Self-diffusion coefficients, D, have been measured in the glass forming liquids salol, glycerol, phenolphthaleine dimethyl ether (PDE), cresolphthaleine dimethyl ether (CDE), and alpha alpha alpha-trinaphthylbenzene (TNB) In the supercooled regime. The NMR static magnetic field gradient technique was applied where D > 10(-14) m(2) s(-1) can be attained. The results are similar to previous diffusion experiments where an enhancement of translational diffusion was found in comparison with rotational diffusion and shear viscosity. Various models of spatial heterogeneity are related to a phenomenological environmental fluctuation model in view of recent diffusion and relaxation data close to the glass transition.