We present the first study of the quark mass dependence of the heavy quark momentum and spatial diffusion coefficients using lattice QCD with light dynamical quarks corresponding to a pion mass of 320 MeV. We find that, for the temperature range 195 MeV<T<293 MeV, the spatial diffusion coefficients of the charm and bottom quarks are smaller than those obtained in phenomenological models that describe the p_{T} spectra and elliptic flow of open heavy flavor hadrons.