The diffusivity in a plasma is enhanced over classical diffusion when the particles undergo L¿vy flight interactions caused by scale-invariant turbulence. In this case classical parallel diffusion (heat flux) is modified. Perpendicular magnetized diffusion coefficients obtained assume a scaling D∝kBT/B1+Δ where Δ<1. This scaling is closer to Bohm-scaling than conventional theories predict. The non-classical diffusion coefficients depend on time. As a consequence, the expected density profiles will not exhibit the usually assumed diffusive shapes. It is suggested that in regions of strong plasma turbulence enhanced superdiffusivity may contribute to the population of the inner LLBL.¿ 1997 American Geophysical Union