There are several factors that affect the dynamics of adsorbed hydrogen atoms on a carbon surface. Using density functional calculations we show that coadsorption can be a highly influential factor. The diffusion of hydrogen adsorbed on graphene is, explored in the presence of H-containing molecules. Without coadsorbates the diffusion barrier of H on graphene is 0.94 eV, while with water/ammonia it is 0.85/0.12 eV. The low barrier in the case of ammonia is attributed to the formation of a stable intermediate state NH4, while such a stable state is not found in the case of water. In addition, hydrogen fluoride, hydrogen sulfide, arsine, and phosphine were also considered. We found that stronger hydrogen-hydride bonds lead to lower diffusion barriers of H on graphene.