Schrödinger Bridges

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A Schrödinger bridge finds the most likely stochastic dynamics, relative to a chosen reference process, that connect specified endpoint distributions; this links entropy-regularized optimal transport, stochastic control, and path-space inference. Methods include Sinkhorn and iterative proportional fitting algorithms, as well as neural bridge matching and score- or flow-based models for learning dynamics from data. Applications range from image and speech generation to medical translation, single-cell trajectory inference, and filtering, with extensions for multiple or unbalanced marginals, non-Euclidean spaces, and control constraints. A central challenge is balancing tractable training and few-step sampling with accurate paths and marginals, especially when the reference process or assumed dynamics poorly fit the data.

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52 papers8 papers in the last four weeks, up 33% on the four weeks before. 0.0% of all new papers.

Generative Modeling via Nonlinear Schrödinger Bridges and Branching Diffusions
Oct 21, 2026Mathias Grau, Pierre Henry-LabordèreGenerative Modeling Schrödinger Bridges
†Qube Research & Technologies, Paris, France.
Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data
Oct 21, 2026Ngoc-Hai Nguyen, Thuan Nguyen, Prakash Ishwar +1Wasserstein Barycenters Schrödinger Bridges
Department of Electrical and Computer Engineering Tufts University · Department of Engineering, Engineering Technology East Tennessee State University · Department of Electrical and Computer Engineering Boston University +1
BridgeTwist: Twisting Schrödinger Bridges for Training-Free Conditional Sampling
Oct 13, 2026Mengyu Li, Qianqian Qu, Jun S. LiuConditional Generative Modeling Posterior Sampling
Department of Statistics and Data Science, Tsinghua University, Beijing, China
SBNO : Schrödinger Bridge Neural Operator for the Forward and Inverse Problems under Missing Information
Oct 9, 2026Jaehyeon Park, Inhyeok Jeong, Noseong ParkPDE Operator Learning PDE Surrogate Modeling
SolverX · KAIST
Tangent Schrödinger Bridge Matching: Learning Stochastic Transport with Mechanistic Sensitivities
Oct 2, 2026Jowaria Khan, Elizabeth Bondi-KellySchrödinger Bridges Optimal Transport
University of Michigan
Cost-augmented Schrödinger bridges on graphs are exactly solvable: a Feynman-Kac tilt replaces learned control
Oct 1, 2026Akshay BalsubramaniStochastic Optimal Control Schrödinger Bridges
Distributionally Robust Schrödinger Bridge
Oct 1, 2026Jinhwan Sul, Panagiotis Theodoropoulos, Vincent Pacelli +2Distribution Shift Robustness Schrödinger Bridges
Department of Aerospace Engineering Georgia Institute of Technology, Atlanta, GA, USA
Tilted Schrödinger Bridge Matching
Sep 28, 2026Sergei Kholkin, Evgeny Burnaev, Alexander KorotinSchrödinger Bridges Unpaired Image-to-Image Translation
Applied AI Institute
The Risk-Sensitive Schrödinger Bridge: Is Not a KL Projection
Sep 23, 2026Hamidreza BehjooKullback-Leibler Divergence Schrödinger Bridges
SE-MSB: End-to-End Unpaired Speech Enhancement using Mamba Schrödinger Bridges
Sep 22, 2026Andreas Bagge, Andreas Nymand, Michael Riis Andersen +1Schrödinger Bridges Speech Enhancement
DTU Compute, Kgs. Lyngby, Denmark · WSA, Lynge, Denmark
Generative models for simulation based filtering: Formulations and Empirical Comparisons
Sep 14, 2026Mohammad Al-Jarrah, Wei Deng, Bamdad Hosseini +1Flow Matching Schrödinger Bridges
Department of Aeronautics & Astronautics, University of Washington, Seattle · Department of Applied Mathematics, University of Washington, Seattle · ML Research, Morgan Stanley
On the Equivalence of Stochastic Control and Path Space Formulations for Schrödinger Bridges over Compact Connected Lie Groups
Sep 12, 2026Hamza Mahmood, Georgiy A. Bondar, Abhishek Halder +1Schrödinger Bridges Stochastic Optimal Control
Dept. of Mechanical & Industrial Engineering at the New Jersey Institute of Technology, Newark, NJ 07102, USA · Department of Applied Mathematics at the University of California at Santa Cruz, CA, 95064, USA · Dept. of Aerospace Engineering at Iowa State University, Ames, IA 50011, USA
Linear Exponential Quadratic Gaussian Covariance Steering
Sep 11, 2026Chiran B. Cherian, Yasemin Isik, Abhishek HalderStochastic Optimal Control Schrödinger Bridges
Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA · Department of Mathematics, Iowa State University, Ames, IA 50011, USA
Schrödinger Bridges on Lie Group Manifolds for Probabilistic Intrinsic Generation
Sep 2, 2026Shizhe Zhang, Mingyang Zhao, Lei MaSchrödinger Bridges Generative Modeling
1National Biomedical Imaging Center, College of Future Technology, Peking University, Beijing, China · 2State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
