A search is presented for an extended Higgs sector with two new particles, (Formula presented) and (Formula presented), in the process (Formula presented). Novel neural networks classify events with diphotons that are merged and determine the diphoton masses. The search uses LHC proton-proton collision data at (Formula presented) collected with the CMS detector, corresponding to an integrated luminosity of (Formula presented). No evidence of such resonances is seen. Upper limits are set on the production cross section for (Formula presented) between 300 and 3000 GeV and (Formula presented) between 0.5% and 2.5%, representing the most sensitive search in this channel.