A turbine airfoil having an external surface defining a curvature, comprising: (a) a leading edge and an axially spaced-part trailing edge, the leading edge having an axially-extending aerodynamic external surface curvature; (b) a root and a tip spaced-apart along a radially-extending span axis; (c) a pressure sidewall and a laterally-spaced-apart suction sidewall; (d) a cooling circuit positioned between the pressure sidewall and the suction sidewall for channeling a fluid flow for cooling the airfoil; (e) a plurality of cooling holes formed in the external surface of the airfoil in fluid communication with the cooling circuit, at least some of the plurality of cooling holes comprising: (i) a metering section downstream of the cooling circuit; (ii) a diffuser section downstream of the metering section and upstream of the external surface of the airfoil, the diffuser section having a top wall, a bottom wall, and opposed side walls (53, 54) defining an exit opening on the external surface for exiting a cooling film; and (f) at least the opposed side walls (53, 54) and the bottom wall of the diffuser section having a downstream diverging, bell-shaped curvature for achieving a flow of the cooling film from the cooling circuit with enhanced spread, enhanced attachment and less turbulence to a downstream surface of the airfoil local to each respective cooling hole; characterised in that: the bottom wall of the diffuser section is convexly curved laterally between the opposed sidewalls (53,54) at the exit opening. (a) a leading edge and an axially spaced-part trailing edge, the leading edge having an axially-extending aerodynamic external surface curvature; (b) a root and a tip spaced-apart along a radially-extending span axis; (c) a pressure sidewall and a laterally-spaced-apart suction sidewall; (d) a cooling circuit positioned between the pressure sidewall and the suction sidewall for channeling a fluid flow for cooling the airfoil; (e) a plurality of cooling holes formed in the external surface of the airfoil in fluid communication with the cooling circuit, at least some of the plurality of cooling holes comprising: (i) a metering section downstream of the cooling circuit; (ii) a diffuser section downstream of the metering section and upstream of the external surface of the airfoil, the diffuser section having a top wall, a bottom wall, and opposed side walls (53, 54) defining an exit opening on the external surface for exiting a cooling film; and (i) a metering section downstream of the cooling circuit; (ii) a diffuser section downstream of the metering section and upstream of the external surface of the airfoil, the diffuser section having a top wall, a bottom wall, and opposed side walls (53, 54) defining an exit opening on the external surface for exiting a cooling film; and (f) at least the opposed side walls (53, 54) and the bottom wall of the diffuser section having a downstream diverging, bell-shaped curvature for achieving a flow of the cooling film from the cooling circuit with enhanced spread, enhanced attachment and less turbulence to a downstream surface of the airfoil local to each respective cooling hole; characterised in that: the bottom wall of the diffuser section is convexly curved laterally between the opposed sidewalls (53,54) at the exit opening. the bottom wall of the diffuser section is convexly curved laterally between the opposed sidewalls (53,54) at the exit opening.