  The spectrum and morphology of the diffuse Galactic gamma-ray emission
carries valuable information on cosmic ray (CR) propagation. Recent results
obtained by analyzing Fermi-LAT data accumulated over seven years of
observation show a substantial variation of the CR spectrum as a function of
the distance from the Galactic Center. The spatial distribution of the CR
density in the outer Galaxy appears to be weakly dependent upon the
galactocentric distance, as found in previous studies as well, while the
density in the central region of the Galaxy was found to exceed the value
measured in the outer Galaxy. At the same time, Fermi-LAT data suggest a
gradual spectral softening while moving outward from the center of the Galaxy
to its outskirts. These findings represent a challenge for standard
calculations of CR propagation based on assuming a uniform diffusion
coefficient within the Galactic volume. Here we present a model of non-linear
CR propagation in which transport is due to particle scattering and advection
off self-generated turbulence. We find that for a realistic distribution of CR
sources following the spatial distribution of supernova remnants and the space
dependence of the magnetic field on galactocentric distance, both the spatial
profile of CR density and the spectral softening can easily be accounted for.
