  In this paper, we aim to study the diffusion approximation for multi-scale
McKean-Vlasov stochastic differential equations. More precisely, we prove the
weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$
towards the limiting process $X$ that is the solution of a distribution
dependent stochastic differential equation in which some new drift and
diffusion terms compared to the original equation appear. The main contribution
is to use two different methods to explicitly characterize the limiting
equations respectively. The obtained diffusion coefficients in the limiting
equations have different form through these two methods, however it will be
asserted that they are essential the same by a comparison.
