  We present a $q_T$-resummed calculation of diphoton production at order
N$^3$LL$^\prime$+NNLO. To reach the primed level of accuracy we have
implemented the recently published three-loop $\mathcal{O}(\alpha_s^3)$ virtual
corrections in the $q\bar{q}$ channel and the three-loop transverse momentum
dependent beam functions and combined them with the existing infrastructure of
CuTe-MCFM, a code performing resummation at order N$^3$LL. While the primed
predictions are parametrically not more accurate, one typically observes from
lower orders and other processes that they are the dominant effect of the next
order. We include in both the $q\bar{q}$ and loop-induced $gg$ channel the hard
contributions consistently together at order $\alpha_s^3$ and find that the
resummed $q\bar{q}$ channel without matching stabilizes indeed. Due to large
matching corrections and large contributions and uncertainties from the $gg$
channel, the overall improvements are small though. We furthermore study the
effect of hybrid-cone photon isolation and hard-scale choice on our fully
matched results to describe the ATLAS 8 TeV data and find that the hybrid-cone
isolation destroys agreement at small $q_T$.
