At the LHC, diphoton production constitutes the main background of Higgs production in the diphoton decay and of many new physics models predicting large-mass diphoton resonances. Underestimated theoretical uncertainties and large perturbative corrections have been a long-standing issue over the years with various suggestions. Especially the transverse momentum spectrum has lead to various prescriptions. We present transverse momentum resummed diphoton predictions at the level of N$^3$LL$'$+NNLO which include the recently published 3-loop hard and beam functions. We discuss the residual uncertainties and challenges for the transverse momentum distribution and address the effect of hybrid-cone photon isolation.