  In this work, high order asymptotic preserving schemes are constructed and
analysed for kinetic equations under a diffusive scaling. The framework enables
to consider different cases: the diffusion equation, the advection-diffusion
equation and the presence of inflow boundary conditions. Starting from the
micro-macro reformulation of the original kinetic equation, high order time
integrators are introduced. This class of numerical schemes enjoys the
Asymptotic Preserving (AP) property for arbitrary initial data and degenerates
when $\epsilon$ goes to zero into a high order scheme which is implicit for the
diffusion term, which makes it free from the usual diffusion stability
condition. The space discretization is also discussed and high order methods
are also proposed based on classical finite differences schemes. The Asymptotic
Preserving property is analysed and numerical results are presented to
illustrate the properties of the proposed schemes in different regimes.
