The diesel particulate filter (DPF) technology with the use of fuel additives as regeneration aids is a promising technology for modern and future low-emissions diesel engines. The development of efficient and reliable DPF systems requires understanding of the regeneration process. Although the role of mathematical models in this respect has been widely recognized, few attempts to model the fuel-additive-assisted regeneration have been presented. In this work, a previously developed simplified authors’ model is extended, to allow deeper investigation of the process. The 1D mathematical model of the catalytic regeneration in the channel of the particulate filter is based on a dynamic oxygen storage/release mechanism of additive action, coupled to the transport phenomena occurring in the filter. A previously published set of full-scale measurements is employed to validate the model in a wide range of possible regeneration modes. The advantages of the present ID model over the previous OD model are illustrated. It is concluded that, at the present stage, the model can sufficiently describe and explain the main features of the regeneration process. The minor deviations of the model results from reality are attributed to the uncertainties of the reaction kinetics and to nonuniformities regarding flow distribution and soot deposition. The possible explanations are discussed, and directions for future work are suggested.