  A manifestly diffeomorphism invariant exact renormalization group requires
extra diffeomorphism invariant ultraviolet regularisation at some effective
cutoff scale $\Lambda$. This motivates construction of a `Parisi-Sourlas'
supergravity, in analogy with the gauge theory case, where the superpartner
fields have the wrong spin-statistics such that they can become Pauli-Villars
regulator fields after spontaneous symmetry breaking. We show that in contrast
to gauge theory, the free theory around flat space is already non-trivial and
in a sense already displays some spontaneous symmetry breaking. We show that
the fluctuating fields form multiplets whose mass matrices imply that the
fields propagate into each other not only with the expected $1/p^2$ but also
through propagators with improved ultraviolet properties, namely $1/p^4$ and
$1/p^6$, despite the fact that the action contains a maximum of two space-time
derivatives.
