Dequantified Diffusion-Schrödinger Bridge for Density Ratio Estimation

Wei Chen, Shigui Li, Jiacheng Li, Junmei Yang, John Paisley, Delu Zeng
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:8427-8452, 2025.

Abstract

Density ratio estimation is fundamental to tasks involving f-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports — the density-chasm and the support-chasm problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We design $\textbf{D}^3\textbf{RE}$, a unified framework for robust, stable and efficient density ratio estimation. We propose the dequantified diffusion bridge interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the proposed dequantified Schrödinger bridge interpolant (DSBI) incorporates optimal transport to solve the Schrödinger bridge problem, enhancing accuracy and efficiency. Our method offers uniform approximation and bounded time scores in theory, and outperforms baselines empirically in mutual information and density estimation tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-chen25aj, title = {Dequantified Diffusion-Schrödinger Bridge for Density Ratio Estimation}, author = {Chen, Wei and Li, Shigui and Li, Jiacheng and Yang, Junmei and Paisley, John and Zeng, Delu}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {8427--8452}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/chen25aj/chen25aj.pdf}, url = {https://proceedings.mlr.press/v267/chen25aj.html}, abstract = {Density ratio estimation is fundamental to tasks involving f-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports — the density-chasm and the support-chasm problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We design $\textbf{D}^3\textbf{RE}$, a unified framework for robust, stable and efficient density ratio estimation. We propose the dequantified diffusion bridge interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the proposed dequantified Schrödinger bridge interpolant (DSBI) incorporates optimal transport to solve the Schrödinger bridge problem, enhancing accuracy and efficiency. Our method offers uniform approximation and bounded time scores in theory, and outperforms baselines empirically in mutual information and density estimation tasks.} }
Endnote
%0 Conference Paper %T Dequantified Diffusion-Schrödinger Bridge for Density Ratio Estimation %A Wei Chen %A Shigui Li %A Jiacheng Li %A Junmei Yang %A John Paisley %A Delu Zeng %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-chen25aj %I PMLR %P 8427--8452 %U https://proceedings.mlr.press/v267/chen25aj.html %V 267 %X Density ratio estimation is fundamental to tasks involving f-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports — the density-chasm and the support-chasm problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We design $\textbf{D}^3\textbf{RE}$, a unified framework for robust, stable and efficient density ratio estimation. We propose the dequantified diffusion bridge interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the proposed dequantified Schrödinger bridge interpolant (DSBI) incorporates optimal transport to solve the Schrödinger bridge problem, enhancing accuracy and efficiency. Our method offers uniform approximation and bounded time scores in theory, and outperforms baselines empirically in mutual information and density estimation tasks.
APA
Chen, W., Li, S., Li, J., Yang, J., Paisley, J. & Zeng, D.. (2025). Dequantified Diffusion-Schrödinger Bridge for Density Ratio Estimation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:8427-8452 Available from https://proceedings.mlr.press/v267/chen25aj.html.

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