• Both types of models were trained and evaluated on the same data, following the same protocol. For instance, the training validation split was fixed to Both models start by transforming the Cartesian coordinates of the system r, containing N atoms, as discussed in the main text, to create a vector x containing 3(N -1) marginal variables. These variables are then rescaled to a fixed model range (e.g., [-1, 1] or [-1, 1), depending on the type of variable). Mapping: Both models used one-dimensional monotonically increasing rational quadratic splines (with five trainable knots) to transform x in an elementwise manner according to coupled flow architecture . This was implemented as in REF . In each system, 4 coupling layers were used in the case of the Hemisphere model, and a maximum number of coupling layers was in the Cartesian model. The partitioning of variables in each layer was based on the heuristic discussed in SI Figure . . The coupling layers invertibly transform x to z. The maps were trained to approach a uniform remapped distribution in z. For this reason, in model H, the variables associated with quaternions are transformed back to 4D unit vectors on the specified hemisphere. The details are discussed in the main text. The amount of data used for training and validating the PGMs was 200,000 samples (20 ns) in each system containing 16 or 32 molecules and 400,000 samples (40 ns) in each system with 64 molecules. A training:validation split of 3 : 1 was used during each training run.