We present the design and experimental verification of a membrane-type resonator-based Schroeder diffuser (MRSD). The membrane-type resonator consists of a decorated membrane and a rigid back cavity. By combining multiple resonators with the phase shift profile based on the quadratic residue sequence, the MRSD can produce a high efficiency diffuse sound field. Furthermore, the designed MRSD has a thickness with deep-subwavelength scale, which is 1 order of magnitude thinner than the conventional diffuser constructed with periodical wells. The proposed MRSD has advantages in low frequency applications and offers versatility for novel manipulations of sound.