Muon spin depolarization rates and hyperfine decoupling curves imply the existence of a neutral muonium center to high temperatures in AlN, providing an experimental model for interstitial atomic hydrogen. This center has a hyperfine interaction close to that of the free atom, but with a small temperature-dependent dipolar contribution indicating weak anisotropy. We discuss the site assignment and present results on the diffusion of these centers in AlN and associated conversion rates obtained from the depolarization data. Low-temperature motion is due to tunneling while thermally activated processes dominate at high temperatures. Diffusion-limited conversion out of the mobile atomic state is observed in both regimes.