{"ID":2825541,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.21261","arxiv_id":"2512.21261","title":"Marginal flows of non-entropic weak Schrödinger bridges","abstract":"This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal constraints are imposed in a weak sense. We establish well-posedness and a convex dual formulation, together with a dual existence result and explicit structural characterizations of primal and dual optimizers. Specifically, the optimal path measure admits an explicit density relative to a reference diffusion, generalizing the classical Schr{ö}dinger system. In the case of zero transport cost, which corresponds to a non-entropic dynamic Schr{ö}dinger problem, we further characterize the flow of time marginals of the optimal bridge, recovering known results in the entropic setting and providing new descriptions for non-entropic divergences, including the $χ^2$-divergence","short_abstract":"This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal constraints are imposed in a weak sense. We establish well-posedness and a conv...","url_abs":"https://arxiv.org/abs/2512.21261","url_pdf":"https://arxiv.org/pdf/2512.21261v2","authors":"[\"Camilo Hernández\",\"Ludovic Tangpi\"]","published":"2025-12-24T16:10:01Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}