We present a novel interpretation of the gamma-ray diffuse emission measured by Fermi-LAT and H.E.S.S. in the Galactic center (GC) region and the Galactic ridge (GR). In the first part we perform a data-driven analysis based on PASS8 Fermi-LAT data: We extend down to a few GeV the spectra measured by H.E.S.S. and infer the primary cosmic-ray (CR) radial distribution between 0.1 and 3 TeV. In the second part we adopt a CR transport model based on a position-dependent diffusion coefficient. Such behavior reproduces the radial dependence of the CR spectral index recently inferred from the Fermi-LAT observations. We find that the bulk of the GR emission can be naturally explained by the interaction of the diffuse steady-state Galactic CR sea with the gas present in the central molecular zone. Although we confirm the presence of a residual radial-dependent emission associated with a central source, the relevance of the large-scale diffuse component prevents to claim a solid evidence of GC pevatrons.