Searches for new phenomena in high-mass diphoton final states with the ATLAS experiment at the LHC are presented. The analysis is based on pp collision data corresponding to an integrated luminosity of 36.7 fb⁻¹ at a centre-of-mass energy √s=13 TeV recorded in 2015 and 2016. Searches are performed for resonances with spin 0, as predicted by theories with an extended Higgs sector, and for resonances with spin 2, using a warped extra-dimension model as a benchmark model, as well as for non-resonant signals, assuming a large extra-dimension scenario. No significant deviation from the Standard Model is observed. Upper limits are placed on the production cross section times branching ratio to two photons as a function of the resonance mass. In addition, lower limits are set on the ultraviolet cutoff scale in the large extra-dimensions model.