A noise damping device is proposed for reducing and smoothing pressure fluctuations in a damping medium, especially in fuel supplied by fuel supply pumps, which serves to reduce pressure fluctuations downstream of the fuel supply pump. The noise damping device includes a diaphragm fluctuation damper which is disposed directly downstream of the pump compression collar and by means of which, by rotating the diaphragm fluctuation damper, an annular fitting is fixable in its axial position between the diaphragm fluctuation damper and the pump compression collar. A check valve in the connection extension of the diaphragm fluctuation damper or in the annular fitting prevents the return flow of fuel out of the fuel circulatory system after the termination of fuel supply.