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Color octet bosons are a universal prediction of models in which the 750 GeV diphoton resonance corresponds to a pion of a QCD-like composite sector. We show that the existing searches for dijet and photon plus jet resonances at the LHC constrain single productions of color octet states and can be translated into stringent limits on the 750 GeV diphoton rate. For a minimal 5 + 5 model, the 750 GeV diphoton signal cross section at the 13 TeV LHC is constrained to be below around 5 fb. Future LHC searches for the photon plus jet resonances can establish evidence of a new color-octet state with 20 fb and validate a pion-like explanation for the 750 GeV resonance.