Discrete Adjoint Schrödinger Bridge Sampler

Wei Guo, Yuchen Zhu, Xiaochen Du, Juno Nam, Yongxin Chen, Rafael Gomez-Bombarelli, Guan-Horng Liu, Molei Tao, Jaemoo Choi
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:38746-38776, 2026.

Abstract

Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is state-space agnostic, and introduce discrete ASBS, a unified framework that extends AM and adjoint Schrödinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability. Our code is available at https://github.com/AlexandreGUO2001/DASBS.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-guo26al, title = {Discrete Adjoint Schrödinger Bridge Sampler}, author = {Guo, Wei and Zhu, Yuchen and Du, Xiaochen and Nam, Juno and Chen, Yongxin and Gomez-Bombarelli, Rafael and Liu, Guan-Horng and Tao, Molei and Choi, Jaemoo}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {38746--38776}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/guo26al/guo26al.pdf}, url = {https://proceedings.mlr.press/v306/guo26al.html}, abstract = {Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is state-space agnostic, and introduce discrete ASBS, a unified framework that extends AM and adjoint Schrödinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability. Our code is available at https://github.com/AlexandreGUO2001/DASBS.} }
Endnote
%0 Conference Paper %T Discrete Adjoint Schrödinger Bridge Sampler %A Wei Guo %A Yuchen Zhu %A Xiaochen Du %A Juno Nam %A Yongxin Chen %A Rafael Gomez-Bombarelli %A Guan-Horng Liu %A Molei Tao %A Jaemoo Choi %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-guo26al %I PMLR %P 38746--38776 %U https://proceedings.mlr.press/v306/guo26al.html %V 306 %X Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is state-space agnostic, and introduce discrete ASBS, a unified framework that extends AM and adjoint Schrödinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability. Our code is available at https://github.com/AlexandreGUO2001/DASBS.
APA
Guo, W., Zhu, Y., Du, X., Nam, J., Chen, Y., Gomez-Bombarelli, R., Liu, G., Tao, M. & Choi, J.. (2026). Discrete Adjoint Schrödinger Bridge Sampler. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:38746-38776 Available from https://proceedings.mlr.press/v306/guo26al.html.

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