  We consider semi-inclusive diphoton+jet and inclusive diphoton production in
high-energy proton-nucleus collisions, treating the target nucleus as a
Color-Glass-Condensate and the projectile proton in the parton model. We obtain
the prompt diphoton production cross-section in terms of fragmentation and
direct contributions. The fragmentation part is given in terms of single-photon
and double-photon fragmentation functions. We study prompt, direct and
fragmentation diphoton correlations in p+p and p+A collisions at the LHC, and
show that at low values of transverse momenta of the produced photon pair,
these correlations are sensitive to saturation effects. We show that
back-to-back (de)-correlations in prompt diphoton production are stronger in
fragmentation part than in the direct one.
