log VS( ) is the 'Vendi force' for x i -a repulsive force applied to x i to drive it away from the other replicas-and ν is an associated learning rate. In our experiments, we explore two types of Langevin sampling to simulate the combined system (eq. 9): we use overdamped Langevin dynamics (Brownian dynamics) for the model systems (the Prinz potential and the double well) and Langevin dynamics for the molecular systems.