![[2511.06856] Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2511.06856] Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges
Summary
This article presents the non-conservative generalized Schrödinger bridge (NCGSB), a novel framework for modeling stochastic processes that allows for energy variation, enhancing the modeling of real-world phenomena.
Why It Matters
The introduction of the NCGSB framework expands the capabilities of stochastic modeling by addressing limitations of traditional methods that assume energy conservation. This advancement has significant implications for fields such as molecular dynamics and image generation, where capturing complex dynamics is crucial.
Key Takeaways
- The NCGSB framework allows for energy variation in stochastic processes.
- Contact Wasserstein geodesics (CWG) provide efficient, non-iterative solutions for complex modeling tasks.
- The framework demonstrates practical applications in manifold navigation, molecular dynamics, and image generation.
Computer Science > Machine Learning arXiv:2511.06856 (cs) [Submitted on 10 Nov 2025 (v1), last revised 22 Feb 2026 (this version, v3)] Title:Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges Authors:Andrea Testa, Søren Hauberg, Tamim Asfour, Leonel Rozo View a PDF of the paper titled Contact Wasserstein Geodesics for Non-Conservative Schr\"odinger Bridges, by Andrea Testa and 3 other authors View PDF HTML (experimental) Abstract: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 ...