In this paper we demonstrate the essential role of molecular diffusion in the structure and propagation of turbulent flames. We first show that mixtures whose concentrations are near or beyond the conventional flammability limits can be rendered to burn strongly in turbulence, provided the controlling molecular mass diffusivity of the mixture exceeds its thermal diffusivity, namely the mixture Lewis number (Le) is less than unity. The associated turbulent flame speeds in such cases can be orders of magnitude greater than the corresponding laminar flame speeds, with distinctive finger-shape structures on the flame surfaces. Furthermore, this facilitation effect is completely flipped for Le > 1 mixtures, leading to actual weakening of the nominally enhancing effect of turbulence on their burning intensity. Mechanistically, such opposite effects are consequences of the coupling between preferential diffusion and the wrinkled laminar flamelets constituting the turbulent flame structure. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.