提出无需完整模拟的反射型桥接生成方法，高效保持样本在数据域内。
Reflected Schrödinger Bridge Matching
- 引入新采样与回归目标，实现反射动力学的近似无模拟训练
- 训练与推理时间几乎不变，生成性能持平或略有提升
- 适合需保证生成样本在数据域内的高维图像生成任务
生成建模近期进展使得高维场景下舒尔丁格桥（SB）的计算更加高效，得益于受流匹配启发的部分无模拟训练方法。然而，这些方法尚未涵盖具有反射动力学的SB，这类模型能内置保证生成样本始终位于数据域内，具有实用价值。现有反射型SB方法依赖更复杂的前向-后向随机微分方程（SDE）理论，需要昂贵的高阶导数计算，并在训练中需采样完整路径。本文提出一种部分无模拟框架，使反射型SB可类似流匹配进行训练，使用新的采样方法和回归目标。我们在多个知名高维图像数据集对上进行了实验验证。采用反射动力学仅带来可忽略的额外墙钟时间开销，且在训练与推理阶段均保持或轻微提升生成性能。
原文摘要 · Abstract (English)
Recent advances in generative modeling have enabled the efficient computation of Schrödinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods inspired by flow matching. However, these have not covered SBs with reflecting dynamics, a useful model choice with built-in guarantees that generated samples stay in the data domain. Existing alternatives for reflected SBs instead rely on more complex training based on forward--backward SDE theory, requiring expensive higher-order derivatives and sampling entire paths during training. In this article, we introduce a partially simulation-free framework that allows reflected SBs to be trained similarly to flow matching, using a new sampling method and regression target. We demonstrate our results by coupling pairs of well-known high-dimensional image datasets. Using reflected dynamics incurs negligible additional wall-clock time during both training and inference while maintaining or slightly improving generative performance.
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