  We present a simple description of moduli spaces of torsion-free D-modules
(``D-bundles'') on general smooth complex curves X, generalizing the
identification of the space of ideals in the Weyl algebra with Calogero-Moser
quiver varieties. Namely, we show that the moduli of D-bundles form twisted
cotangent bundles to stacks of torsion sheaves on X, answering a question of
Ginzburg. The corresponding (untwisted) cotangent bundles are identified with
moduli of ``perverse vector bundles'' on T^*X, which contain as open subsets
the moduli of framed torsion-free sheaves (the Hilbert schemes (T^*X)^[n] in
the rank one case). The proof is based on the description of the derived
category of D-modules on X by a noncommutative version of the Beilinson
transform on the projective line.
