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

Diffusion Approximation for Multi-Scale McKean-Vlasov SDEs Through Different Methods