How exactly does inflation convert random gravity fluctuations into coherent gravitational waves?
When inflation occurs the stretching of the gravitational field is dependent on the perturbations within that field originally. These perturbations are caused by quantum fluctuations. This leads to fluctuations in the magnitude of the inflation itself at a given point in space, causing gravitational waves due to the gravitational potential between neighboring points. The waves are fed by the inflationary energy, but are seeded by these quantum fluctuations.

This site gives a good explanation, as well as this particular quote:


  Gravitational-wave perturbations are different. They are not modulated
  by some unknown potential; they are produced by inflation, and we
  observe them directly. In straightforward models of inflation, the
  amplitude of the gravitational waves is directly proportional to the
  inflationary energy scale.