River water intruding into a lake or ocean typically results in a surface layer of warm, sediment-laden water overriding relatively dense, cold fluid. Though this system is stable with respect to density, instability may arise as a result of the different diffusivities of sediment and heat. A series of experiments were conducted which indicated that double-diffusive convection (DDC) was responsible for rapid sedimentation of slowly settling particles. A simple theory, based upon relevant physical processes, is developed that describes this behavior. It also incorporates the previously neglected effects of ambient stratification on the strength of the DDC. Application of the theory and our results to field data taken from oceanic river plumes demonstrates that the flux due to double-diffusive sedimentation (DDS) can be at least as strong as flocculation-enhanced gravitational settling.