OpenNovelty.org

Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Schrödinger BridgeGenerative ModelsHamiltonianContact HamiltonianDifferential GeometryWasserstein metric
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.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces a non-conservative generalized Schrödinger bridge (NCGSB) using contact Hamiltonian mechanics to model energy-varying stochastic processes between distributions. Within the taxonomy, it occupies the 'Contact Hamiltonian and Wasserstein Geodesic Methods' leaf under 'Non-Conservative and Energy-Varying Stochastic Bridges'. Notably, this leaf contains only the original paper itself—no sibling papers appear in the taxonomy. This isolation suggests the work explores a relatively sparse research direction, distinct from the broader energy-based generative modeling and physical thermodynamics branches that dominate the field.

The taxonomy reveals neighboring leaves focused on diffusion and score-based methods, which handle conservative or standard noisy processes, and energy-based generative models that treat energy as a learned potential rather than a time-varying dynamical quantity. The original paper diverges by lifting the bridge problem to Wasserstein manifolds via contact geometry, contrasting with purely thermodynamic frameworks (e.g., stochastic thermodynamics and fluctuation theorems) and control-oriented approaches (e.g., distributed energy management). The scope note explicitly excludes conservative bridges and standard diffusion models, positioning the work at the intersection of optimal transport geometry and non-equilibrium dynamics.

Among the three contributions analyzed, the literature search examined twenty-seven candidates total. For the NCGSB formulation, ten candidates were reviewed with zero refutable overlaps; similarly, the Contact Wasserstein Geodesic framework examined ten candidates with no refutations, and the guided generation method examined seven candidates with none refutable. These statistics indicate that, within the limited search scope, no prior work among the top semantic matches and citation expansions directly anticipates the contact Hamiltonian reformulation or the ResNet-based geodesic solver. The absence of refutable candidates across all contributions suggests the approach introduces mechanisms not prominently represented in the examined literature.

Given the limited search scale and the paper's placement in a singleton taxonomy leaf, the work appears to occupy a novel niche combining contact mechanics with stochastic bridge theory. However, the analysis covers only top-K semantic matches and does not exhaustively survey all geometric optimal transport or non-equilibrium stochastic process literature. The lack of sibling papers and refutable candidates may reflect either genuine novelty or underrepresentation of this specific geometric formulation in the candidate pool.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
27
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: modeling stochastic processes with energy-varying dynamics between distributions. The field encompasses diverse approaches to understanding how systems evolve when energy is not conserved or when transitions between probability distributions involve explicit energy considerations. At the highest level, the taxonomy divides into energy-based generative models and probabilistic learning (including works like Deep directed generative models[1] and Learning energy-based models by[10]), non-conservative and energy-varying stochastic bridges (which explore geodesic and contact Hamiltonian frameworks), physical systems and thermodynamics (covering stochastic thermodynamics fluctuation theorems[17] and biophysical processes[18]), control and optimization in energy systems (such as Stochastic optimal control of[21] and distributed filtering methods[6]), and stochastic process models without explicit energy formulation. These branches reflect a spectrum from purely data-driven generative modeling to physics-grounded thermodynamic descriptions, with intermediate areas addressing optimal transport and control under energy constraints. Recent activity highlights contrasting themes: some lines pursue rigorous geometric formulations of non-equilibrium transitions, while others focus on practical energy management or learning-based inference. Contact Wasserstein Geodesics for[0] sits within the non-conservative stochastic bridges branch, emphasizing contact Hamiltonian mechanics and Wasserstein geometry to model energy-varying paths between distributions. This approach contrasts with purely thermodynamic perspectives like Stochastic thermodynamics fluctuation theorems[17], which center on entropy production and fluctuation relations, and with control-oriented methods such as Stochastic optimal control of[21] that prioritize decision-making under uncertainty. The work also differs from energy-based generative models (e.g., Energy-inspired models[8]) that treat energy as a learned potential rather than a dynamical quantity. Open questions remain about how to best integrate geometric, thermodynamic, and computational viewpoints, and whether contact geometry offers advantages over alternative frameworks for capturing dissipative or non-conservative dynamics in practical applications.

Claimed Contributions

Non-conservative generalized Schrödinger bridge (NCGSB)

The authors propose NCGSB, a novel formulation of the Schrödinger Bridge problem that allows energy to vary over time by leveraging contact Hamiltonian mechanics. This overcomes the energy-conservation constraint of existing methods and enables modeling of a broader class of real-world stochastic processes with dissipative or energy-varying behaviors.

10 retrieved papers
Contact Wasserstein Geodesic (CWG) framework

The authors introduce CWG, a geometric solver that reformulates the NCGSB problem as a geodesic computation in a finite-dimensional parameterized space. This approach avoids iterative optimization loops and achieves near-linear complexity, making it computationally efficient and compatible with all Schrödinger Bridge variants.

10 retrieved papers
Guided generation method for CWG

The authors develop a guided generation technique that steers the learned stochastic process by embedding a task-specific loss into the potential energy, thereby modulating the Riemannian metric. This allows the resulting geodesic to align with desired outcomes or constraints without requiring full retraining.

7 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Non-conservative generalized Schrödinger bridge (NCGSB)

The authors propose NCGSB, a novel formulation of the Schrödinger Bridge problem that allows energy to vary over time by leveraging contact Hamiltonian mechanics. This overcomes the energy-conservation constraint of existing methods and enables modeling of a broader class of real-world stochastic processes with dissipative or energy-varying behaviors.

Contribution

Contact Wasserstein Geodesic (CWG) framework

The authors introduce CWG, a geometric solver that reformulates the NCGSB problem as a geodesic computation in a finite-dimensional parameterized space. This approach avoids iterative optimization loops and achieves near-linear complexity, making it computationally efficient and compatible with all Schrödinger Bridge variants.

Contribution

Guided generation method for CWG

The authors develop a guided generation technique that steers the learned stochastic process by embedding a task-specific loss into the potential energy, thereby modulating the Riemannian metric. This allows the resulting geodesic to align with desired outcomes or constraints without requiring full retraining.

Table of Contents