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Discrete Adjoint Schr\"odinger Bridge Sampler

Wei Guo,Yuchen Zhu,Xiaochen Du,Juno Nam,Yongxin Chen,Rafael G'omez-Bombarelli,Guan-Horng Liu,Molei Tao,Jaemoo Choi

Published 2026 in Unknown venue

ABSTRACT

Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schr\"odinger 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 $\mathit{state}\text{-}\mathit{space~agnostic}$, and introduce $\mathbf{discrete~ASBS}$, a unified framework that extends AM and adjoint Schr\"odinger 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.

PUBLICATION RECORD

  • Publication year

    2026

  • Venue

    Unknown venue

  • Publication date

    2026-02-09

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 2602.08243
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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