HybridSB-MoE: Dual-Domain Schrödinger Bridges with Scene-Adaptive Expert Routing for Speech Enhancement
Aug 13, 2026Zhengyi Lu, Aswini Sivakumar, Jie Hu +1Sparse Mixture-of-Experts Schrödinger Bridges
Department of Computer Science and Engineering, Oakland University, Rochester, MI 48309
KANResDiff: Learning Local Residual Diffusion via Kolmogorov-Arnold Network for Ambiguous Medical Image Segmentation
Aug 12, 2026Fanding Li, Chenglin Wang, Xiangyu Li +9Schrödinger Bridges Medical Image Segmentation
Faculty of Computing, Harbin Institute of Technology, Harbin, China · College of Computer and Control Engineering, Northeast Forestry University, Harbin, China · Faculty of Computing, Harbin Institute of Technology, Shenzhen, China +1
PRISM: Principled Reference Identification for Schrodinger Bridge Model
Aug 7, 2026Forouzan Fallah, Yezhou YangDiffusion Models for Image Restoration Schrödinger Bridges
Arizona State University
Twisted Schrödinger Bridge Matching
Jul 18, 2026Maxence Noble, Marie Scheid, Yazid Janati +2Schrödinger Bridges Trajectory Inference
CMAP, Ecole polytechnique · Institute of Foundation Models · MBZUAI +1
Heterogeneity-Adaptive Diffusion Schrodinger Bridge for PET-Guided Whole-Body MRI Translation
Jul 8, 2026Chengbo Wang, Jiacheng Yu, Linjie Bian +7Diffusion Model Guidance Image-to-Image Translation
The University of Sydney, Sydney, Australia · Department of Nuclear Medicine, Fudan University Shanghai Cancer Center, Shanghai, China · State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
Reflected Schrödinger Bridge Matching
Jul 3, 2026Marcus Häggbom, Viktor Nilsson, Pierre Nyquist +1Schrödinger Bridges Image Generation
SEB Group and Department of Mathematics KTH Royal Institute of Technology Stockholm, Sweden · Department of Mathematical Sciences Chalmers University of Technology and University of Gothenburg and Department of Mathematics KTH Royal Institute of Technology
Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge
Jun 29, 2026Titouan VayerFlow Matching Schrödinger Bridges
COMPACT · Inria, Rennes, France.
Statistical Matching via Schrödinger Bridge beyond Conditional Independence
Jun 22, 2026Eunho Koo, Tongseok Lim, Jinwon SohnIncomplete Data Imputation Schrödinger Bridges
Department of Big Data Convergence Chonnam National University · Mitch Daniels School of Business Purdue University · Booth School of Business University of Chicago
Feynman Kac Reweighted Schrödinger Bridge Matching for Surface-Based Tau PET Harmonization
Jun 16, 2026Jianwei Zhang, Xinyu Nie, Jiaxin Yue +1Schrödinger Bridges Neuroimaging
Stevens Neuroimaging and Informatics Institute, University of Southern California, Los Angeles, CA 90089 USA · Ming Hsieh Department of Electrical and Computer Engineering of Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089 USA · Alfred E. Mann Department of Biomedical Engineering of Viterbi School of Engineering, University of Southern California, Los Angeles, CA, USA
Stochastic Thermodynamics and SDE-based Generative Models
Jun 13, 2026Yaowen ZhangSchrödinger Bridges Diffusion Models
Department of Physics, The Hong Kong University of Science and Technology
FreeBridge: Variational Schrödinger Bridges for Cellular Transition Dynamics
Jun 9, 2026Xurui Wang, Qin Ren, Jun Ma +2Schrödinger Bridges Single-Cell Perturbation Modeling
Stony Brook University, Stony Brook, NY, USA · University of Toronto, Toronto, ON, Canada · University Health Network, Toronto, ON, Canada
SB-RF: Schrödinger Bridge Rectified Flow for One-Step Robust Speech Enhancement
Jun 4, 2026Caixia Lu, Xueyang Lv, Penglong Hu +1Rectified Flow Schrödinger Bridges
Nonlocal Mean Field Schrödinger Bridge with Learned Interactions
Jun 2, 2026Daisuke Inoue, Dante Kalise, Mathieu LaurièreNeural Surrogate Modeling Schrödinger Bridges
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom. · Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU-ECNU Institute of Mathematical Sciences, NYU Shanghai, Shanghai 200126, People’s Republic of China.
Kernel-based potential mean-field games with unbiased random Fourier $U$ -statistics
May 28, 2026Yumiharu NakanoMulti-Agent Coordination Mean Field Games
Department of Mathematical and Computing Science, Institute of Science Tokyo
Triangular-Reference Schrödinger Bridges for Time Series Generation
May 26, 2026Gabriele BocchiStochastic Differential Equations Schrödinger Bridges
Arakne S.r.l., Roma.
Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions
May 24, 2026Siddhartha Ganguly, George Rapakoulias, Panagiotis TsiotrasStochastic Optimal Control Schrödinger Bridges
S. Ganguly, G. Rapakoulias, and P. Tsiotras are with Daniel Guggenheim School of Aerospace, Georgia Institute of Technology, ½ Atlanta, USA.

