Recently, there has been a surge of interest in mesogens exhibiting the twist-bend nematic (N TB ) phase that is shown to be chiral even though formed by effectively achiral molecules. Although it now seems to be clear that the N TB phase in the bulk is formed by degenerate domains having opposite handedness, the presence of a supramolecular heliconical structure proposed in the Dozov model has been contradicted by the Hoffmann et al. model in which the heliconical arrangement is replaced by a polar nematic phase. The evidence in support of this is that the quadrupolar splitting tensor measured in various experiments is uniaxial and not biaxial as expected for the twist-bend nematic structure. In this debate, among other evidence, the molecular translational diffusion, and its magnitude with respect to that in the nematic phase above the N TB phase, has been also invoked to eliminate or to confirm one model or the other. We attempt to resolve this issue by reporting the first measurements of the translational self-diffusion coefficients in the nematic and twist-bend nematic phases formed 1",7"-bis-4-(4'-cyanobiphenyl) heptane (CB7CB). Such measurements certainly appear to resolve the differences between the two models in favour of that for the classic twist-bend nematic phase.