  The long wavelength diffusion coefficient of a critical fluid confined
between two parallel plates separated by a distance L is strongly affected by
the finite size. Finite size scaling leads us to expect that the vanishing of
the diffusion coefficient as \xi^{-1} for \xi<<L, \xi being the correlation
length, would crossover to \L^{-1} for \xi>>L. We show that this is not
strictlytrue. There is a logarthmic scaling violation. We construct a Kawasaki
like scaling function that connects the thermodynamic regime to the extreme
critical (\xi>>L) regime.
