Catalytic cores for a wall-flow filter include juxtaposed channels extending longitudinally between an inlet side and an outlet side of the core, wherein the inlet channels are plugged at the outlet side and outlet channels are plugged at the inlet side. Longitudinal walls forming the inlet and outlet channels separate the inlet channels from the outlet channels. The walls include pores that create passages extending across a width of the walls from the inlet channels to the outlet channels. Catalysts are distributed across the width and length of the walls within internal surfaces of the pores in a manner such that the loading of each catalyst across the width varies by less than 50% from an average loading across the width.