A significant contribution to vertical dispersion of tracers in the stratosphere arises from the variability in the diabatic heating of air parcels. Air parcels starting on a given isentropic surface experience different time histories of diabatic heating, which causes vertical dispersion across isentropic surfaces. We refer to this process as diabatic cross-isentropic dispersion, or diabatic dispersion for brevity. The present study investigates diabatic dispersion in the lower stratosphere by computing parcel trajectories initialized uniformly over the 500 K surface on January 1, 1993. Parcels are followed for 2 months using analyzed winds and diabatic heating rates computed from analyzed temperatures. Diabatic dispersion depends on the statistics of the large-scale horizontal eddy motion as well as on the spatial structure of the diabatic heating field. The trajectory statistics suggest that the polar vortex, surf zone, tropics, and extratropical summer hemisphere are, to varying extents, isolated from each other and that the diabatic dispersion within each of these regions is different. In both the surf zone and southern hemisphere extratropics the dispersion is initially advective, with potential temperature variance ⟨Δ&thgr;(t)2⟩ increasing as t2 as time t increases. After about 1 month, the dispersion becomes diffusive in the sense that ⟨Δ&thgr;(t)2⟩~2K&thgr;&thgr;t and with a diffusivity K&thgr;&thgr; in the range 2--6 K2 d-1, roughly equivalent to Kzz~0.1--0.2 m2 s-1. The emergence of a diffusive regime is discussed in terms of loss of memory of diabatic heating along parcel paths, as measured by the decay of the Lagrangian autocorrelation function. Diabatic dispersion within the tropics and polar vortex over the 2-month period is more than an order of magnitude smaller and is less clearly diffusive. The diabatic dispersion of parcels moving poleward out of the tropics into either hemisphere is faster than either differential advection or diffusion, and in this case, ⟨Δ&thgr;(t)2⟩ increases as t3. For the total ensemble of all parcels, the potential temperature variance increases as t2, consistent with global-scale differential advection by the mean diabatic circulation. This is inconsistent, at least on the 2-month timescale considered here, with a one-dimensional diffusive model of vertical dispersion. ¿ 1997 American Geophysical Union