Assessing generative modeling approaches for free energy estimates in condensed matter

The accurate estimation of free energy differences between two states is a long-standing challenge in molecular simulations. Traditional approaches generally rely on sampling multiple intermediate states to ensure sufficient overlap in phase space and are, consequently, computationally expensive. Several generative-model-based methods have recently addressed this challenge by learning a direct bridge between distributions, bypassing the need for intermediate states. However, it remains unclear which approaches provide the best trade-off between efficiency, accuracy, and scalability. In this work, we systematically review these methods and benchmark selected approaches with a focus on condensed-matter systems. In particular, we investigate the performance of discrete and continuous normalizing flows in the context of targeted free energy perturbation as well as FEAT (Free energy Estimators with Adaptive Transport) together with the escorted Jarzynski equality, using coarse-grained monatomic ice and Lennard-Jones solids as benchmark systems. We evaluate accuracy, data efficiency, computational cost, and scalability with system size. Our results provide a quantitative framework for selecting effective free energy estimation strategies in condensed-phase systems.