  Supersymmetry is generally broken by the non-vanishing vacuum energy density
present during inflation. In supergravity models, such a source of
supersymmetry breaking typically makes a contribution to scalar masses of order
${\tilde m}^2 \sim H^2$, where $H^2 \sim V/M_P^2$ is the Hubble parameter
during inflation. We show that in supergravity models which possess a
Heisenberg symmetry, supersymmetry breaking makes no contribution to scalar
masses, leaving supersymmetric flat directions flat at tree-level. One-loop
corrections in general lift the flat directions, but naturally give small
negative squared masses $\sim - g^2 H^2/(4\pi)^2$ for all flat directions that
do not involve the stop. No-scale supergravity of the SU(N,1) type and the
untwisted sectors from orbifold compactifications are special cases of this
general set of models. We point out the importance of the preservation of flat
directions for baryogenesis.
