As is (supposedly) well known, Electromagnetic coupling can be "explained" as a closure term to a langrangian comprising a free Dirac field and a free vector field that are required to be invariant under transformations that add arbitrary gradient quantities to the vector field and matching local phase $U(1)$ adjustments to the Dirac field, a construction better known as gauge invariance.
There are similar gauge invariant arguments to obtain the electro-weak and chromodynamic couplings. None of such applies so far to gravity in a way that is entirely satisfactory (to me, yes), specially with all the non-sense that its straightforward application would imply (such as no local observables, etc.)
This particular question is about the Higgs field; from my understanding it is entirely added by hand to all (or most?) fermion fields. It couples also to gauge vector bosons but unlike those, i've never seen any allegations that such coupling would arise naturally from a gauge invariance schema. Are there any attempts to produce any of such constructions that is worth mentioning?