  The Galactic gamma-ray diffuse emission is currently observed in the GeV-TeV
energy range with unprecedented accuracy by the Fermi satellite. Understanding
this component is crucial as it provides a background to many different signals
such as extragalactic sources or annihilating dark matter. It is timely to
reinvestigate how it is calculated and to assess the various uncertainties
which are likely to affect the accuracy of the predictions. The Galactic
gamma-ray diffuse emission is mostly produced above a few GeV by the
interactions of cosmic ray primaries impinging on the interstellar material.
The theoretical error on that component is derived by exploring various
potential sources of uncertainty. Particular attention is paid to cosmic ray
propagation. Nuclear cross sections, the proton and helium fluxes at the Earth,
the Galactic radial profile of supernova remnants and the hydrogen distribution
can also severely affect the signal. The propagation of cosmic ray species
throughout the Galaxy is described in the framework of a semi-analytic two-zone
diffusion/convection model. This allows to convert the constraints set by the
boron-to-carbon data into a theoretical uncertainty on the diffuse emission.
New deconvolutions of the HI and CO sky maps are also used to get the hydrogen
distribution within the Galaxy. The thickness of the cosmic ray diffusive halo
is found to have a significant effect on the Galactic gamma-ray diffuse
emission while the interplay between diffusion and convection has little
influence on the signal. The uncertainties related to nuclear cross sections
and to the primary cosmic ray fluxes at the Earth are significant. The radial
distribution of supernova remnants along the Galactic plane turns out to be a
key ingredient. As expected, the predictions are extremely sensitive to the
spatial distribution of hydrogen within the Milky Way.
