Parallel Tempering

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Posterior sampling by source-space MCMC via prior-based few-step transport maps
Oct 1, 2026Hoang Phuc Hau Luu, Marcelo Hartmann, Zhongjian WangMarkov Chain Monte Carlo Bayesian Inference
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore. · Department of Computer Science, Faculty of Science, University of Helsinki, Finland.
A Direct Route to Markov Chain Convergence via Asymptotic Equivalence with the Target
Aug 4, 2026Patrick ForréMarkov Chain Monte Carlo Convergence Analysis
AI4Science Lab Korteweg-de Vries Institute for Mathematics University of Amsterdam
Equilibrium Training of Energy-Based Models with Parallel Trajectory Tempering
Jul 29, 2026Nicolas Béreux, Aurélien Decelle, Cyril Furtlehner +1Markov Chain Monte Carlo Energy-Based Models
Université Paris-Saclay, CNRS, INRIA, LISN, 91190 Gif-sur-Yvette, France · Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, 28006 Madrid, Spain · Departamento de Física Teórica & IPARCOS, Universidad Complutense de Madrid, 28040 Madrid, Spain.
Parallel Noising in Neural Markov Logic Networks
Jul 21, 2026Peter Jung, Giuseppe Marra, Ondrej KuzelkaMarkov Chain Monte Carlo Graph Generation
Czech Technical University, Prague, Czech Republic · Department of Computer Science, KU Leuven, Leuven, Belgium
BayesPO: Bayesian Prompt Optimization via Parallel-Tempered Gradient-Guided Discrete MCMC
Jul 17, 2026Junjie Zhou, Zhijian OuMarkov Chain Monte Carlo LLM Prompting
Speech Processing and Machine Intelligence (SPMI) Lab Tsinghua University, China
Towards Diverse Scientific Hypothesis Search with Large Language Models
Jun 9, 2026Haorui Wang, Parshin Shojaee, Kazem Meidani +7Automated Algorithm Discovery Scientific Hypothesis Generation
Georgia Institute of Technology · Virginia Tech · Carnegie Mellon University +3
Parallel Tempering Initial Sampling in Inference-Time Reward Alignment
May 29, 2026Myeongjun Oh, Gwangho Kim, Sungyoon LeeDiffusion Model Alignment Markov Chain Monte Carlo
Department of Artificial Intelligence 2Department of Computer Science Hanyang University, Seoul, Korea
Solving Integer Linear Programming with Parallel Tempering
May 28, 2026Kyuil Sim, Sanghyeok Choi, Jinkyoo ParkMarkov Chain Monte Carlo Mixed-Integer Linear Programming
1KAIST · University of Edinburgh

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

Hoang Phuc Hau Luu, Marcelo Hartmann, Zhongjian Wang

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore. · Department of Computer Science, Faculty of Science, University of Helsinki, Finland.

Markov Chain Monte Carlo Bayesian Inference Posterior Sampling Parallel Tempering Inference-Time Guidance

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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.

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