Composing diffusion priors with explicit physical context via generative Gibbs sampling

2026-05-11

AI Summary

This work addresses the challenge of sampling from target distributions in scientific applications, where physical context often renders pretrained diffusion models directly inapplicable. The authors propose the GG-PA framework, which constructs a joint distribution in an augmented state space to seamlessly integrate diffusion priors with explicit physical constraints—without requiring model retraining—and introduces a corresponding Gibbs sampler. Theoretically, the method yields asymptotically exact samples in the zero-diffusion-time limit and remains exact at finite times for quadratic interactions. To accelerate mixing, replica exchange along the diffusion time dimension is incorporated. Empirical validation on benchmark systems—including a double-well potential, the φ⁴ lattice model, and atomistic peptide ensembles—demonstrates the framework’s ability to accurately reproduce context-induced distributional shifts and emergent collective behaviors, confirming its efficacy and broad applicability.

Abstract

Pretrained diffusion models provide powerful learned priors, but in scientific sampling the target distribution often depends on physical context that is not fully represented by one generative model. We introduce Generative Gibbs for Physics-Aware Sampling (GG-PA), a training-free framework that formulates the composition of learned partial priors and explicit physical context as inference over a joint target distribution in an augmented state space. We derive a Gibbs sampler for this joint target, show that it is asymptotically exact as the diffusion time approaches zero, and prove that in settings with quadratic interactions it remains exact at finite diffusion times. We further introduce replica exchange over diffusion time to accelerate mixing. Experiments on a double-well system, a $φ^4$ lattice model, and atomistic peptide systems show that GG-PA recovers context-induced distribution shifts and emergent collective behavior in interacting systems using partial priors without retraining. These results demonstrate GG-PA as a practical approach for combining pretrained generative priors with explicit physical context.

Problem

• diffusion priors
• physical context
• scientific sampling
• generative models
• distribution composition

Innovation

• Generative Gibbs Sampling
• Diffusion Priors
• Physics-Aware Sampling
• Replica Exchange
• Joint Target Distribution