  We report a measurement of the rate of prompt diphoton production in
$p\bar{p}$ collisions at $\sqrt{s}=1.96 ~\hbox{TeV}$ using a data sample of 207
pb$^{-1}$ collected with the upgraded Collider Detector at Fermilab (CDF II).
The background from non-prompt sources is determined using a statistical method
based on differences in the electromagnetic showers. The cross section is
measured as a function of the diphoton mass, the transverse momentum of the
diphoton system, and the azimuthal angle between the two photons and is found
to be consistent with perturbative QCD predictions.
