We study light transport in optically thick luminescent random media. Using radiative transport theory for luminescent media and applying asymptotic and computational methods, a corrected diffusion approximation is derived with the associated boundary conditions and boundary layer solution. The accuracy of this approach is verified for a plane-parallel slab problem. In particular, the reduced system models accurately the effect of reabsorption. The impacts of varying the Stokes shift and using experimentally measured luminescence data are explored in detail. The results of this study have application to the design of luminescent solar concentrators, fluorescence medical imaging, and optical cooling using anti-Stokes fluorescence.