  Dust is the usual minor component of the interstellar medium. Its dynamic
role in the contraction of the diffuse gas into molecular clouds is commonly
assumed to be negligible because of the small mass fraction, $f \simeq 0.01$.
However, as shown in this study, the collective motion of dust grains with
respect to the gas may considerably contribute to the destabilisation of the
medium on scales $\lambda \lesssim \lambda_J$, where $\lambda_J$ is the Jeans
length-scale. The linear perturbations of the uniform self-gravitating gas at
rest are marginally stable at $\lambda \simeq \lambda_J$, but as soon as the
drift of grains is taken into account, they begin growing at a rate
approximately equal to $(f \tau)^{1/3} t^{-1}_{ff}$, where $\tau$ is the
stopping time of grains expressed in units of the free fall time of the cloud,
$t_{ff}$. The physical mechanism responsible for such a weak dependence of the
growth rate on $f$ is the resonance of heavy sound waves stopped by the
self-gravity of gas with weak gravitational attraction caused by perturbations
of the dust fraction. Once there is stationary subsonic bulk drift of the dust,
the growing gas-dust perturbations at $\lambda < \lambda_J$ become waves
propagating with the drift velocity projected onto the wavevector. Their growth
has a resonant nature as well and the growth rate is substantially larger than
that of the recently discovered resonant instability of gas-dust mixture in the
absence of self-gravity. The new instabilities can facilitate gravitational
contraction of cold interstellar gas into clouds and additionally produce dusty
domains of sub-Jeans size at different stages of molecular cloud formation and
evolution.
