[1] Understanding the longevity of volcanic ash-clouds generated by powerful explosive eruptions is a long standing problem for assessing volcanic hazards and the nature and time scale of volcanic forcings on climate change. It is well known that the lateral spreading and longevity of these clouds is influenced by stratospheric winds, particle settling and turbulent diffusion. Observations of the recent 2010 Eyjafjallajökull and 2011 Grimsvötn umbrella clouds, as well as the structure of atmospheric aerosol clouds from the 1991 Mt Pinatubo event, suggest that an additional key process governing the cloud dynamics is the production of internal layering. Here, we use analog experiments on turbulent particle-laden umbrella clouds to show that this layering occurs where natural convection driven by particle sedimentation and the differential diffusion of primarily heat and fine particles give rise to a large scale instability. Where umbrella clouds are particularly enriched in fine ash, this "particle diffusive convection" strongly influences the cloud longevity. More generally, cloud residence time will depend on fluxes due to both individual settling and diffusive convection. We develop a new sedimentation model that includes both sedimentation processes, and which is found to capture real-time measurements of the rate of change of particle concentration in the 1982 El Chichon, 1991 Mt Pinatubo and 1992 Mt Spurr ash-clouds. A key result is that these combined sedimentation processes enhance the fallout of fine particles relative to expectations from individual settling suggesting that particle aggregation is not the only mechanism required to explain volcanic umbrella longevity.