  The state-dependent diffusion, which concerns the Brownian motion of a
particle in inhomogeneous media has been described phenomenologically in a
number of ways. Based on a system-reservoir nonlinear coupling model we present
a microscopic approach to quantum state-dependent diffusion and multiplicative
noise in terms of a quantum Markovian Langevin description and an associated
Fokker-Planck equation in position space in the overdamped limit. We examine
the thermodynamic consistency and explore the possibility of observing a
quantum current, a generic quantum effect, as a consequence of this
state-dependent diffusion similar to one proposed by B\"{u}ttiker [Z. Phys. B
{\bf 68}, 161 (1987)] in a classical context several years ago.
