提出可变能量的随机桥模型，实现更真实的过程建模。
Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges
- 基于接触哈密顿力学重构非保守薛定谔桥
- 通过ResNet实现近线性复杂度的非迭代求解
- 适用于分子动力学、图像生成等多场景引导生成
薛定谔桥为分布间随机过程建模提供了严谨框架，但现有方法受限于能量守恒假设，难以刻画能量变化的现实过程。为此，我们提出非保守广义薛定谔桥（NCGSB），基于接触哈密顿力学构建能量可变的新形式。通过参数化沃瑟斯坦流形，将桥问题转化为有限维空间中的测地线计算。与计算昂贵的迭代方法不同，我们的接触沃瑟斯坦测地线（CWG）可自然由ResNet实现，采用非迭代求解器，复杂度接近线性。此外，CWG支持通过调节任务相关距离度量实现引导生成。我们在流形导航、分子动力学预测和图像生成任务上验证了该框架的实用性与通用性。
原文摘要 · Abstract (English)
The Schrödinger Bridge provides a principled framework for modeling stochastic processes between distributions; however, existing methods are limited by energy-conservation assumptions, which constrains the bridge's shape preventing it from model varying-energy phenomena. To overcome this, we introduce the non-conservative generalized Schrödinger bridge (NCGSB), a novel, energy-varying reformulation based on contact Hamiltonian mechanics. By allowing energy to change over time, the NCGSB provides a broader class of real-world stochastic processes, capturing richer and more faithful intermediate dynamics. By parameterizing the Wasserstein manifold, we lift the bridge problem to a tractable geodesic computation in a finite-dimensional space. Unlike computationally expensive iterative solutions, our contact Wasserstein geodesic (CWG) is naturally implemented via a ResNet architecture and relies on a non-iterative solver with near-linear complexity. Furthermore, CWG supports guided generation by modulating a task-specific distance metric. We validate our framework on tasks including manifold navigation, molecular dynamics predictions, and image generation, demonstrating its practical benefits and versatility.
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