  We calculate the extragalactic diffuse emission originating from the
up-scattering of cosmic microwave photons by energetic electrons and positrons
produced in particle dark matter annihilation events at all redshifts and in
all halos. We outline the observational constraints on this emission and we
study its dependence on both the particle dark matter model (including the
particle mass and its dominant annihilation final state) and on assumptions on
structure formation and on the density profile of halos. We find that for
low-mass dark matter models, data in the X-ray band provide the most stringent
constraints, while the gamma-ray energy range probes models featuring large
masses and pair-annihilation rates, and a hard spectrum for the injected
electrons and positrons. Specifically, we point out that the all-redshift,
all-halo inverse Compton emission from many dark matter models that might
provide an explanation to the anomalous positron fraction measured by the
Pamela payload severely overproduces the observed extragalactic gamma-ray
background.
