An analytic method is presented for calculating transient diffusive electromagnetic fields in stratified media. The method is inspired by the modified Cagniard method for calculating transient wave fields in media of this kind. Closed-form time domain expressions are constructed for the fields generated by a localized source. The expressions have the form of a superposition of diffusive generalized-ray constituents. The case of the two-dimensional E-polarized field generated by a line source of electric current is worked out in detail.