  Light diffusion is usually associated with thick, opaque media. Indeed,
multiple scattering is necessary for the onset of the diffusive regime and such
condition is generally not met in almost transparent media. Nonetheless, at
long enough times, transport in an infinite thin slab is still determined by a
multiple scattering process whose complete characterization is lacking. In this
paper we show that, after a short transient, the mean square width of the
transmitted intensity still exhibits a simple linear increase with time as
predicted by diffusion theory, even at optical thickness as low as one.
Interestingly, such linear growth is predicted not to depend neither on the
slab thickness nor on its refractive index contrast, yet the accuracy of this
simple approximation in the ballistic-to-diffusive regime hasn't been
investigated so far. By means of Monte Carlo simulations, we find clear
evidence that boundary conditions play an active role in redefining the very
asymptotic value of the diffusion coefficient by directly modifying the
statistical distributions underlying light transport in such media. In this
respect, we demonstrate the need to distinguish between a set of intrinsic and
effective transport parameters, whose relation and interplay with boundary
conditions remains to be fully understood.
