  We are interested in the transverse-momentum ($q_T$) distribution of a
diphoton pair produced in hadron collisions. We resum the
logarithmically-enhanced perturbative QCD contributions at small values of
$q_T$ up to next-to-next-to-leading logarithmic accuracy. We consistently
combine resummation with the known next-to-leading order perturbative result at
intermediate and large values of $q_T$ . We include all perturbative terms up
to order $\alpha_S^2$ in our computation which, after integration over $q_T$ ,
reproduces the known next-to-next-to-leading order result for the diphoton pair
production total cross section. A comparison with LHC data is presented. We
estimate the perturbative accuracy of the theoretical calculation by performing
the corresponding variation of scales. We anticipate that the effect of the
transverse momentum resummation is not only to recover the predictivity of the
calculation at small $q_T$ , but also to improve substantially the agreement
with the experimental data.
