A moments method is applied to the non‐self‐similar problem of the diffusion of radiation from a cavity, in the case that the transport of energy is purely radiative. The energy in the cavity is assumed to be introduced instantaneously, and the diffusion into the surrounding wall, particularly the motion of the radiation front, is followed for subsequent times. The moments method used has the characteristic that it gives, for the physical model assumed, exact results for the position of the front in both the short‐ and long‐time limits for all geometries.Both plane and spherical cavities are treated in detail. Series solutions which apply in the limits of short and long times are given. Equations describing the first‐order departure of spherical radiation flow from plane flow are derived, and the short‐time solution is given. In plane geometry all quantities of interest can be written in parametric form in terms of elementary functions, and numerical results are presented in this case. Spherical geometry yields a more complex parametric solution, which is also given.