The bulk of the energy release from hydrogen bombs is not generated by fusion. The general design of a hydrogen bomb is that a hydrogen "blanket" surrounds a fission "core". When the fission "core" goes supercritical, it releases enough energy to initiate fusion in the "blanket".

What the "blanket" does at this point is exert pressure on the "core", which would be beginning to blow apart in a conventional nuclear device. Keeping the "core" together for just that small bit of time longer allows it to remain supercritical for just that small bit of time longer, with the energy release growing exponentially with a time constant of 10^-7 seconds.