mlsanityData to 7 Oct 2026

Riemannian Diffusion Schr"odinger Bridge

arXiv 2207.03024 ↗First posted 7 Jul 2022stat.ML cs.LGcited by 10

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize data living on Riemannian manifolds. Existing methods to accelerate sampling of diffusion models are typically not applicable in the Riemannian setting and Riemannian score-based methods have not yet been adapted to the important task of interpolation of datasets. To overcome these issues, we introduce Riemannian Diffusion Schr"odinger Bridge. Our proposed method generalizes Diffusion Schr"odinger Bridge introduced in citedebortoli2021neurips to the non-Euclidean setting and extends Riemannian score-based models beyond the first time reversal. We validate our proposed method on synthetic data and real Earth and climate data.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 12 of its 21 references that are in the map. First posted on arXiv 7 Jul 2022.

Builds on

12 of 21 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022Riemannian Score-Based Generative Modelling6 Feb
  2. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  3. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  5. 2020Denoising Diffusion Implicit Models6 Oct

Other references · 7

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  2. 2018Computational Optimal Transportcited by 765
  3. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  4. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  5. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  6. 2015Entropic and displacement interpolation: a computational approach using the Hilbert metriccited by 34
  7. 2022Stability of Schr"odinger Potentials and Convergence of Sinkhorn's Algorithmcited by 13

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 3; 2026: 1.

10 papers.

  1. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  2. 2023Unpaired Image-to-Image Translation via Neural Schr"odinger Bridgecited by 96
  3. 2024Schr"odinger Bridge Flow for Unpaired Data Translationcited by 47
  4. 2023Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processescited by 21
  5. 2024Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifoldscited by 13
  6. 2025Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Modelscited by 7
  7. 2025The Spacetime of Diffusion Models: An Information Geometry Perspectivecited by 6
  8. 2025Neural Guided Diffusion Bridgescited by 4
  9. 2024Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphscited by 1
  10. 2026Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networkscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Reflected Schr"odinger Bridge for Constrained Generative Modeling
  2. 2025A Closed-Form Framework for Schr"odinger Bridges Between Arbitrary Densities
  3. 2026Foundations of Schr"odinger Bridges for Generative Modeling
  4. 2026Sampling from multi-modal distributions on Riemannian manifolds with training-free stochastic interpolants
  5. 2022Riemannian Diffusion Models
  6. 2024Simplified Diffusion Schr"odinger Bridge
  7. 2024Variational Schr"odinger Diffusion Models
  8. 2025Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity