We present a calculation of inclusive diboson ($${\textrm{WZ, ZZ, WW}}$$
WZ, ZZ, WW
) processes at the LHC in the presence of intermediate polarised weak bosons decaying leptonically, matching next-to-leading-order accuracy in QCD with parton-shower effects. Starting from recent developments in polarised-boson simulation based on the helicity selection at the amplitude level, we have carried out the implementation in the Powheg-Box-Res framework, and validated it against independent fixed-order calculations. A phenomenological analysis in realistic LHC setups, as well as a comparison with recent ATLAS measurements, are presented.