Absorbent members, especially bulked absorbent members, and methods of making the same are disclosed. The absorbent member may be in the form of a unitary absorbent fibrous layer comprising at least some cellulose fibers. The unitary absorbent fibrous layer is at least partially stratified through its thickness. The absorbent member may also have a plurality of discrete deformations, such as depressions and/or apertures in its surfaces. The method involves subjecting a precursor web to at least one cycle (or pass) through a mechanical deformation process. The mechanical deformation process utilizes a first forming member and a second forming member that form a nip therebetween through which the precursor web is passed. The first and second forming members are moving at different speeds relative to each other when they come together to form the nip.