FreeFlow: Latent Flow Matching for Free Energy Difference Estimation

Estimating free energy differences between molecular systems is fundamental for understanding molecular interactions and accelerating drug discovery. Current techniques use molecular dynamics to sample the Boltzmann distributions of the two systems and of several intermediate "alchemical" distributions that interpolate between them. From the resulting ensembles, free energy differences can be estimated by averaging importance weight analogs for multiple distributions. We replace slow alchemical simulations with a fast-to-train flow model bridging two systems. After training, we obtain free energy differences by integrating the flow's instantaneous change of variables when transporting samples between the two distributions. To map between molecular systems with different numbers of atoms, we replace the previous solutions of simulating auxiliary "dummy atoms" by additionally training two autoencoders that project the systems to a same-dimensional latent space in which our flow operates. A generalized change of variables formula for trans-dimensional mappings motivates the use of autoencoders in our free energy estimation pipeline. We validate our approach on pharmaceutically relevant ligands in solvent and results show strong agreement with reference values.