Coarse-Grained Boltzmann Generators

Abstract: Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but their practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack the reweighting process required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a principled framework that unifies scalable reduced-order modeling with the exactness of importance sampling. CG-BGs act in a coarse-grained coordinate space, using a learned potential of mean force (PMF) to reweight samples generated by a flow-based model. Crucially, we show that this PMF can be efficiently learned from rapidly converged data via force matching. Our results demonstrate that CG-BGs faithfully capture complex interactions mediated by explicit solvent within highly reduced representations, establishing a scalable pathway for the unbiased sampling of larger molecular systems.