  Using a density matrix description in space we study the evolution of
wavepackets in a fluctuating space-time background. We assume that space-time
fluctuations manifest as classical fluctuations of the metric. From the
non-relativistic limit of a non-minimally coupled Klein-Gordon equation we
derive a Schr\"odinger equation with an additive gaussian random potential.
This is transformed into an effective master equation for the density matrix.
The solutions of this master equation allow to study the dynamics of
wavepackets in a fluctuating space-time, depending on the fluctuation scenario.
We show how different scenarios alter the diffusion properties of wavepackets.
