We establish a coupling between the P(ϕ)₂ measure and the Gaussian free field on the two-dimensional unit torus at all spatial scales, quantified by probabilistic regularity estimates on the difference field. Our result includes the well-studied ϕ⁴₂ measure. The proof uses an exact correspondence between the Polchinski renormalisation group approach, which is used to define the coupling, and the Boué–Dupuis stochastic control representation for P(ϕ)₂. More precisely, we show that the difference field is obtained from a specific minimiser of the variational problem. This allows to transfer regularity estimates for the small-scales of minimisers, obtained using discrete harmonic analysis tools, to the difference field. As an application of the coupling, we prove that the maximum of the P(ϕ)₂ field on the discretised torus with mesh-size ϵ > 0 converges in distribution to a randomly shifted Gumbel distribution as ϵ → 0 .