  The jet Trimming procedure has been demonstrated to greatly improve event
reconstruction in hadron collisions, by mitigating contamination due initial
state radiation, multiple interactions, and event pileup. Meanwhile, Qjets -- a
nondeterministic approach to tree-based jet substructure has been shown to be a
powerful technique in decreasing random statistical fluctuations, yielding
significant effective luminosity improvements. This manifests through an
improvement in the significance $S/\delta B$, relative to conventional methods.
Qjets also provide novel observables in many cases, like mass-volatility, that
could be used to further discriminate between signal and background events. The
statistical robustness and volatility observables, for tagging, are obtained
simultaneously. We explore here a combination of the two techniques, and
demonstrate that significant enhancements in discovery potentials may be
obtained in non-trivial ways. We will illustrate this by considering a diboson
resonance analysis as a case study -- enabling us to interpolate between
scenarios where the gains are purely due to statistical robustness and
scenarios where the gains are also reinforced by volatility variable
discriminants. The former, for instance, is applicable to digluon/diquark
resonances, while the latter will be of relevance to di-$W^\pm$/di-$Z^0$
resonances, where the boosted vector bosons are decaying hadronically and have
an intrinsic mass scale attached to them. We argue that one can enhance signal
significance and discovery potentials markedly through stochastic grooming, and
help augment studies at the Large Hadron Collider and future hadron colliders.
