aiqbench analysis
This research advances Bayesian inference by introducing a framework that efficiently samples from implicit priors using few-step transport maps in source space. By combining parallel tempering with Hamiltonian Monte Carlo, the method achieves stable posterior approximations even when guided by large-scale pretrained models like CLIP. The work offers significant theoretical guarantees on Wasserstein error bounds, making it a robust tool for test-time adaptation and generalized Bayes tasks.
Posterior sampling by source-space MCMC via prior-based few-step transport maps
arXiv:2610.01034v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2610.01034 [stat.ML]
(or arXiv:2610.01034v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.01034 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 277 words
Related coverage
P(Anyone Builds It & Everyone Dies) = 0.62?
LessWrong · Oct 16, 2026
Latent reasoning architectures would likely undermine CoT, our strongest oversight tool
AI Alignment Forum · Sep 23, 2026
[AINews] not much happened today
Latent Space · Oct 3, 2026
How can LLM RL Work Despite Information-Theoretic Inefficiency
LessWrong · Oct 16, 2026