Vector sets with no repeated differences

We consider the question when a set in a vector space over the rationals, with no differences occurring more than twice, is the union of countably many sets, none containing a difference twice. The answer is "yes" if the set is of size at most ${\displaystyle {\aleph }_2}$, "not" if the set is allowed to be of size ${\displaystyle {\left(2^{2^{{\aleph }_0}}\right)}^{+}}$. It is consistent that the continuum is large, but the statement still holds for every set smaller than continuum.