High-Fidelity Boltzmann Samplingvia Physical Prior Lifted Continuous GFlowNets

Sampling high-dimensional Boltzmann distributions is fundamental yet challenging. Classical MCMC methods incur prohibitive computational costs, while modern generative approaches such as diffusion models and Schrödinger bridges struggle to incorporate informative physical priors. GFlowNets offer a promising alternative, yet existing continuous variants suffer from training instability. In this paper, we propose Physical Prior Lifted continuous GFlowNets (PPL), a framework that encodes physical prior information through a reference space equipped with a reference distribution and a mapping to the original configuration space. The sampling process is learned via a Reference-Weighted Trajectory Balance (RWTB) loss, yielding stable training dynamics, efficient learning, and rigorous theoretical guarantees. Empirically, PPL achieves state-of-the-art performance across five benchmarks spanning synthetic, molecular, and protein systems. On the synthetic LJ-55, we obtain significantly lower error than the diffusion-based ASBS with ${\sim}36\times$ speedup; Notably, on the 267-dimensional Chignolin protein, PPL attains near-ground-truth sampling fidelity.