Learning Escorted Protocols For Multistate Free-Energy Estimation

Estimating relative free energy differences between multiple thermodynamic states lies at the core of numerous problems in computational biochemistry. Traditional estimators, such as Free Energy Perturbation and its non-equilibrium counterpart based on the Jarzynski equality, rely on defining a switching protocol between thermodynamic states and computing the free energy difference from the work performed during this process. In this work, we present a method for learning such switching protocols within the class of escorted protocols, which combine deterministic and stochastic steps. For this purpose, we use Conditional Flow Matching and introduce Conditional Density Matching (CDM) to estimate changes in free energy. We further reduce the variance in the multi-state setting by coupling multiple flows between thermodynamic states into a flow graph of escorted protocols, enforcing estimator consistency across different transition paths.