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RuiKang OuYang

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TMLR Journal 2026 Journal Article

BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching

RuiKang OuYang
Bo Qiang
José Miguel Hernández-Lobato

Generating independent samples from a Boltzmann distribution is a highly relevant problem in scientific research, \textit{e.g.} in molecular dynamics, where one has initial access to the underlying energy function but not to samples from the Boltzmann distribution. We address this problem by learning the energies of the convolution of the Boltzmann distribution with Gaussian noise. These energies are then used to generate independent samples through a denoising diffusion approach. The resulting method, \textsc{Noised Energy Matching} (NEM), has lower variance and only slightly higher cost than previous related works. We also improve NEM through a novel bootstrapping technique called \textsc{Bootstrap NEM} (BNEM) that further reduces variance while only slightly increasing bias. Experiments on a collection of problems demonstrate that NEM can outperform previous methods while being more robust and that BNEM further improves on NEM. Codes are available at \url{https://github.com/tonyauyeung/BNEM}.

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ICML Conference 2025 Conference Paper

Progressive Tempering Sampler with Diffusion

Severi Rissanen
Ruikang Ouyang
Jiajun He 0003
Wenlin Chen
Markus Heinonen
Arno Solin
José Miguel Hernández-Lobato

Recent research has focused on designing neural samplers that amortize the process of sampling from unnormalized densities. However, despite significant advancements, they still fall short of the state-of-the-art MCMC approach, Parallel Tempering (PT), when it comes to the efficiency of target evaluations. On the other hand, unlike a well-trained neural sampler, PT yields only dependent samples and needs to be rerun—at considerable computational cost—whenever new samples are required. To address these weaknesses, we propose the Progressive Tempering Sampler with Diffusion (PTSD), which trains diffusion models sequentially across temperatures, leveraging the advantages of PT to improve the training of neural samplers. We also introduce a novel method to combine high-temperature diffusion models to generate approximate lower-temperature samples, which are minimally refined using MCMC and used to train the next diffusion model. PTSD enables efficient reuse of sample information across temperature levels while generating well-mixed, uncorrelated samples. Our method significantly improves target evaluation efficiency, outperforming diffusion-based neural samplers.

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