mlsanityData to 7 Oct 2026

Score-based Generative Neural Networks for Large-Scale Optimal Transport

arXiv 2110.03237 ↗First posted 7 Oct 2021cs.LGcited by 59

Not on the map. Why?

Cited by 25 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the target support, but learning or even approximating such a map is computationally challenging for large and high-dimensional datasets due to the high cost of linear programming routines and an intrinsic curse of dimensionality. We study instead the Sinkhorn problem, a regularized form of optimal transport whose solutions are couplings between the source and the target distribution. We introduce a novel framework for learning the Sinkhorn coupling between two distributions in the form of a score-based generative model. Conditioned on source data, our procedure iterates Langevin Dynamics to sample target data according to the regularized optimal coupling. Key to this approach is a neural network parametrization of the Sinkhorn problem, and we prove convergence of gradient descent with respect to network parameters in this formulation. We demonstrate its empirical success on a variety of large scale optimal transport tasks.

Key facts. Cited by 59 papers in the map (data through 7 Oct 2026). Builds on 17 of its 26 references that are in the map. First posted on arXiv 7 Oct 2021.

Builds on

17 of 26 references.

References · 17

  1. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  2. 2021Convex optimizationcited by 2,479
  3. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  4. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  5. 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 572
  6. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  7. 2020On the linearity of large non-linear models: when and why the tangent kernel is constantcited by 129
  8. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 120
  9. 2018An introduction to domain adaptation and transfer learningcited by 112
  10. 2019Wasserstein-2 Generative Networkscited by 96
  11. 2020Adversarial score matching and improved sampling for image generationcited by 95
  12. 2017Smooth and Sparse Optimal Transportcited by 83
5 more
  1. 2019Width Provably Matters in Optimization for Deep Linear Neural Networkscited by 52
  2. 2020Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networkscited by 49
  3. 2020Continuous Regularized Wasserstein Barycenterscited by 32
  4. 2019Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithmcited by 27
  5. 2019Adversarial Computation of Optimal Transport Mapscited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 18; 2024: 15; 2025: 14; 2026: 5.

59 papers.

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  1. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  2. 2022Diffusion Models in Vision: A Surveycited by 1,008
  3. 2022Neural Optimal Transportcited by 123
  4. 2023TrojDiff: Trojan Attacks on Diffusion Models with Diverse Targetscited by 88
  5. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  6. 2024Guidance with Spherical Gaussian Constraint for Conditional Diffusioncited by 69
  7. 2023Dif-Fusion: Towards High Color Fidelity in Infrared and Visible Image Fusion with Diffusion Modelscited by 56
  8. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 49
  9. 2024Light and Optimal Schr"odinger Bridge Matchingcited by 45
  10. 2024Curriculum Direct Preference Optimization for Diffusion and Consistency Modelscited by 36
  11. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  12. 2024Attacks and Defenses for Generative Diffusion Models: A Comprehensive Surveycited by 32
38 more
  1. 2022Kernel Neural Optimal Transportcited by 31
  2. 2023A Denoising Diffusion Model for Fluid Field Predictioncited by 31
  3. 2023SpectralDiff: A Generative Framework for Hyperspectral Image Classification with Diffusion Modelscited by 28
  4. 2023Diffusion Model for Camouflaged Object Detectioncited by 27
  5. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  6. 2023Conditional Optimal Transport on Function Spacescited by 26
  7. 2024Multi-marginal Schr"odinger Bridges with Iterative Reference Refinementcited by 26
  8. 2023Energy-guided Entropic Neural Optimal Transportcited by 25
  9. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  10. 2023Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmarkcited by 19
  11. 2023Light Schr"odinger Bridgecited by 18
  12. 2024Human-Object Interaction Detection Collaborated with Large Relation-driven Diffusion Modelscited by 15
  13. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  14. 2023Extremal Domain Translation with Neural Optimal Transportcited by 12
  15. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  16. 2024NoiseDiffusion: Correcting Noise for Image Interpolation with Diffusion Models beyond Spherical Linear Interpolationcited by 12
  17. 2024Adversarial Schr"odinger Bridge Matchingcited by 12
  18. 2023Optimal Transport-Guided Conditional Score-Based Diffusion Modelscited by 11
  19. 2024Graph Edit Distance with General Costs Using Neural Set Divergencecited by 10
  20. 2024Frequency-Guided Posterior Sampling for Diffusion-Based Image Restorationcited by 10
  21. 2024Accelerating Sinkhorn Algorithm with Sparse Newton Iterationscited by 9
  22. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  23. 2023Light Unbalanced Optimal Transportcited by 8
  24. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  25. 2023Reverse Stable Diffusion: What prompt was used to generate this image?cited by 7
  26. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  27. 2025Score-Based Diffusion Policy Compatible with Reinforcement Learning via Optimal Transportcited by 6
  28. 2025Improved Stochastic Optimization of LogSumExpcited by 4
  29. 2025UniCon: Unidirectional Information Flow for Effective Control of Large-Scale Diffusion Modelscited by 3
  30. 2025CD-TVD: Contrastive Diffusion for 3D Super-Resolution with Scarce High-Resolution Time-Varying Datacited by 3
  31. 2023OT-Net: A Reusable Neural Optimal Transport Solvercited by 2
  32. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  33. 2025Neural Estimation for Scaling Entropic Multimarginal Optimal Transportcited by 2
  34. 2025A Physics-preserved Transfer Learning Method for Differential Equationscited by 1
  35. 2025DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guaranteecited by 1
  36. 2025Incorporating Pre-trained Diffusion Models in Solving the Schr"odinger Bridge Problemcited by 1
  37. 2025Neural Hamilton--Jacobi Characteristic Flows for Optimal Transportcited by 1
  38. 2026Variational Entropic Optimal Transportcited by 1

50 most cited of 59 All 59 (JSON)

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  4. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance
  5. 2025On the Relation between Rectified Flows and Optimal Transport
  6. 2026Expected Batch Optimal Transport Plans and Consequences for Flow Matching
  7. 2022A Variational Perspective on Generative Flow Networks
  8. 2025No-Regret Generative Modeling via Parabolic Monge-Amp`ere PDE