Models of stratigraphic completeness and bed formation in fluvial depositional environments have most often assumed that successive depositional and erosional events deposit or erode amounts of sediment independently. This results in a random-walk model for the total amount of deposited sediment locally as a function of time. We consider an extension of the random-walk model of sedimentation in an alluvial plain in which deposition or erosion is concentrated in randomly avulsing channels and sediment transport is modeled by the diffusion equation (Culling's model). In contrast to the random-walk model, this model results in an anticorrelated sequence locally as a function of time, i.e., after an area has aggraded it has a higher elevation and a lower rate of future aggradation. In a previous paper we analyzed the topography generated by the model and argued that porosity variations could be associated with topographic variations. The power spectrum S (the square of the coefficients in a Fourier series) of one-dimensional transects of topography and porosity horizontally and vertically in this model have a power-law dependence on wave number k : S ( k ) congruent to k (super -beta ) , with values of beta close to those observed. In this paper we show that the model deposits sediment with a rate depending on time interval as a power law with exponent -3/4, more consistent with observations than the random-walk model. The model produces an exponential bed-thickness distribution with a skew dependent on the sedimentation rate of the basin in accordance with observations. We also examine the persistence in the series of bed thicknesses as a function of depth. For the stochastic diffusion model of sedimentation no persistence is observed. If the model fully characterizes the autocyclic dynamics in fluvial sedimentary basins, the lack of persistence in the synthetic bed sequences suggests that observed persistence and cyclicity in real bed-thickness sequences must be the result of allocyclic processes.