  By using the heat kernel parameter expansion with respect to the frozen SDEs,
the intrinsic derivative is estimated for the law of Mckean-Vlasov SDEs with
respect to the initial distribution. As an application, the total variation
distance between the laws of two solutions is bounded by the Wasserstein
distance for initial distributions. These extend some recent results proved for
distribution-free noise by using the coupling method and Malliavin calculus.
