New neural transport method estimates free energy on any state space

Free energy estimation is a cornerstone challenge from physics to machine learning, but classical methods like thermodynamic integration and finite-time averaging are often slow or limited to continuous spaces. Recent work by He and Du et al. (2025) introduced neural transport to accelerate finite-time estimation, but it remained confined to continuous settings. Now, He and six co-authors generalize this framework to arbitrary state spaces—including discrete, multimodal, and autoregressive distributions—by developing a generalized neural transport learning approach. Experiments show their method significantly improves efficiency and accuracy across these diverse spaces, outperforming both traditional techniques and prior neural approaches.

Beyond the algorithmic innovation, the paper uncovers deep algebraic structure: they establish identities and a group-theoretic connection between infinitesimal time reversal and generalized Doob's h-transforms, proving their compositions form a generalized dihedral group. This theoretical insight could inspire new methods for sampling and inference. The work spans machine learning (stat.ML, cs.LG), chemical physics (physics.chem-ph), and computational physics (physics.comp-ph), making it broadly relevant. For practitioners, this means faster, more flexible free energy calculations in drug discovery, statistical mechanics, and Bayesian inference where state spaces are rarely purely continuous.