Wall flow particulate filters have been used as a standard exhaust aftertreatment device for many years. Modern filters serve as multi-functional reactor/separator incorporating different types of catalytic functionalities. The interaction of particulate matter (PM) regeneration and catalytically supported reactions strongly depends on the given operating conditions. Temperature, inlet species concentration and mass flow cause a change from advective to diffusive-controlled flow conditions and influence the rate controlling dominance of individual reactions. A transient 1D+1D simulation model is presented considering advective and diffusive transport phenomena in the filter cake and wall. The reaction scheme focuses on passive PM conversion and catalytically supported oxidation of NO. The numerical implementation addresses the changing heights of the PM cake and real-time capable computational efforts. The model is validated with analytical reference solutions of NO2 turn-factor for passive PM conversion in a coated filter. The impact of back-diffusion phenomena on cake conversion is explored simulating pure advective and combined advective diffusive species transport. Experimentally validated rate approaches from literature are applied to investigate the passive PM conversion in different types of filter coatings at various operating conditions. Results of the spatial NO/NO2 profiles over the cake/wall height and filter length are discussed and the transient evolution of axial cake height profiles is presented. The results reveal that the impact of back-diffusion on PM cake conversion cannot be purely assessed by the Péclet number. Conversion reactions strongly influence local species fractions, concentration gradients and therefore the magnitude of diffusive fluxes. The comparison of different spatial coating designs shows that coatings in the inlet channel near the filter inlet feature superior performance in passive PM cake conversion.