A turbine engine comprising: - a compressor stage including an impeller, - a system for cooling an annular cavity downstream of the impeller, - a diffuser connected to an outlet of the compressor stage, said diffuser including an annular flange which extends downstream and along the impeller and delimits the annular cavity downstream of the impeller, said cavity being ventilated by air bleed-off at the outlet of the compressor stage, the system for cooling comprising: - an annular sheet, mounted coaxially around said annular flange of the diffuser and delimiting with the annular flange an annular passage, said annular sheet including at least one radial opening for supplying the annular passage with air, and - means adapted to have air, at a temperature lower than that of the air leaving the compressor stage, which circulates in the annular passage from upstream to downstream for ensuring the cooling and ventilation of the annular flange of the diffuser, Characterised in that: - said compressor is a centrifugal compressor, and, - said means adapted to have air, at a temperature lower than that of the air leaving the compressor stage, which circulates in the annular passage from upstream to downstream for ensuring the cooling and ventilation of the annular flange of the diffuser, comprise a supplying duct for supplying with cool air the radial opening of the annular sheet, the supplying duct being connected, downstream, to said radial opening, and upstream, to air extracting means on an upstream axial compressor stage or at the output of a cooling thermal exchanger. - a compressor stage including an impeller, - a system for cooling an annular cavity downstream of the impeller, - a diffuser connected to an outlet of the compressor stage, said diffuser including an annular flange which extends downstream and along the impeller and delimits the annular cavity downstream of the impeller, said cavity being ventilated by air bleed-off at the outlet of the compressor stage, the system for cooling comprising: - an annular sheet, mounted coaxially around said annular flange of the diffuser and delimiting with the annular flange an annular passage, said annular sheet including at least one radial opening for supplying the annular passage with air, and - means adapted to have air, at a temperature lower than that of the air leaving the compressor stage, which circulates in the annular passage from upstream to downstream for ensuring the cooling and ventilation of the annular flange of the diffuser, Characterised in that: - said compressor is a centrifugal compressor, and, - said means adapted to have air, at a temperature lower than that of the air leaving the compressor stage, which circulates in the annular passage from upstream to downstream for ensuring the cooling and ventilation of the annular flange of the diffuser, comprise a supplying duct for supplying with cool air the radial opening of the annular sheet, the supplying duct being connected, downstream, to said radial opening, and upstream, to air extracting means on an upstream axial compressor stage or at the output of a cooling thermal exchanger. - an annular sheet, mounted coaxially around said annular flange of the diffuser and delimiting with the annular flange an annular passage, said annular sheet including at least one radial opening for supplying the annular passage with air, and - means adapted to have air, at a temperature lower than that of the air leaving the compressor stage, which circulates in the annular passage from upstream to downstream for ensuring the cooling and ventilation of the annular flange of the diffuser, - said compressor is a centrifugal compressor, and, - said means adapted to have air, at a temperature lower than that of the air leaving the compressor stage, which circulates in the annular passage from upstream to downstream for ensuring the cooling and ventilation of the annular flange of the diffuser, comprise a supplying duct for supplying with cool air the radial opening of the annular sheet, the supplying duct being connected, downstream, to said radial opening, and upstream, to air extracting means on an upstream axial compressor stage or at the output of a cooling thermal exchanger.