  We consider a special class of mean field SDEs with common noise which depend
on the image of the solution (i.e. the conditional distribution given noise).
The strong well-posedness is derived under a monotone condition which is weaker
than those used in the literature of mean field games, the Feynman-Kac formula
is established to solve Schr\"ordinegr type PDEs on $\scr P_2$, and the
ergodicity is proved for a class of measure-valued diffusion processes.
