Biochemical reaction networks (RNs) are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of RNs with mass-action kinetics, focusing on the identifiability of the stochastic differential equations associated to the reaction network. We derive conditions under which the law of the diffusion approximation is identifiable and provide theorems for verifying identifiability in practice. Notably, our results show that some RNs have non-identifiable reaction rates, even when the law of the corresponding stochastic process is completely known. Moreover, we show that RNs with distinct graphical structures can generate the same diffusion law under specific choices of reaction rates. Finally, we compare our framework with identifiability results in the deterministic ordinary differential equation setting and the discrete continuous-time Markov chain models for RNs.
