We present a theory for spin diffusion in disordered organic semiconductors, based on incoherent hopping of a charge carrier and coherent precession of its spin in an effective magnetic field, composed of the random hyperfine field of hydrogen nuclei and an applied magnetic field. From Monte Carlo simulations and an analysis of the waiting-time distribution of the carrier we predict a surprisingly weak temperature dependence, but a considerable magnetic-field dependence of the spin-diffusion length. We show that both predictions are in agreement with experiments on organic spin valves.