  We present a novel approach of discretizing variable coefficient diffusion
operators in the context of meshfree generalized finite difference methods. Our
ansatz uses properties of derived operators and combines the discrete Laplace
operator with reconstruction functions approximating the diffusion coefficient.
Provided that the reconstructions are of a sufficiently high order, we prove
that the order of accuracy of the discrete Laplace operator transfers to the
derived diffusion operator. We show that the new discrete diffusion operator
inherits the diagonal dominance property of the discrete Laplace operator.
Finally, we present the possibility of discretizing anisotropic diffusion
operators with the help of derived operators. Our numerical results for
Poisson's equation and the heat equation show that even low-order
reconstructions preserve the order of the underlying discrete Laplace operator
for sufficiently smooth diffusion coefficients. In experiments, we demonstrate
the applicability of the new discrete diffusion operator to interface problems
with point clouds not aligning to the interface and numerically show
first-order convergence.
