  Motivated by recent experiments pertaining to the interaction of weak
SASE-FEL pulses with atoms and molecules, we investigate the conditions under
which such interactions can be described in the framework of a simple
phase-diffusion model with decorrelated atom-field dynamics. The nature of the
fluctuations that are inevitably present in SASE-FEL pulses is shown to play a
pivotal role in the success of the decorrelation. Our analysis is performed in
connection with specific recent experimental results from FLASH in the soft
X-ray regime.
