The microscopic diffusional dynamics of H and D on Pt(111) have been studied over length scales between 3 and 14 Angstrom by quasielastic helium atom scattering. Data taken over a wide range of parallel wave vectors (0.3 A(-1)less than or equal to\Delta K\less than or equal to 3.1 Angstrom(-1)) in the surface temperature range 140 K less than or equal to T(s)less than or equal to 250 K and at coverages 0.05 ML less than or equal to Theta(H)less than or equal to 0.66 ML, provide evidence for an isotropic single jump mechanism with an activation energy of 68+/-5 meV and a pre-exponential factor of D-0=1.1+/-0.5x10(-3) cm(2) s(-1) at low coverages. The diffusion coefficient is 2 to 3 orders of magnitude higher than found in an earlier laser induced desorption experiment, whereas the dependence on coverage is similar.