Wasserstein Distance

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8 papers in the last four weeks, up 33% on the four weeks before. 0.1% of all new papers.

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RW-Flow: One-Step Generation on Compact Manifolds via Wasserstein Gradient Flows
Sep 30, 2026Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn +1Wasserstein Gradient Flows One-Step Generative Modeling
KAIST
Towards Universal Wasserstein Barycenters through Flow Matching
Sep 29, 2026Eduardo Fernandes MontesumaWasserstein Barycenters Optimal Transport
Sigma Nova Paris, France
A Spectral Theory of Distortion in LLM Graph Reconstruction: Sharp Bounds and Empirical Characterization
Sep 29, 2026Jianru ShenLLMs for Graph Learning Wasserstein Distance
Columbia University New York, NY, USA
Geometry-Adaptive Mechanisms for Private Synthetic Data
Sep 27, 2026Raoof Zare Moayedi, Amir R. Asadi, Mohammad Hossein Yassaee +1Intrinsic Dimensionality Synthetic Data Generation
Sharif University of Technology · University of Birmingham · The Alan Turing Institute
Averaged Mirror Descent and Dual Gradient Methods: Convergent Algorithms for Entropic Gromov-Wasserstein Problems
Sep 25, 2026Joanna Marks, Gabriel Rioux, Riccardo PasseggeriGradient Descent Mirror Descent
⋆Denotes equal contribution to this work.
Toscani-Fourier Distance on Probability Measures: Wasserstein Control, Topological Equivalence on Model Classes, and Duality
Sep 19, 2026Mehrdad MohammadiIntegral Probability Metrics Wasserstein Distance
Department of Statistics University of Illinois Urbana-Champaign Champaign, IL 61820, USA
Graph Matching Relaxations and Amortization for Supervised Graph Prediction
Sep 14, 2026Federico Méndez, Paul Krzakala, Gabriel Melo +3Learning to Optimize Graph Matching
LTCI, Télécom Paris · Institut Polytechnique de Paris · CMAP, École Polytechnique
Gaussian Approximation for Multivariate Martingale Sums from Uniformly Ergodic Markov Chains
Sep 8, 2026Yixuan Zhang, Qiaomin XieWasserstein Distance
Department of Industrial & Systems Engineering, University of Wisconsin–Madison
Sierpiński--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation
Sep 1, 2026Sebastien Tchitchek, Julien TiernyPersistent Homology Wasserstein Distance
CNRS and Sorbonne Université
Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality
Aug 27, 2026Clément Soubrier, Geoffrey Woollard, Andrew Warren +1Optimal Transport Wasserstein Distance
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada · Department of Computer Science, University of British Columbia, Vancouver, BC V6T 1Z4, Canada · Mathematical Institute, Utrecht University, Utrecht, 3584 CD, The Netherlands
Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications
Aug 27, 2026James Hyun, François G. MeyerOptimal Transport Wasserstein Distance
University of Colorado, Boulder, CO 80309, United States
CoSWA-YOLOv12: Scale-Invariant Tiny Object Detection and Segmentation of Malaria Parasites
Aug 25, 2026Ahmed Tahiru Issah, Carine MukamakuzaSmall Object Detection Object Detection
Carnegie Mellon University, Kigali, Rwanda
A Local Sinkhorn Framework for Conditional Distribution Reconstruction of Multidimensional Random Fields
Aug 12, 2026Mingtao Xia, Qijing ShenUncertainty Quantification Conditional Distribution Estimation
School of Mathematics, University of Birmingham, Watson Building, Edgbaston, Birmingham, B15 2TT, United Kingdom · Department of Mathematics, University of Houston, 3551 Cullen Blvd, Houston, 77204, Texas, United States · Nuffield Department of Medicine, University of Oxford, United Kingdom, Old Road Campus, Oxford, OX3 7BN, United Kingdom
Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms
Aug 11, 2026Florian Beier, Stephan EcksteinClustering Vector Quantization
Department of Mathematics, University of Tübingen, Germany
Sub-Quadratic Bisimulation Metrics via Approximate Nearest Neighbors: Coverage-Augmented Guarantees and Computable Two-Sided Certificates
Aug 7, 2026Ibne Farabi Shihab, Joyanta Jyoti MondalMarkov Decision Processes Approximation Algorithms
Department of Computer Science, Iowa State University, USA · Department of Computer and Information Sciences, University of Delaware, USA
Wasserstein mixing time of the unadjusted Langevin algorithm
Aug 3, 2026Francesco Pedrotti, Peter A. WhalleyMarkov Chain Monte Carlo Langevin Dynamics
ETH Zürich
Diffusion enabled Optimal Transport distances for graph matching
Jul 7, 2026Iman Seyedi, Francesco ArchettiGraph Matching Wasserstein Distance
Department of Computer Science Systems and Communication, University of Milano-Bi- cocca, 20126 Milan, Italy
Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functions
Jun 29, 2026Christophe Vauthier, Quentin Mérigot, Anna KorbaSliced Wasserstein Distance Optimal Transport
Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay Gif-sur-Yvette, France · Centre de recherche en économie et statistique, ENSAE Palaiseau, France
Adjusted Wasserstein distances for bridging empirical and true distributions with applications to MDS
Jun 29, 2026Flor Martinez-Sermeno, Arturo Jaramillo, Johan Van HorebeekDimensionality Reduction Heavy-Tailed Distributions
A Transport-Based Geometry of Belief-Cost
Jun 19, 2026Laurent CaraffaInformation Geometry Optimal Transport
Université Gustave Eiffel, LASTIG, IGN-ENSG
Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees
Jun 15, 2026Marta Gentiloni Silveri, Giovanni Conforti, Alain DurmusDiffusion Sampling Flow-Based Generative Modeling
Ecole Polytechnique, Massy Palaiseau, France · Università degli Studi di Padova, Padua, Italy
$k$ -Nearest Neighbors in Gromov--Wasserstein Space
Jun 9, 2026Kaitlyn Hohmeier, Nicolas Fraiman, Caroline MoosmuellerGraph Classification k-Nearest Neighbors
University of North Carolina at Chapel Hill, Department of Mathematics · University of North Carolina at Chapel Hill, Department of Statistics and Operations Research
A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space
Jun 5, 2026Munsik KimMinimax Estimation Spatiotemporal Forecasting
A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decoding
Jun 4, 2026Chen Hu, Rui Wang, Jiale Zhou +4EEG Decoding Domain Generalization
Westlake University Hangzhou, China · School of Artificial Intelligence and Computer Science Jiangnan University Wuxi, China · Zhejiang University Hangzhou, China +1
Cone-Compatible Monge Geometry for High-Dimensional Ordered Optimal Transport
Jun 3, 2026Lei Luo, Hongliang Zhang, Jian YangOptimal Transport Wasserstein Distance
PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China
Wasserstein Contraction of Coordinate Ascent Variational Inference
May 28, 2026Rocco Caprio, Adrien Corenflos, Sam PowerBayesian Inference Variational Inference
University of Warwick and Bocconi University. · University of Warwick. · University of Bristol.
Optimizing Computational-Statistical Runtime for Wasserstein Distance Estimation
May 19, 2026Peter Matthew Jacobs, Jeff M. PhillipsRandomized Sketching Approximation Algorithms
Department of Statistics University of Wisconsin-Madison Madison, WI 53706 · Kahlert School of Computing University of Utah Salt Lake City, UT 84101
Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons
May 18, 2026Pierre Houédry, Iskander Legheraba, Léo Buecher +1Kernel Methods Optimal Transport
INRIA Rennes · LPHI, UMR 5294, CNRS, INSERM · IRISA, UMR 6074, CNRS
Wasserstein Equilibrium Decoding for Reliable Medical Visual Question Answering
May 18, 2026Luca Hagen, Johanna P. Müller, Weitong Zhang +2Healthcare Efficient VLM Inference
Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany · Imperial College London, London, United Kingdom · University College London, London, United Kingdom
Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process
May 18, 2026Yuta KoikeDiffusion Sampling Diffusion Models
*Graduate School of Mathematical Sciences, University of Tokyo · †CREST, Japan Science and Technology Agency

