  We present a possible interpretation of the recent diphoton excess reported
by the $\sqrt s=13$ TeV LHC data in quark seesaw left-right models with
vectorlike fermions proposed to solve the strong $CP$ problem without the
axion. The gauge singlet real scalar field responsible for the mass of the
vectorlike fermions has the right production cross section and diphoton
branching ratio to be identifiable with the reported excess at around 750 GeV
diphoton invariant mass. Various ways to test this hypothesis as more data
accumulates at the LHC are proposed.
