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.
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