  We study the high latitude (|b|>10) diffuse gamma-ray emission in the Galaxy
in light of the recently published data from the Fermi collaboration at
energies between 100 MeV and 100 GeV. The unprecedented accuracy in these
measurements allows to probe and constrain the properties of sources and
propagation of cosmic rays (CRs) in the Galaxy, as well as confirming
conventional assumptions made on the interstellar medium (ISM). Using the
publicly available DRAGON code, that has been shown to reproduce local
measurements of CRs, we study assumptions made in the literature on HI and H2
gas distributions in the ISM, and non spatially uniform models of diffusion in
the Galaxy. By performing a combined analysis of CR and gamma-ray spectra, we
derive constraints on the properties of the ISM gas distribution and the
vertical scale height of galactic CR diffusion, which may have implications
also on indirect Dark Matter detection. We also discuss some of the possible
interpretations of the break at ~230 GV in CR protons and helium spectra,
recently observed by PAMELA and their impact on gamma-rays.
