Restrained Diffusion Bridges: Targeted Denoiser Training and Refinement
Abstract
Diffusion models are often inaccurate in critical, data-sparse regions of the target distribution. Sampling from restrained distributions, biased distributions used in classical enhanced sampling to concentrate data near chosen configurations, can control where training data are collected but biases the learned distribution. We establish that this bias cancels exactly when forward noising from restrained data is conditioned on the restrained configuration at an appropriately chosen intermediate time. This allows a pretrained model fine-tuned on restrained data to achieve high accuracy in any chosen region of the target distribution, regardless of its probability, using standard denoising or flow matching objectives without importance weights. When no target data are available, Gibbs sampling enables inference from a model trained exclusively on restrained data.
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BibTeX
@misc{zhang2026restrained,
title = {{Restrained Diffusion Bridges: Targeted Denoiser Training and Refinement}},
author = {Xuanxi Zhang and Kevin S. Cheng and Weizhou Wang and Jonathan Weare},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02170},
eprint = {2611.02170},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02170},
}
RIS
TY - UNPB
TI - Restrained Diffusion Bridges: Targeted Denoiser Training and Refinement
AU - Xuanxi Zhang
AU - Kevin S. Cheng
AU - Weizhou Wang
AU - Jonathan Weare
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02170
UR - https://arxiv.org/abs/2611.02170
AB - Diffusion models are often inaccurate in critical, data-sparse regions of the target distribution. Sampling from restrained distributions, biased distributions used in classical enhanced sampling to concentrate data near chosen configurations, can control where training data are collected but biases the learned distribution. We establish that this bias cancels exactly when forward noising from restrained data is conditioned on the restrained configuration at an appropriately chosen intermediate time. This allows a pretrained model fine-tuned on restrained data to achieve high accuracy in any chosen region of the target distribution, regardless of its probability, using standard denoising or flow matching objectives without importance weights. When no target data are available, Gibbs sampling enables inference from a model trained exclusively on restrained data.
ER -