Focusing on the entropic contribution to the lattice free energy difference, we propose a stringent criterion to assess the accuracy of the free energy estimates from PGMs trained by maximum likelihood, akin to our previous work. When comparing methods, we consider results from any two methods to be significantly consistent when the respective free energy estimates fall within each other's standard error bars. Table , based on raw data reported in SI Figure , reports the lattice Helmholtz free energy differences (in units of k B T ) between the two forms of ice, computed using all of the methods (i.e., from models H and C, and from the ECM). These comparisons show a significant level of agreement between the different methods, indicating that the results from the PGMs are accurate. We note, however, that the error bars are higher in larger systems and at higher temperatures because such ensembles occupy a larger volume of configurational space. That being said, we consistently observe smaller error bars from results of model H, compared to model C. This indicates that model H (based on the decoupled, quaternion-based representation of the Cartesian blocks) is better suited for modeling configurational distributions of ice crystals. Moreover, since both models we compare used the same architecture for the trainable part of the model (spline coupling layers; see Fig. ), we expect that the computational gains from using the decoupled representation of the Cartesian block can be generalized to other types of crystals.