  We consider the diffuse gamma ray data from FERMI first year observations and
compare them to the gamma ray fluxes predicted by Dark Matter annihilation or
decay (both from prompt emission and from Inverse Compton Scattering), for
different observation regions of the sky and a range of Dark Matter masses,
annihilation/decay channels and Dark Matter galactic profiles. We find that the
data exclude large regions of the Dark Matter parameter space not constrained
otherwise and discuss possible directions for future improvements. Also, we
further constrain Dark Matter interpretations of the e+e- PAMELA/FERMI spectral
anomalies, both for the annihilating and the decaying Dark Matter case: under
very conservative assumptions, only models producing dominantly mu+mu- and
assuming a cored Dark Matter galactic profile can fit the lepton data with
masses around 2 TeV.
