从静态数据重建动态过程，突破高维限制
Multi-marginal temporal Schrödinger Bridge Matching from unpaired data
- 基于多边缘量子桥接思想，设计新型迭代马尔可夫拟合算法
- 在100维转录组数据上达到顶尖性能，首次实现高维图像动态恢复
- 适合生物发育、疾病进展等隐性动态建模研究者使用
许多自然动态过程（如活体细胞分化或疾病进展）只能通过静态样本快照观测。重建其时间演化以揭示内在动力学特性对科学研究具有重要意义。现有方法虽能沿时间轴传输数据，但在高维场景下扩展性差且依赖严格假设。为此，本文提出无配对数据下的多边缘时序薛定谔桥匹配（MMtSBM），通过创新的分解式策略，将扩散型薛定谔桥匹配（arXiv:2303.16852）的理论保证与实证效率推广至多个边缘分布。实验表明，MMtSBM在合成数据上保持理论性质，在真实世界数据集如100维转录组轨迹推断中达到当前最优表现，并首次实现了高维图像场景下耦合关系与动态过程的恢复。本工作确立了多边缘薛定谔桥作为从静态数据恢复隐藏动态的实用且原理严谨的方法。
原文摘要 · Abstract (English)
Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher underlying dynamic properties is of major interest to scientific research. Existing approaches enable data transport along a temporal axis but are poorly scalable in high dimension and require restrictive assumptions to be met. To address these issues, we propose Multi-Marginal temporal Schrödinger Bridge Matching (MMtSBM) from unpaired data, extending the theoretical guarantees and empirical efficiency of Diffusion Schrödinger Bridge Matching (arXiv:2303.16852) by deriving the Iterative Markovian Fitting algorithm to multiple marginals in a novel factorized fashion. Experiments show that MMtSBM retains theoretical properties on toy examples, achieves state-of-the-art performance on real-world datasets such as transcriptomic trajectory inference in 100 dimensions, and, for the first time, recovers couplings and dynamics in very high-dimensional image settings. Our work establishes multi-marginal Schrödinger bridges as a practical and principled approach for recovering hidden dynamics from static data.
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