Pretrained diffusion models provide powerful learned priors, but in scientific sampling the target distribution often depends on physical context that a single generative model can neither fully represent nor learn from scarce joint-system data. We introduce Generative Gibbs for Physics-Aware Sampling (GG-PA), a training-free framework that composes learned partial priors with explicit physical context through Gibbs sampling. We prove that this sampler is asymptotically exact as the diffusion time vanishes and remains exact at finite diffusion time for quadratic interactions. As a special case, the finite-time result corrects a finite-noise bias in plug-and-play split Gibbs samplers for linear inverse problems at no additional cost. We further introduce replica exchange over diffusion time to accelerate mixing. In experiments, a one-dimensional double-well prior recovers a context-induced distribution shift when coupled to an environment, and copies of such a prior composed on a lattice reproduce the emergent collective behavior of the $φ^4$ model. In atomistic peptide systems, GG-PA captures a context-induced distribution shift and the spontaneous formation of hydrogen-bonded dimers from two copies of a prior trained only on the monomer.
Xuanxi Zhang, Kevin S. Cheng, Weizhou Wang, Aaron R. Dinner, Jonathan Weare
原文摘要
Diffusion models are often inaccurate in critical, data-sparse regions of the target distribution. Sampling from restrained distributions, biased distributions used in classical enhanced sampling to concentrate data near chosen configurations, can control where training data are collected but biases the learned distribution. We establish that this bias cancels exactly when forward noising from restrained data is conditioned on the restrained configuration at an appropriately chosen intermediate time. This allows a pretrained model fine-tuned on restrained data to achieve high accuracy in any chosen region of the target distribution, regardless of its probability, using standard denoising or flow matching objectives without importance weights. When no target data are available, Gibbs sampling enables inference from a model trained exclusively on restrained data.
Most molecular transitions occur on time scales far beyond direct molecular dynamics simulations. The committor, the probability that a configuration reaches a product state before a reactant state, is a central kinetic statistic, providing a mechanism-independent reaction coordinate and a foundation for transition path theory and the calculation of rates. This review surveys modern approaches for estimating the committor and related kinetic statistics from molecular simulations, with an emphasis on self-supervised methods that learn solutions of their defining dynamical equations rather than relying on labeled shooting data. We develop a common operator viewpoint connecting generator-based partial differential equations, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks. Empirical and theoretical evidence points to the efficiency of these methods. We provide theoretical and practical guidance for realizing their full potential in applications, including strategies for treating non-Markovian effects and for sampling. We conclude by identifying opportunities for further research, including connections to reinforcement learning and generative modeling.