  We calculate the fully differential next-to-next-to-leading order (NNLO) QCD
corrections to vector-boson fusion (VBF) Higgs pair production. This
calculation is achieved in the limit in which there is no colored cross-talk
between the colliding protons, using the projection-to-Born method. We present
differential cross sections of key observables, showing corrections of up to
3-4% at this order after typical VBF cuts, with the total cross section
receiving contributions of about 2%. In contrast to single Higgs VBF
production, we find that the NNLO corrections are for the most part within the
next-to-leading order scale uncertainty bands.
