Deep unfolding of MCMC kernels: scalable, modular&explainable GANs for high-dimensional posterior sampling

2026-02-24

AI Summary

This work addresses the computational inefficiency of traditional MCMC methods in high-dimensional Bayesian posterior sampling and the limited modularity and generalizability of existing generative models across varying likelihood functions. The authors propose a modular GAN architecture based on deep unfolding of Langevin MCMC, explicitly embedding MCMC iterations into a neural network to enable end-to-end supervised training. This approach allows flexible adjustment of likelihood parameters at inference time while preserving physical interpretability, computational efficiency, and adaptability to changes in the likelihood. Experimental results demonstrate that the method significantly improves both sampling efficiency and accuracy in Bayesian imaging tasks, while retaining the robustness and tunability characteristic of conventional MCMC algorithms.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Markov chain Monte Carlo (MCMC) methods are fundamental to Bayesian computation, but can be computationally intensive, especially in high-dimensional settings. Push-forward generative models, such as generative adversarial networks (GANs), variational auto-encoders and normalising flows offer a computationally efficient alternative for posterior sampling. However, push-forward models are opaque as they lack the modularity of Bayes Theorem, leading to poor generalisation with respect to changes in the likelihood function. In this work, we introduce a novel approach to GAN architecture design by applying deep unfolding to Langevin MCMC algorithms. This paradigm maps fixed-step iterative algorithms onto modular neural networks, yielding architectures that are both flexible and amenable to interpretation. Crucially, our design allows key model parameters to be specified at inference time, offering robustness to changes in the likelihood parameters. We train these unfolded samplers end-to-end using a supervised regularized Wasserstein GAN framework for posterior sampling. Through extensive Bayesian imaging experiments, we demonstrate that our proposed approach achieves high sampling accuracy and excellent computational efficiency, while retaining the physics consistency, adaptability and interpretability of classical MCMC strategies.

Problem

• posterior sampling
• MCMC
• generative adversarial networks
• high-dimensional inference
• Bayesian computation

Innovation

• deep unfolding
• MCMC
• generative adversarial networks
• posterior sampling
• modular architecture