The 3D scalar transport equation for unpolarized photons is used to give a detailed description of the fluorescence photon diffusion from a homogeneous slab. As an example, the paper considers, with a complete 3D spatial description in plane geometry, the distribution both in physical and momentum space of the primary photons induced by a narrow radiation beam crossing the slab. Then it is shown how the 3D geometry influences the shape of the continuous spectra due to a second Compton collision which modifies the distribution of the primaries due to photoelectric effect. The possibility of isolating the effect of a particular interaction is one of the strengths of the multiple-scattering scheme in the framework of transport techniques, which allows a better understanding of photon diffusion. In order to evaluate the effects of boundary conditions, the integral transport equation is used instead of the integro-differential equation, which has the advantage of treating the flow of photons from the outer space as an external source. The results are compared with those obtained for a half-infinite medium uniformly irradiated with a plane infinite slant source of monochromatic photons previously solved in 1D.