We discuss the possibility of generating adiabatic density perturbations from spatial fluctuations in the inflaton decay rate which are due to quantum fluctuations of light moduli fields coupling to the inflaton. We point out that non-renormalizable operators, which lift the flatness of the moduli potential, play an important role for the density perturbations. In particular, the non-renormalizable terms give rise to a considerable damping of the fluctuations and thereby pose an obstruction to the construction of possible models.