  We investigate the 750 GeV diphoton excess in terms of supersymmetric models
which preserve grand unification in the ultraviolet. We show that minimal
extensions of the MSSM by a singlet and a vector-like 5-plet or 10-plet of
SU(5) can explain the observed signal while remaining perturbative up to the
GUT scale. Different from previous analyses we rely on light sfermions in the
loops which - compared to the analog non-supersymmetric models - enhance the
diphoton cross section by up to a factor of seven. While the resonance decay
width is narrow, mass splitting of the scalar and pseudoscalar components may
result in a double resonance. We perform a likelihood analysis on the ATLAS and
CMS data to show that the significance of the diphoton excess increases from
3.3 sigma (single narrow resonance) to 3.9 sigma for the double resonance. We
also provide signal predictions in other diboson channels to be tested at
LHC-13.
