Composing diffusion priors with explicit physical context via generative Gibbs sampling

원문 초록

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 $\phi^4$ 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.