The nature of hydrogen bonding and diffusion in crystalline Si was investigated using an ab initio self-consistent pseudopotential method. The relative energies of interstitial atomic hydrogen, diatomic hydrogen complexes, and shallow dopant-hydrogen complexes were examined. We present a mechanism for hydrogen diffusion which involves a new metastable diatomic complex with a much lower activation barrier for diffusion than molecular hydrogen. The effects on diffusion of diatomic-complex dissociation or its conversion to molecular hydrogen are discussed. The influence of temperature, hydrogen concentration, and dopant (n or p type) on hydrogen diffusion are examined. Metastable diatomic-complex formation is proposed to be highly likely at low temperatures and at high hydrogen concentrations, particularly in n-type Si. Diffusion through an ionized ${\mathrm{H}}^{+}$ form is most likely to occur in p-type Si.