Generative Replica-Exchange: A Flow-based Framework for Accelerating Replica Exchange Simulations

Inference-time control steers a pretrained generative model towards a target distribution without retraining. We study tilted targets $π_0\propto G_0\,p_0$, where $p_0$ is the sampler output distribution and $G_0$ is an evaluable reweighting function. Existing approaches rely on sequential annealing with sequential Monte Carlo (SMC) or parallel annealing with replica exchange (RE). Sequential control is exact but needs large particle populations, whereas no exact parallel control method exists: existing RE corrections approximate an intractable time reversal and are biased. We propose Exact Non-equilibrium COntrol with Replica Exchange (ENCORE), the first exact parallel control method. Each replica stores its generation trajectory, so the upward move is a truncation and the intractable time reversal is never simulated. We prove target invariance and show that the resulting dynamics are those of non-equilibrium replica exchange with the exact time reversal as forward proposal. Under regularity conditions, our diffusion analysis shows that both sequential and parallel control become unstable under refinement of the time discretisation without guidance, whereas guided proposals remain stable and yield diagnostics for tuning the schedule and the computational budget. Across synthetic targets, Boltzmann sampling of biomolecules, and image generation, ENCORE achieves competitive accuracy and diversity, remains robust to sampler perturbations, and applies to distilled samplers where existing RE corrections are unavailable.

Sampling physical systems with rough energy landscapes is hindered by rare events and metastable trapping. While Boltzmann generators already offer a solution, their reliance on the reverse Kullback--Leibler divergence frequently induces catastrophic mode collapse, missing specific modes in multi-modal distributions. Here, we introduce the Jeffreys Flow, a robust generative framework that mitigates this failure by distilling empirical sampling data from Parallel Tempering trajectories using the symmetric Jeffreys divergence. This formulation effectively balances local target-seeking precision with global modes coverage. We show that minimizing Jeffreys divergence suppresses mode collapse and structurally corrects inherent inaccuracies via distillation of the empirical reference data. We demonstrate the framework's scalability and accuracy on highly non-convex multidimensional benchmarks, including the systematic correction of stochastic gradient biases in Replica Exchange Stochastic Gradient Langevin Dynamics and the massive acceleration of exact importance sampling in Path Integral Monte Carlo for quantum thermal states.

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to discrete or mixed-variable systems remains difficult due to ill-defined gradients or high variance in estimators. We propose a unified, target-gradient-free generative sampling framework applicable across diverse state spaces. Building on the fact that detailed balance implies the time-reversibility of the equilibrium stochastic process, we enforce this symmetry as a statistical constraint. Specifically, using a prescribed physical transition kernel (such as Metropolis-Hastings), we minimize the Maximum Mean Discrepancy (MMD) between the joint distributions of forward and backward Markov trajectories. Crucially, this training procedure relies solely on energy evaluations via acceptance ratios, circumventing the need for target score functions or continuous relaxations. We demonstrate the versatility of our method on three distinct benchmarks: (1) a continuous multi-modal Gaussian mixture, (2) the discrete high-dimensional Ising model, and (3) a challenging hybrid system coupling discrete indices with continuous dynamics. Experiments show that our framework accurately reproduces thermodynamic observables and captures mode-switching behavior across all regimes, offering a physically grounded and universally applicable alternative for equilibrium sampling.