Predictions of diesel particulate filtration are typically made by modeling of a particle collection, and providing particle trapping levels in terms of a pressure drop. In the present study, a series of single channel diesel particulate filter (DPF) experiments are conducted, the pressure traces are inversely analyzed and essential filtration parameters are deducted for model closure. A DPF filtration model is formulated with a non-linear description of soot cake regression. Dependence of soot cake porosity, packing density, permeability, and soot density in filter walls on convective-diffusive particle transportation is examined. Sensitivity analysis was conducted on model parameters, relevant to the mode of transition. Soot cake porosity and soot packing density show low degrees of dispersion with respect to the Peclet number and have asymptotes at 0.97 and $70;kg/m^3$, respectively, at high Peclet number. Soot density in the filter wall, which is inversely proportional to filter wall Peclet number, controls the filtration mode transition but exerts no influence on termination pressure drop. The percolation constant greatly alters the extent of pressure drop, but is insensitive to volumetric flow rate or temperature of exhaust gas at fixed operation mode.