  Consider the unsteady neutron transport equation with diffusive boundary
condition in 2D convex domains. We establish the diffusive limit with both
initial layer and boundary layer corrections. The major difficulty is the lack
of regularity in the boundary layer with geometric correction. Our contribution
relies on a detailed analysis of asymptotic expansions inspired by the
compatibility condition and an intricate $L^{2m}-L^{\infty}$ framework which
yields stronger remainder estimates.
