A turbomachine diffuser, comprising: a. a first annular wall incorporating a central opening configured to receive a fluid to be compressed or pumped; b. a second annular wall; c. a cavity between said first and second annular walls, wherein said cavity is shaped to receive an impeller that is in fluid communication with said central opening, said impeller provides for compressing or pumping said fluid into an annular portion (10.1, 10.2) of said cavity that is radially outboard of said impeller when said impeller is located in said cavity, said annular portion of said cavity comprises first (10.1) and second (10.2) annular portions, said first annular portion is concentric with, radially adjacent to, and downstream of a radially-outermost circumferential boundary of said impeller when said impeller is located within said cavity, said first annular portion is vaneless, said second annular portion is concentric with, radially adjacent to, and around a radially-outermost circumferential boundary of said first annular portion, said second annular portion is downstream of said first annular portion, an axial gap (40, 40') between said first and second annular walls increases with respect to radial distance within said second annular portion, wherein said radial distance is with respect to a central longitudinal axis of said impeller, and a ratio of a magnitude of said axial gap at a radially-outermost location of said second annular portion to a magnitude of said axial gap a radially-innermost location of said second annular portion is at least 1.4 and at most 2.0; d. a collector radially outboard of, and in fluid communication with, and downstream of, said second annular portion of said cavity, wherein said collector is in fluid communication with an outlet duct that provides for a discharge from said collector of said fluid compressed or pumped by said impeller within said cavity and thence into said collector; and e. a plurality of vanes incorporated in said second annular portion, wherein each vane of said plurality of vanes is twisted along a length thereof in a meridional direction, a ratio of a chord length of said vane to a mean circumferential separation distance between adjacent vanes of said plurality of vanes is at least 1.8 and at most 4.0, and a ratio of a maximum value of a radius of said second annular portion to a minimum value of said radius of said second annular portion is at least 1.08 and at most 1.20, wherein said radius of said second annular portion is with respect to said central longitudinal axis of said impeller. a. a first annular wall incorporating a central opening configured to receive a fluid to be compressed or pumped; b. a second annular wall; c. a cavity between said first and second annular walls, wherein said cavity is shaped to receive an impeller that is in fluid communication with said central opening, said impeller provides for compressing or pumping said fluid into an annular portion (10.1, 10.2) of said cavity that is radially outboard of said impeller when said impeller is located in said cavity, said annular portion of said cavity comprises first (10.1) and second (10.2) annular portions, said first annular portion is concentric with, radially adjacent to, and downstream of a radially-outermost circumferential boundary of said impeller when said impeller is located within said cavity, said first annular portion is vaneless, said second annular portion is concentric with, radially adjacent to, and around a radially-outermost circumferential boundary of said first annular portion, said second annular portion is downstream of said first annular portion, an axial gap (40, 40') between said first and second annular walls increases with respect to radial distance within said second annular portion, wherein said radial distance is with respect to a central longitudinal axis of said impeller, and a ratio of a magnitude of said axial gap at a radially-outermost location of said second annular portion to a magnitude of said axial gap a radially-innermost location of said second annular portion is at least 1.4 and at most 2.0; d. a collector radially outboard of, and in fluid communication with, and downstream of, said second annular portion of said cavity, wherein said collector is in fluid communication with an outlet duct that provides for a discharge from said collector of said fluid compressed or pumped by said impeller within said cavity and thence into said collector; and e. a plurality of vanes incorporated in said second annular portion, wherein each vane of said plurality of vanes is twisted along a length thereof in a meridional direction, a ratio of a chord length of said vane to a mean circumferential separation distance between adjacent vanes of said plurality of vanes is at least 1.8 and at most 4.0, and a ratio of a maximum value of a radius of said second annular portion to a minimum value of said radius of said second annular portion is at least 1.08 and at most 1.20, wherein said radius of said second annular portion is with respect to said central longitudinal axis of said impeller.