{"ID":2843831,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.06856","arxiv_id":"2511.06856","title":"Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges","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 metric. We validate our framework on tasks including manifold navigation, molecular dynamics predictions, and image generation, demonstrating its practical benefits and versatility.","short_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-conserva...","url_abs":"https://arxiv.org/abs/2511.06856","url_pdf":"https://arxiv.org/pdf/2511.06856v4","authors":"[\"Andrea Testa\",\"Søren Hauberg\",\"Tamim Asfour\",\"Leonel Rozo\"]","published":"2025-11-10T08:56:21Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.DG\"]","methods":"[]","has_code":false}