  We examine the conformal equivalence between the $f(R)$ gravity and the
interacting dark sector model. We review the well-known result that the
conformal transformation physically corresponds to the mass dilation which
marks the strength of interaction between dark sectors. Instead of modeling
f(R) gravity in the Jordan frame, we construct the $f(R)$ gravity in terms of
mass dilation function in the Einstein frame. We find that the condition to
keep $f(R)$ gravity consistent with CMB observations ensures the energy flow
from dark energy to dark matter in the corresponding interacting model, which
meets the requirement to alleviate the coincidence problem in the Einstein
framework.
