A measurement is presented of differential cross sections for Higgs boson (H) production in pp collisions at s√=8s=8 TeVTeV . The analysis exploits the H→γγH→γγ decay in data corresponding to an integrated luminosity of 19.7 fb-1fb-1 collected by the CMS experiment at the LHC. The cross section is measured as a function of the kinematic properties of the diphoton system and of the associated jets. Results corrected for detector effects are compared with predictions at next-to-leading order and next-to-next-to-leading order in perturbative quantum chromodynamics, as well as with predictions beyond the standard model. For isolated photons with pseudorapidities |η|<2.5|η|<2.5 , and with the photon of largest and next-to-largest transverse momentum ( pγTpTγ ) divided by the diphoton mass mγγmγγ satisfying the respective conditions of pγT/mγγ>1/3pTγ/mγγ>1/3 and >1/4>1/4 , the total fiducial cross section is 32±1032±10 \,fb\,fb .