  We show that the dominant channel proposed for the determination of the Higgs
boson trilinear coupling, $pp\to HH+X$ via gluon fusion, exhibits an
interference structure that is independent of the collider energy for collider
energies in the range $8\,{\rm TeV}\leq \sqrt{s}\leq 100\,{\rm TeV}$ and is
almost maximally destructive. This insensitivity to the collider energy remains
approximately true for a variety of other two Higgs production mechanisms
although the magnitude of the interference varies widely.
