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[2602.08535] Causal Schrödinger Bridges: Constrained Optimal Transport on Structural Manifolds
Summary
The paper introduces the Causal Schrödinger Bridge (CSB) framework, enhancing generative modeling by addressing challenges in causal inference through robust transport methods on structural manifolds.
Why It Matters
This research is significant as it presents a novel approach to counterfactual inference, overcoming limitations of traditional deterministic methods. By leveraging diffusion processes, CSB enhances the robustness of generative models in high-dimensional spaces, which is crucial for applications in machine learning and statistics where causal relationships are complex.
Key Takeaways
- CSB reformulates counterfactual inference using Entropic Optimal Transport.
- It effectively addresses issues of numerical instability in high-dimensional data.
- CSB demonstrates significant performance improvements over traditional methods.
- The Structural Decomposition Theorem proves local transitions can factor into global solutions.
- Empirical results show CSB's efficiency in computation, completing tasks much faster than existing methods.
Computer Science > Machine Learning arXiv:2602.08535 (cs) [Submitted on 9 Feb 2026 (v1), last revised 14 Feb 2026 (this version, v3)] Title:Causal Schrödinger Bridges: Constrained Optimal Transport on Structural Manifolds Authors:Rui Wu, Li YongJun View a PDF of the paper titled Causal Schr\"odinger Bridges: Constrained Optimal Transport on Structural Manifolds, by Rui Wu and Li YongJun View PDF HTML (experimental) Abstract:Generative modeling typically seeks the path of least action via deterministic flows (ODE). While effective for in-distribution tasks, we argue that these deterministic paths become brittle under causal interventions, which often require transporting probability mass across low-density regions (``off-manifold'') where the vector field is ill-defined. This leads to numerical instability and spurious correlations. In this work, we introduce the Causal Schrödinger Bridge (CSB), a framework that reformulates counterfactual inference as Entropic Optimal Transport. Unlike deterministic approaches that require strict invertibility or rely on low-rank approximations, CSB leverages diffusion processes (SDEs) to robustly ``tunnel'' through support mismatches while strictly enforcing structural admissibility constraints. We prove the Structural Decomposition Theorem, showing that the global high-dimensional bridge factorizes exactly into local, robust transitions. Crucially, we demonstrate that CSB breaks the Curse of Dimensionality in regimes of high intrinsic di...
