 meV energy. The slow decay is ascribed to a spin‐forbidden transition between an oxygen‐related DX− S=1 state and a deep acceptor, which for higher temperatures turns into a donor‐acceptor pair transition between the effective‐mass‐like shallow oxygen donor state to the same deep acceptor. The acceptor is tentatively assigned to carbon or a carbon‐related complex.