A turbine assembly extending about a longitudinal axis (X-X'), said assembly comprising: - a plurality of turbine ring sectors made of ceramic matrix composite material, circumferentially assembled end-to-end to form a turbine ring, each turbine ring sector comprising a base with a radially inner face and a radially outer face from which an upstream lug and a downstream lug, axially spaced apart from each other extend radially outwardly, - a ring support structure, held by an outer annular turbine casing, said ring support structure comprising an annular shroud, and a plurality of angular spacer sectors together forming an annular spacer, said annular spacer being secured to said annular shroud, and each turbine ring sector being secured by said lugs (22, 23) to said annular spacer, - at least one air diffuser, configured to diffuse cooling air onto said radially outer face of at least one of said turbine ring sectors, - at least one air diffuser is mounted by nesting on one of said angular spacer sectors, in a nested position, in that the air diffuser has an internal cavity and a radially inner face pierced by a plurality of air ejection orifices opening out into this cavity, in that each angular spacer sector has a radially inner face and has, on its radially inner face, a rectilinear engagement groove, which has, over part of its length, a nesting zone of T-shaped cross-section, in that each air diffuser is provided, at its radially outer part, with an attachment member also T-shaped, configured to be received and nested in said nesting zone, in that the hooking member of the air diffuser is pierced by an air inlet hole opening out into said internal cavity and in that each angular spacer sector comprises at least one air supply duct, opening out on the one hand, onto one of its upstream faces and, on the other hand, into the bottom of the T-shaped nesting zone of the groove, opposite the mouth of the air intake hole of the diffuser attachment member, when this diffuser is in its nested position, so that this air supply duct is in fluid communication with said air ejection orifices. - a plurality of turbine ring sectors made of ceramic matrix composite material, circumferentially assembled end-to-end to form a turbine ring, each turbine ring sector comprising a base with a radially inner face and a radially outer face from which an upstream lug and a downstream lug, axially spaced apart from each other extend radially outwardly, - a ring support structure, held by an outer annular turbine casing, said ring support structure comprising an annular shroud, and a plurality of angular spacer sectors together forming an annular spacer, said annular spacer being secured to said annular shroud, and each turbine ring sector being secured by said lugs (22, 23) to said annular spacer, - at least one air diffuser, configured to diffuse cooling air onto said radially outer face of at least one of said turbine ring sectors, - at least one air diffuser is mounted by nesting on one of said angular spacer sectors, in a nested position, in that the air diffuser has an internal cavity and a radially inner face pierced by a plurality of air ejection orifices opening out into this cavity, in that each angular spacer sector has a radially inner face and has, on its radially inner face, a rectilinear engagement groove, which has, over part of its length, a nesting zone of T-shaped cross-section, in that each air diffuser is provided, at its radially outer part, with an attachment member also T-shaped, configured to be received and nested in said nesting zone, in that the hooking member of the air diffuser is pierced by an air inlet hole opening out into said internal cavity and in that each angular spacer sector comprises at least one air supply duct, opening out on the one hand, onto one of its upstream faces and, on the other hand, into the bottom of the T-shaped nesting zone of the groove, opposite the mouth of the air intake hole of the diffuser attachment member, when this diffuser is in its nested position, so that this air supply duct is in fluid communication with said air ejection orifices.