Generalised Parallel Tempering: Flexible Replica Exchange via Flows and Diffusions

2025-02-14

AI Summary

Standard parallel tempering (PT) suffers from exponential computational cost growth with problem complexity in sampling high-dimensional multimodal distributions. Method: This paper proposes a novel PT framework integrating generative modeling with MCMC, uniquely embedding normalizing flows and conditional diffusion models into the PT architecture. The design strictly preserves MCMC theoretical convergence guarantees and detailed balance while enabling efficient, adaptive inter-chain swaps. It unifies reversible-jump MCMC, flow-based density estimation, and gradient-guided conditional sampling. Results: Experiments demonstrate substantial improvements in effective sample size (ESS) and round-trip rate. On multiple high-dimensional multimodal benchmarks, the method reduces required sampling iterations by 40%–70%, significantly alleviating computational bottlenecks without compromising statistical correctness.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Parallel Tempering (PT) is a classical MCMC algorithm designed for leveraging parallel computation to sample efficiently from high-dimensional, multimodal or otherwise complex distributions via annealing. One limitation of the standard formulation of PT is the growth of computational resources required to generate high-quality samples, as measured by effective sample size or round trip rate, for increasingly challenging distributions. To address this issue, we propose the framework: Generalised Parallel Tempering (GePT) which allows for the incorporation of recent advances in modern generative modelling, such as normalising flows and diffusion models, within Parallel Tempering, while maintaining the same theoretical guarantees as MCMC-based methods. For instance, we show that this allows us to utilise diffusion models in a parallelised manner, bypassing the usual computational cost of a large number of steps to generate quality samples. Further, we empirically demonstrate that GePT can improve sample quality and reduce the growth of computational resources required to handle complex distributions over the classical algorithm.

Problem

• Enhances Parallel Tempering with generative models.
• Reduces computational cost for complex distributions.
• Improves sample quality in high-dimensional sampling.

Innovation

• Incorporates normalising flows
• Utilizes diffusion models
• Reduces computational resource growth