  We present a QCD calculation of the transverse momentum distribution of
photon pairs produced at hadron colliders, including all-orders soft-gluon
resummation valid at next-to-next-to-leading logarithmic accuracy. We specify
the region of phase space in which the calculation is most reliable, compare
our results with data from the Fermilab Tevatron, and make predictions for the
Large Hadron Collider. The uncertainty of predictions for production of
diphotons from fragmentation of final-state quarks is examined.
