We report measurements of the transverse and longitudinal spin diffusi
on coefficients for 0.1 - 0.24 monolayers of He-3 adsorbed on thin He-
3 films as a function of temperature and He-4 coverage. A strong He-4
coverage dependence is observed in the spin diffusion which suggests t
hat the He-3 quasiparticles in the film are strongly scattered by subs
trate inhomogeneities for He-4 coverages below 0.5 angstrom-2.