  Inverse nodal problem on diffusion operator is the problem of finding the
potential functions and parameters in the boundary conditions by using nodal
data. In particular, we solve the reconstruction and stability problems using
nodal set of eigenfunctions. Furthermore, we show that the space of all
potential functions q is homeomorphic to the partition set of all
asymptotically equivalent nodal sequences induced by an equivalence relation.
To show this stability which is known Lipschitz stability, we have to construct
two metric spaces and a map {\Phi}_{dif} between these spaces. We find that
{\Phi}_{dif} is a homeomorphism when the corresponding metrics are magnified by
the derivatives of q. Basically, this method is similar to Tsay and Cheng which
is given for Sturm-Liouville and Hill operators, respectively and depends on
the explicit asymptotic expansions of nodal points and nodal lengths.
