A measurement of the rate of prompt diphoton production in p anti-p
collisions at s**(1/2) = 1.96 TeV using the CDF detector is presented.  The
results are compared to a NLO calculation.  We also measured the gamma + b
and gamma + c cross sections comparing the results with PYTHIA LO
predictions.  The background from non-prompt sources is estimated using a
statistical method based on differences in electromagnetic showers initiated
by photons and by the background.