Posterior sampling by source-space MCMC via prior-based few-step transport maps

2026-10-01

AI Summary

This study addresses the computational inefficiency of Bayesian inference and test-time guidance with implicit priors by proposing an efficient generalized Bayesian inference framework that integrates few-step prior transport with source-space MCMC. The core methodology introduces an iMF source-space parallel tempering and hybrid HMC algorithm, which combines an improved MeanFlow mapping with Crank–Nicolson updates, supported by rigorous Wasserstein error bounds. Experimental results demonstrate that the proposed approach accurately approximates posterior distributions on synthetic data and successfully achieves text-preference alignment in CLIP-guided image generation tasks. Overall, this work effectively balances inference efficiency and stability for implicit-prior-based Bayesian modeling.

Abstract

Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, and pretrained generative models. The same computational problem appears in the test-time guidance task (generalized Bayes), where an explicit positive weight, e.g., an exponentiated reward, tilts an implicit prior. We develop a framework for source-space generalized Bayesian inference that combines inexpensive few-step prior transports with posterior stability guarantees. Specifically, we represent the prior using a one- or few-step improved MeanFlow (iMF) map and perform posterior sampling in its Gaussian source space. We establish Wasserstein error bounds between the exact and learned posteriors in terms of the joint population iMF and auxiliary-velocity loss, decomposed into training suboptimality and model-class approximation error. In the iMF source space, we adopt parallel tempering with preconditioned Crank-Nicolson updates and introduce a hybrid variant that incorporates split Hamiltonian Monte Carlo to improve sampling efficiency. Synthetic experiments show that the proposed framework can approximate posterior distributions accurately and efficiently, while CLIP-guided ImageNet experiments demonstrate its ability to steer a pretrained iMF image prior toward text-specified preferences.

Problem

• Bayesian inference
• implicit prior
• posterior sampling
• generalized Bayes
• transport maps

Innovation

• Generalized Bayesian inference
• Improved MeanFlow (iMF)
• Source-space MCMC
• Wasserstein error bounds
• Parallel tempering