A thin layer of low mean-pore-size filter material that permanently accommodates the accumulation of exhaust particulates (as soot or a soot cake) is carried on a porous ceramic support. The supported filter material is closely coupled with the exhaust manifold of the engine, for the purpose of passive regeneration of stored particulates, and removes particulate matter from the exhaust which is directed through the filter layer and ceramic support. The oxygen content of the exhaust oxidizes the particulate matter on the filter material. In a preferred embodiment, a thin layer of the filter material is supported on inlet channel walls of a wall flow-through ceramic filter body to remove the particles from the exhaust. The filter body comprises an upstream exhaust gas flow inlet face with openings to a plurality of inlet channels and a downstream face with a like plurality of openings from outlet channels. The inlet channels are closed at the downstream face and the outlet channels are closed at the inlet face. So the exhaust stream enters the inlet channels and flows through the filter layers and supporting channel walls to an outlet channel. The filtered exhaust stream exits the outlet end of the filter body and is combined into an exhaust passage downstream of the filter body for further treatment as may be necessary.