  We consider the inverse problem of reconstructing the optical parameters of
the radiative transfer equation (RTE) from boundary measurements in the
diffusion limit. In the diffusive regime (the Knudsen number $\mathsf{Kn}\ll
1$), the forward problem for the stationary RTE is well approximated by an
elliptic equation. However, the connection between the inverse problem for the
RTE and the inverse problem for the elliptic equation has not been fully
developed. This problem is particularly interesting because the former one is
mildly ill-posed , with a Lipschitz type stability estimate, while the latter
is well known to be severely ill-posed with a logarithmic type stability
estimate. In this paper, we derive stability estimates for the inverse problem
for RTE and examine its dependence on $\mathsf{Kn}$. We show that the stability
is Lipschitz in all regimes, but the coefficient deteriorates as
$e^{\frac{1}{\mathsf{Kn}}}$, making the inverse problem of RTE severely
ill-posed when $\mathsf{Kn}$ is small. In this way we connect the two inverse
problems. Numerical results agree with the analysis of worsening stability as
the Knudsen number gets smaller.
