  We investigate the dynamics of diatomic molecules subjected to both a
femtosecond mid-infrared laser pulse and Gaussian white noise. The stochastic
Schr\"odinger equation with a Morse potential is used to describe the molecular
vibrations under noise and the laser pulse. For weak laser intensity, well
below the dissociation threshold, it is shown that one can find an optimum
amount of noise that leads to a dramatic enhancement of the dissociation
probability. The enhancement landscape which is shown as a function of both the
noise and the laser strength, exhibits a global maximum. A frequency-resolved
gain profile is recorded with a pump-probe set-up which is experimentally
realizable. With this profile we identify the linear and nonlinear multiphoton
processes created by the interplay between laser and noise and assess their
relative contribution to the dissociation enhancement.
