Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states changes abruptly and many sampling algorithms stall. Nested sampling is a particle method that traverses the density of states under a hard energy constraint and is known to be robust to such transitions, but its application in high dimension is limited by the difficulty of sampling under that constraint. In this work we introduce Quenched Ensemble Sampling, which generalises the hard constraint to a family of repulsive potentials at the energy boundary. This preserves the quenched path of monotonically decreasing energy while making the constrained target amenable to scalable gradient-based kernels. We demonstrate on synthetic models of phase transitions that our method estimates the marginal likelihood and draws posterior samples across a first-order transition where popular alternatives such as tempering fail. We apply the procedure to marginal likelihood estimation in Bayesian neural networks, enabling model comparison between network architectures. Finally, in a high-dimensional continuous lattice field theory, we show that this method traverses a first-order transition and estimates the partition function.
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