  We report the finding of a new, local diffusion instability in a
protoplanetary disk, which can operate in a dust fluid, subject to mass
diffusion, shear viscosity, and dust-gas drag, provided diffusivity, viscosity,
or both decrease sufficiently rapidly with increasing dust surface mass
density. We devise a vertically averaged, axisymmetric hydrodynamic model to
describe a dense, mid-plane dust layer in a protoplanetary disk. The gas is
modeled as a passive component, imposing an effective, diffusion-dependent
pressure, mass diffusivity, and viscosity onto the otherwise collisionless dust
fluid, via turbulence excited by the gas alone, or dust and gas in combination.
In particular, we argue that such conditions are met when the dust-gas mixture
generates small-scale turbulence through the streaming instability, as
supported by recent measurements of dust mass diffusion slopes in simulations.
We hypothesize that the newly discovered instability may be the origin of
filamentary features, almost ubiquitously found in simulations of the streaming
instability. In addition, our model allows for growing oscillatory modes, which
operate in a similar fashion as the axisymmetric viscous overstability in dense
planetary rings. However, it remains speculative if the required conditions for
such modes can be met in protoplanetary disks.
