Following the introduction of the Brownian motion model for sediment transport by Einstein, several stochastic models have been explored in the literature motivated by the need to reproduce the observed non-Gaussian probability density functions (PDFs) of the sediment transport rates observed in laboratory experiments. Recent studies have presented evidence that PDFs of bed elevation and sediment transport rates depend on time scale (sampling time), but this dependence is not accounted for in any previous stochastic models. Here we propose an extension of Brownian motion, called fractional Laplace motion, as a model for sediment transport which acknowledges the fact that the time over which the gravel particles are in motion is in itself a random variable. We show that this model reproduces the multiscale statistics of sediment transport rates as quantified via a large-scale laboratory experiment.