Searches for the high transverse momentum ($p_{T}$) or boosted regime of the Higgs boson via gluon-gluon fusion and vector boson fusion productions are presented, where the Higgs boson decays to either a pair of bottom quarks or $\tau$ leptons. The results are based on proton-proton collision data collected by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV. The data corresponds to an integrated luminosity of 138 ${\rm fb}^{-1}$. The decay of a high-$p_{T}$ Higgs boson to a boosted bottom quark-antiquark pair is isolated by selecting large-radius jets and exploiting jet substructure, as well as heavy flavor taggers based on advanced machine learning techniques. The signal production cross sections, relative to the expectations, targeting vector boson fusion and gluon-gluon fusion processes are extracted simultaneously by performing a fit to data in the large-radius jet mass. On the other hand, the decay of a high-$p_{T}$ Higgs boson to a pair of $\tau$ leptons is reconstructed using a dedicated algorithm. The product of the production cross section and branching fraction is measured. The fiducial differential cross section of the Higgs boson is also provided as a function of the Higgs boson and leading jet transverse momenta.