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 that combine deterministic and stochastic steps. For this purpose, we use Conditional Flow Matching, and introduce Conditional Density Matching (CDM) for the purpose of estimating the change in Free-Energy. We further reduce the variance in the multistate setting by coupling multiple flows between thermodynamic states into a Flow Graph, enforcing estimator consistency across different transition paths.