  We investigate the Cauchy problem and the diffusion asymptotics for a
spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck
operator. Its solution describes the density evolution of interacting particles
whose mobility is hampered by their aggregation. When the initial data lies
below a Maxwellian, we derive the global well-posedness with instantaneous
smoothness. The proof relies on hypoelliptic analogue of the classical
parabolic theory, as well as a positivity-spreading result based on the Harnack
inequality and barrier function methods. Moreover, the scaled equation leads to
the fast diffusion flow under the low field limit. The relative phi-entropy
method enables us to see the connection between the overdamped dynamics of the
nonlinearly coupled kinetic model and the correlated fast diffusion. The global
in time quantitative diffusion asymptotics is then derived by combining
entropic hypocoercivity, relative phi-entropy and barrier function methods.
