Hoyer et al. proved that the Additive Noise Model (ANM) is generally identifiable, demonstrating that if a joint distribution $P_{X, Y}$ satisfies an additive noise model with orientation $X ightarrow Y$, then $P_{X, Y}$ cannot satisfy an additive model with orientation $Y ightarrow X$. However, specific cases exist where ANM is non-identifiable; in particular, the linear Gaussian case is non-identifiable.