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RW-Flow: One-Step Generation on Compact Manifolds via Wasserstein Gradient Flows

Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn, Minhyuk Sung

KAIST

Wasserstein Gradient Flows One-Step Generative Modeling Generative Modeling Flow-Based Generative Modeling Wasserstein Distance

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Manifold-valued data, and consequently the distributions they induce, are prevalent across many domains, ranging from the locations of geospatial events, such as earthquakes, to biomolecular torsion angles that encode information about three-dimensional structure. While diffusion and flow-based generative models have been successfully extended to compact manifolds, sampling typically requires tens or hundreds of sequential network evaluations. We introduce RW-Flow, a theoretically grounded framework for learning one-step generative models on compact manifolds via Wasserstein gradient flows. The main challenge is identifiability: driving the velocity field to zero should guarantee that the model distribution matches the target distribution. We establish a necessary and sufficient condition for identifiability on compact, connected Riemannian manifolds. We specifically show that, for a symmetric, Lipschitz-continuous cost function, the velocity field induced by the Sinkhorn divergence is identifiable if and only if the associated Gibbs kernel is nondegenerate. This characterization provides a general principle for designing identifiable costs on compact manifolds. It also reveals that the squared geodesic distance, the natural manifold analogue of the squared Euclidean distance, does not always guarantee identifiability. Across benchmarks involving geospatial events, protein side chain torsion angles, RNA backbone torsion angles, and general manifolds discretized as triangular meshes, RW-Flow outperforms existing one-step methods in nearly all settings under fair comparison conditions.