An analysis method for time-dependent broadband diffuse sound fields in enclosures is described. Beginning with a formulation utilizing time-dependent broadband intensity boundary sources, the strength of these wall sources is expanded in a series in powers of an absorption parameter, thereby giving a separate boundary integral problem for each power. The temporal behavior is characterized by a Taylor expansion in the delay time for a source to influence an evaluation point. The lowest-order problem has a uniform interior field proportional to the reciprocal of the absorption parameter, as expected, and exhibits relatively slow exponential decay. The next-order problem gives a mean-square pressure distribution that is independent of the absorption parameter and is primarily responsible for the spatial variation of the reverberant field. This problem, which is driven by input sources and the lowest-order reverberant field, depends on source location and the spatial distribution of absorption. Additional problems proceed at integer powers of the absorption parameter, but are essentially higher-order corrections to the spatial variation. Temporal behavior is expressed in terms of an eigenvalue problem, with boundary source strength distributions expressed as eigenmodes. Solutions exhibit rapid short-time spatial redistribution followed by long-time decay of a predominant spatial mode.