A system for cooling the impeller of a centrifugal compressor in a turbomachine is disclosed. The compressor supplies an annular diffuser. The diffuser includes an end-piece that extends downstream and along the impeller of the compressor and is covered on the upstream side by an annular metal sheet. The sheet delimits, with the impeller of the compressor, a first annular passageway to carry away the air taken from the outlet of the compressor and, with the end-piece of the diffuser, a second annular passageway to carry away a portion of the air flow coming out of the diffuser.