We present a continuity-based approach for calculating flow delivered to a main channel from an adjacent floodplain and use the values in a linear diffusion model to generalize fluxes across a floodplain. Using interferometric synthetic aperture radar (SAR) measurements of floodplain water level changes and the continuity equation, we demonstrate that flow rates are not the same throughout Amazonian floodplains. Also, rates of floodplain storage change are found to be least in areas of greatest distance from a main channel which suggests a long residence time. Linear diffusion modeling of floodplain drainage represents the composite behavior of flow through channels, swamps and lakes and provides a simple method of defining storage changes. The key parameter necessary for diffusion modeling is floodplain conductivity which can be constrained by a simple description of floodplain topography and measurements of temporal changes in floodplain water levels.