  This paper introduces a method for computing the Helmholtz free energy using
the flow matching technique. Unlike previous work that utilized flow-based
models for variational free energy calculations, this method provides bounds
for free energy estimation based on targeted free energy perturbation, by
performing calculations on samples from both ends of the mapping. We
demonstrate applications of the present method by estimating the free energy of
the classical Coulomb gas in a harmonic trap.
