The proposed pseudometric framework for continuous-time diffusions could be extended to handle more general continuous-time stochastic processes by considering a broader class of transition systems. One approach could be to generalize the notion of behavioral equivalence and pseudometrics to encompass a wider range of stochastic processes beyond diffusions. This could involve adapting the functional definitions and mathematical techniques to accommodate the specific characteristics and dynamics of different types of continuous-time processes. Additionally, incorporating additional constraints or properties specific to the new class of processes could help in defining suitable pseudometrics for quantifying behavioral differences in these systems.