  The recent observation of the 750 GeV diphoton excess at 13 TeV LHC has
motivated many scenarios of physics beyond the Standard Model. In this work, we
begin by showing that many models which explain the observed excess tend to get
strongly coupled well below the Planck scale. We then study a simple scenario
involving colored vector-like fermions with exotic charges, which is expected
to stay weakly coupled till the Planck scale. We find the conditions under
which this happens, derive the Renormalization Group equations for such models
and solve them to show that perturbativity till Planck scale can be maintained
for a very reasonable choice of parameters. Finally, we discuss issues related
to vacuum stability and the possibility of inflation in the scenarios we study.
