We construct a random process with stationary increments associated to the hamiltonianof the spin boson model consisting of a component describing the spin and a componentgiven by a Schwartz distribution-valued Ornstein-Uhlenbeck process describing the bosoneld. As consequence, We use a functional integral representation of the Hamiltonian toprove a functional central limit theorem for additive functionals and we derive explicitexpressions of the diusion constant.