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February 19, 2026Mathematics of Computation

Sampling via gradient flows in the space of probability measures

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Authors

YCYifan ChenDHDaniel Zhengyu HuangJHJiaoyang Huang

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Overview

Algorithm developments demonstrate new sampling approaches in probability distributions using gradient flows.

Key Points

  • This research aims to improve sampling techniques for probability distributions by analyzing gradient flows and their components.
  • Investigated the role of Kullback-Leibler divergence as an energy functional for sampling.
  • Analyzed the choice of metric, focusing on the Fisher-Rao metric and its invariance properties.
  • Developed various affine invariant gradient flows and compared them with non-affine-invariant methods.
  • Constructed efficient algorithms based on Gaussian approximations of gradient flows.
  • Showed that Kullback-Leibler divergence does not rely on normalization constants when used in gradient flows.
  • Established affine invariance as beneficial for sampling anisotropic distributions in both theory and simulation.
  • Demonstrated the effectiveness of Gaussian approximate gradient flows compared to particle methods.

Cite This Study

Chen et al. (2026) studied this question.

synapsesocial.com/papers/6996a898ecb39a600b3ef836https://doi.org/10.1090/mcom/4186
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