A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation
Abstract
Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal, ground-truth objective by a crucial, overlooked term: the path variance of the score function. We propose the MVP (**M**imum **V**ariance **P**ath) Principle to minimize this path variance. Our key contribution is deriving a closed-form expression for the variance, making optimization tractable. By parameterizing the path with a flexible Kumaraswamy Mixture Model, our method learns data-adaptive, low-variance paths without heuristic manual selection. This principled optimization of the complete objective yields more accurate and stable estimators, establishing new state-of-the-art results on challenging benchmarks and providing a general framework for optimizing score-based interpolation. Our code can be found in https://github.com/Hoemr/OpenDRE.git.
Cite
Text
Chen et al. "A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation." International Conference on Learning Representations, 2026.Markdown
[Chen et al. "A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation." International Conference on Learning Representations, 2026.](https://mlanthology.org/iclr/2026/chen2026iclr-minimum/)BibTeX
@inproceedings{chen2026iclr-minimum,
title = {{A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation}},
author = {Chen, Wei and Li, Jiacheng and Li, Shigui and Lin, Zhiqi and Yang, Junmei and Paisley, John and Zeng, Delu},
booktitle = {International Conference on Learning Representations},
year = {2026},
url = {https://mlanthology.org/iclr/2026/chen2026iclr-minimum/}
}