We establish that Polchinski's equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a relative entropy. This provides a compelling information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. A striking consequence is that the pertinent relative entropy is in fact an RG monotone. We compute this monotone perturbatively in several examples. Our results apply more broadly to other exact renormalization group flow equations, including widely used specializations of Wegner-Morris flow. Moreover, our optimal transport framework for RG allows us to reformulate RG flow as a variational problem, enabling new numerical techniques.
