  We present a calculation of the next-to-leading order (NLO) QCD corrections
to gluon-induced electroweak gauge boson pair production, $gg \to ZZ$ and $gg
\to W^+W^-$, matched to the PYTHIA8 parton shower in the POWHEG approach. The
calculation consistently incorporates the continuum background, the
Higgs-mediated $gg\to H^* \to VV$ process, and their interference. We consider
leptonic decay modes of the massive vector bosons and retain offshell and
non-resonant contributions. The processes considered are loop-induced at
leading order and thus contain two-loop virtual contributions as well as
loop-squared real contributions. Parton-shower effects are found to be marginal
in inclusive observables and quite sizeable in observables that are exclusive
in additional jet radiation. The Monte Carlo generator presented here allows
for realistic experimental effects to be incorporated in state-of-the-art
precision analyses of diboson production and of the Higgs boson in the offshell
regime.
