Submarine fans are important components of continental margins; they contain a stratigraphic record of environmental changes and host large accumulations of oil and gas. The grain size and volume of sediment supply to fans is thought to control the heterogeneity of deep-water deposits; predicting spatial variability of sandy and muddy deposits is an important applied challenge in the characterization of fans. Here, we use DionisosFlow stratigraphic-forward models to evaluate the sensitivity of submarine-fan deposition to a range of grain sizes, with corresponding diffusion coefficients ranging from 10 to 100 km 2 /kyr for coarse sand to silt/clay, and discharges. In general, finer grains are transported farther in our models because they have larger diffusion coefficients. Coarser grains typical of a sand-rich fan tend to pile up and compensationally stack at the mouth of a proximal feeder channel. Increasing sediment-gravity-flow discharge resulted in a thicker depositional system; however, relatively coarse sediment piled up at the mouth of the feeder channel, which created a slope that promoted basinward sediment transport. Our modeling results can be applied to predict the overall geometry, stacking, and grain-size distribution of submarine fans. Improved understanding of grain-size and discharge controls also informs interpretation of the stratigraphic record of submarine fans. For example, outcrop observations of heterogeneity and compensational stacking of depocenters can be related to changing boundary conditions, namely changes in the caliber and overall supply of sediment delivery to deep-water basin margins.