A search is presented for decays beyond the standard model of the 125 GeV Higgs bosons to a pair of light bosons, based on models with extended scalar sectors. Light boson masses between 5 and 62.5 GeV are probed in final states containing four τ leptons, two muons and two b quarks, or two muons and two τ leptons. The results are from data in proton-proton collisions corresponding to an integrated luminosity of 19.7 fb⁻¹, accumulated by the CMS experiment at the LHC at a center-of-mass energy of 8 TeV. No evidence for such exotic decays is found in the data. Upper limits are set on the product of the cross section and branching fraction for several signal processes. The results are also compared to predictions of two-Higgs-doublet models, including those with an additional scalar singlet.