Pressure solution is widely regarded as a mechanism of ductile deformation in the upper crust. It is driven by stress differences and its rate is affected by temperature, grain size, and fluid chemistry. Pressure solution involves dissolution at grain contacts under high stress and precipitation at grain contacts on pore surfaces under low stress, leading to porosity reduction by precipitation in the pore space or by grain indentation. For a system closed at a grain scale, pressure solution is traditionally described by a mechanism involving three steps: (1) dissolution at intergranular interfaces, (2) diffusion of solutes inside the contact between two grains, and (3) precipitation on the surface of the grains in contact with the pore fluid. In this paper we propose a model where we have added a fourth step to this process, diffusive transport to other open pores, to account for the macroscopic diffusion of solutes in pore fluids, such that the deformation is not closed at the grain scale. In this model, differences in mineral solubility due to variations in stress and grain size produce concentration gradients which drive diffusive mass transport. The interaction between pressure solution at a grain scale and transport over distances of several grains can lead to the amplification of initial porosity heterogeneities and subsequent localization of deformation. Regions of intense dissolution compact and form bands in close proximity to regions where the porosity reduction is mainly due to cementation. Pressure solution augmented by large-scale diffusional transport will cause mass transport from fine-grained to coarse-grained rock volumes. We show that such processes are important during both diagenesis of sediments and compaction of fault gouge.