Summary: We prove the consistency of an adaptive importance sampling strategy based on biasing the potential energy function \(V\) of a diffusion process \(\mathrm{d} X_t^0 = - \nabla V(X_t^0) \mathrm{d} t + \mathrm{d} W_t\); for the sake of simplicity, periodic boundary conditions are assumed, so that \(X_t^0\) lives on the flat \(d\)-dimensional torus. The goal is to sample its invariant distribution \(\mu = Z^{- 1} \exp (- V(x)) \mathrm{d} x\). The bias \(V_t - V\), where \(V_t\) is the new (random and time-dependent) potential function, acts only on some coordinates of the system, and is designed to flatten the corresponding empirical occupation measure of the diffusion \(X\) in the large-time regime. The diffusion process writes \(\mathrm{d} X_t = - \nabla V_t(X_t) \mathrm{d} t + \mathrm{d} W_t\), where the bias \(V_t - V\) is a function of the key quantity \(\overline{\mu}_t\): a probability occupation measure which depends on the past of the process, i.e. on \((X_s)_{s \in [0, t]}\). We are thus dealing with a self-interacting diffusion. In this note, we prove that when \(t\) goes to infinity, \(\overline{\mu}_t\) almost surely converges to \(\mu\). Moreover, the approach is justified by the convergence of the bias to a limit that has an interpretation in terms of a free energy. The main argument is a change of variables, which formally validates the consistency of the approach. The convergence is then rigorously proved adapting the ODE method from stochastic approximation.