  We prove a variation norm Carleson theorem for Walsh-Fourier series of
functions with values in a UMD Banach space. Our only hypothesis on the Banach
space is that it has finite tile-type, a notion introduced by Hyt\"onen and
Lacey. Given q \geq 2 we show that, if the space X has tile-type t for all t>q,
then the r-variation of the Walsh-Fourier sums of any function f \in L^p ([0,1)
; X) belongs to L^p, whenever q<r \leq \infty and (r/(q-1))' < p < \infty. We
also show that if this conclusion is true for a variant of the variational
Carleson operator then the space X necessarily has tile-type t for all t >q.
For intermediate spaces, i.e. spaces X= [Y,H]_s which are complex interpolation
spaces between some UMD space Y and a Hilbert space H, the tile-type is q=2/s.
We show that in this case the variation norm Carleson theorem remains true for
all r > q in the larger range p > (2r/q)'.
