  The well-posedness for SDEs with singularity in both space and distribution
variables is derived, where the drift is bounded and Lipschitz continuous under
weighted variation distance and the diffusion is allowed to be Lipschitz
continuous under $L^\eta$($\eta\in(0,1]$)-Wasserstein distance. Moreover, the
regularity estimate is established when the drift is bounded and Lipschitz
continuous under total variation distance.
