Go to ICLR 2025 Conference homepageFreeFlow: 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. Instead of time-intensive simulations of intermediate alchemical systems, we learn a fast-to-train flow to bridge the two systems of interest. 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 into a same-dimensional latent space in which our flow operates. A generalized change of variables formula for trans-dimensional mappings allows us to employ the dimensionality collapsing and expanding autoencoders in our free energy estimation pipeline. We validate our approach on systems of increasing complexity: mapping between Gaussians, between subspaces of alanine dipeptide, and between pharmaceutically relevant ligands in solvent. All results show strong agreement with reference values.