mlsanityData to 7 Oct 2026

Aligned Diffusion Schr"odinger Bridges

arXiv 2302.11419 ↗First posted 22 Feb 2023cs.LG q-bio.QMcited by 38

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Abstract (arXiv)

Diffusion Schr"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms for solving DSBs have so far failed to utilize the structure of aligned data, which naturally arises in many biological phenomena. In this paper, we propose a novel algorithmic framework that, for the first time, solves DSBs while respecting the data alignment. Our approach hinges on a combination of two decades-old ideas: The classical Schr"odinger bridge theory and Doob's h-transform. Compared to prior methods, our approach leads to a simpler training procedure with lower variance, which we further augment with principled regularization schemes. This ultimately leads to sizeable improvements across experiments on synthetic and real data, including the tasks of predicting conformational changes in proteins and temporal evolution of cellular differentiation processes.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 26 of its 63 references that are in the map. First posted on arXiv 22 Feb 2023.

Builds on

26 of 63 references.

References · 26

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  6. 2021E(n) Equivariant Graph Neural Networkscited by 951
  7. 2018Computational Optimal Transportcited by 765
  8. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  9. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  11. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  12. 2018Tune: A Research Platform for Distributed Model Selection and Trainingcited by 395
14 more
  1. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  2. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  3. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  4. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  5. 2022e3nn: Euclidean Neural Networkscited by 171
  6. 2020TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamicscited by 155
  7. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  8. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 96
  9. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 91
  10. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
  11. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  12. 2022Supervised Training of Conditional Monge Mapscited by 60
  13. 2021Simulating Diffusion Bridges with Score Matchingcited by 51
  14. 2022Deep Generalized Schr"odinger Bridgecited by 47

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 9; 2024: 12; 2025: 14; 2026: 3.

38 papers.

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  1. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  2. 2023Diffusion Schr"odinger Bridge Matchingcited by 151
  3. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  4. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  5. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  6. 2023On the Generalization Properties of Diffusion Modelscited by 67
  7. 2024How to Build the Virtual Cell with Artificial Intelligence: Priorities and Opportunitiescited by 50
  8. 2024Diffusion Bridge Implicit Modelscited by 47
  9. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 44
  10. 2023Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesiscited by 29
  11. 2024Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Samplingcited by 25
  12. 2024Consistency Diffusion Bridge Modelscited by 22
26 more
  1. 2024Trajectory Flow Matching with Applications to Clinical Time Series Modelingcited by 21
  2. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  3. 2023Generative modeling for time series via Schr"odinger bridgecited by 18
  4. 2024Conditional sampling within generative diffusion modelscited by 18
  5. 2025h-Edit: Effective and Flexible Diffusion-Based Editing via Doob's h-Transformcited by 18
  6. 2023Unbalanced Diffusion Schr"odinger Bridgecited by 9
  7. 2024Bridge-IF: Learning Inverse Protein Folding with Markov Bridgescited by 9
  8. 2025Momentum Multi-Marginal Schr"odinger Bridge Matchingcited by 9
  9. 2025Bidirectional Diffusion Bridge Modelscited by 8
  10. 2025InfoBridge: Mutual Information estimation via Bridge Matchingcited by 7
  11. 2024BM2: Coupled Schr"odinger Bridge Matchingcited by 4
  12. 2024Feedback Schr"odinger Bridge Matchingcited by 4
  13. 2025Branched Schr"odinger Bridge Matchingcited by 4
  14. 2025System-Embedded Diffusion Bridge Modelscited by 4
  15. 2025Fractional Diffusion Bridge Modelscited by 3
  16. 2024Exploring the Design Space of Diffusion Bridge Modelscited by 2
  17. 2024Bridging Geometric States via Geometric Diffusion Bridgecited by 2
  18. 2025Sample and Computationally Efficient Continuous-Time Reinforcement Learning with General Function Approximationcited by 2
  19. 2025Grasp2Grasp: Vision-Based Dexterous Grasp Translation via Schr"odinger Bridgescited by 2
  20. 2023DockGame: Cooperative Games for Multimeric Rigid Protein Dockingcited by 1
  21. 2025Minimum-Excess-Work Guidancecited by 1
  22. 2025A Unified and Fast-Sampling Diffusion Bridge Framework via Stochastic Optimal Controlcited by 1
  23. 2026Generalized Schr"odinger Bridge on Graphscited by 1
  24. 2026Rectified Schr"odinger Bridge Matching for Few-Step Visual Navigationcited by 1
  25. 2025Dynamic Diffusion Schr"odinger Bridge in Astrophysical Observational Inversionscited by 0
  26. 2026Residual Diffusion Implicit Modelscited by 0