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

Image Dependent Conditional McKean-Vlasov SDEs for Measure-Valued Diffusion Processes