  We prove diffusion for a quantum particle coupled to a field of bosons
(phonons or photons). The importance of this result lies in the fact that our
model is fully Hamiltonian and randomness enters only via the initial (thermal)
state of the bosons. This model is closely related to the one considered in [De
Roeck, Fr\"ohlich 2011], but various restrictive assumptions of the latter have
been eliminated. In particular, depending on the dispersion relation of the
bosons, the present result holds in dimension $d \geq 3$.