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Generative Modeling via Nonlinear Schrödinger Bridges and Branching Diffusions

Mathias Grau, Pierre Henry-Labordère

†Qube Research & Technologies, Paris, France.

Generative Modeling Schrödinger Bridges

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We propose a new generative modeling framework grounded in forward-backward partial differential equations (PDEs). These equations arise naturally in mean-field game (MFG) theory, and are closely related to nonlinear Schrödinger systems. Our main contribution is to reinterpret this connection within the setting of generative modeling and to develop an efficient numerical methodology for its practical implementation. Specifically, we derive and characterize a nonlinear extension of the classical Schrödinger bridge problem through a coupled system of PDEs, yielding a model we call SBNL (Schrödinger Bridge NonLinear). To compute its solution, we design a simulation algorithm based on branching diffusions and the probabilistic representation of semilinear PDEs. The resulting method is embarrassingly parallel, scalable to high dimensions, and applicable to a broad class of nonlinear interaction functionals. We validate the approach through numerical experiments, including recovery of the classical Schrödinger bridge, nonlinear extensions with convex penalties (Gross-Pitaevskii) as well as potential interaction terms, and high-dimensional generative tasks such as image synthesis on the MNIST and FFHQ human face dataset. Furthermore, the same framework embeds score-based generative modeling, diffusion models, and tractable gaussian Schrödinger bridges.