将连续空间的高效采样方法拓展至离散空间，提升训练效率与可扩展性。
Discrete Adjoint Schrödinger Bridge Sampler
- 提出离散自适应辛桥采样框架，突破梯度缺失难题
- 在离散空间实现与连续方法相当的采样质量
- 适合需要高效训练的大规模离散生成任务
由于缺乏梯度和组合复杂性，学习离散神经采样器极具挑战。尽管随机最优控制（SOC）和薛定谔桥（SB）提供了原则性解决方案，但高效连续域求解器如伴随匹配（AM）在离散空间中仍未被探索。本文揭示了AM的核心机制具有状态空间无关性，提出离散ASBS，统一扩展AM与伴随薛定谔桥采样器（ASBS）至离散空间。理论上，分析了离散SB问题的最优性条件及其与SOC的关系，识别出状态空间需具备循环群结构才能实现该扩展。实验上，离散ASBS在采样质量上表现优异，且在训练效率和可扩展性方面有显著优势。
原文摘要 · Abstract (English)
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 $\mathit{state}\text{-}\mathit{space~agnostic}$, and introduce $\mathbf{discrete~ASBS}$, 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.
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