Existence of both gradient and countergradient diffusion of the turbulent progress variable flux,<(u"c")over tilde>, in premixed flames has been observed in earlier studies. It is shown here that the nature of the turbulent diffusion is related to the dilatation-scalar fluctuation correlation and hence to the detailed structure of the instantaneous flame front. The equation for the Favre-averaged variance of the progress variable is analysed using data from two different direct numerical simulation data bases. It is shown that there exists only countergradient diffusion in the laminar flamelet regime of a statistically stationary reacting flows. For gradient diffusion the flame front must be greatly perturbed from that of a laminar flamelet; i.e., the flame is thick. In unsteady flows, the temporal term plays a significant role in determining the direction of the turbulent scalar flux. Positive and negative dilatation-scalar fluctuation correlation respectively yield countergradient and gradient diffusion of the turbulent scalar flux. Associated physical mechanisms are also discussed.