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This paper introduces a novel generative sampling framework that enforces time-reversibility as a statistical constraint for learning to sample from complex distributions, including those with discrete parameters. The method minimizes the Maximum Mean Discrepancy (MMD) between forward and backward Markov trajectories generated by a prescribed physical transition kernel, relying only on energy evaluations via acceptance ratios. Experiments on continuous Gaussian mixtures, the discrete Ising model, and a hybrid system demonstrate the framework's ability to accurately reproduce thermodynamic observables and capture mode-switching behavior.
Forget gradients: this new sampler learns complex distributions, even with discrete parameters, by enforcing time-reversibility and comparing forward and backward Markov trajectories.
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.
