  We continue our analysis of the thresholding scheme from the variational
viewpoint and prove a conditional convergence result towards Brakke's notion of
mean curvature flow. Our proof is based on a localized version of the
minimizing movements interpretation of Esedo\u{g}lu and the second author. We
apply De Giorgi's variational interpolation to the thresholding scheme and pass
to the limit in the resulting energy-dissipation inequality. The result is
conditional in the sense that we assume the time-integrated energies of the
approximations to converge to those of the limit.
