mlsanityData to 14 Oct 2026

Stochastic interpolants with data-dependent couplings

arXiv 2310.03725 ↗First posted 5 Oct 2023cs.LG stat.MLcited by 100

Not on the map. Why?

Cited by 66 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to textitcouple the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

Key facts. Cited by 100 papers in the map (data through 14 Oct 2026). Builds on 36 of its 47 references that are in the map. First posted on arXiv 5 Oct 2023.

Builds on

36 of 47 references.

References · 36

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  6. 2022Classifier-Free Diffusion Guidancecited by 5,847
  7. 2022Flow Matching for Generative Modelingcited by 5,702
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  9. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  10. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  11. 2022Video Diffusion Modelscited by 2,305
  12. 2015Variational Inference with Normalizing Flowscited by 2,170
24 more
  1. 2016Density estimation using Real NVPcited by 2,042
  2. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  3. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,163
  4. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  5. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  6. 2016Deep Networks with Stochastic Depthcited by 979
  7. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  8. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  9. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  11. 2019Neural Spline Flowscited by 596
  12. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 395
  13. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transportcited by 283
  14. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 278
  15. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 276
  16. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 236
  17. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  18. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 217
  19. 2023Flow Matching in Latent Spacecited by 160
  20. 2023Equivariant flow matchingcited by 135
  21. 2022Soft Diffusion: Score Matching for General Corruptionscited by 102
  22. 2023Minimizing Trajectory Curvature of ODE-based Generative Modelscited by 89
  23. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 60
  24. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusionscited by 29

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 20; 2025: 40; 2026: 37.

100 papers.

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  1. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 737
  2. 2025PaperBench: Evaluating AI's Ability to Replicate AI Researchcited by 321
  3. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 109
  4. 2024DepthFM: Fast Monocular Depth Estimation with Flow Matchingcited by 76
  5. 2025Any-Order Flexible Length Masked Diffusioncited by 51
  6. 2023Boosting Latent Diffusion with Flow Matchingcited by 44
  7. 2024Improved motif-scaffolding with SE(3) flow matchingcited by 43
  8. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 43
  9. 2026Meta Flow Maps enable scalable reward alignmentcited by 37
  10. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 36
  11. 2025Much Ado About Noising: Dispelling the Myths of Generative Robotic Controlcited by 36
  12. 2024Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restorationcited by 34
38 more
  1. 2024Flow matching achieves almost minimax optimal convergencecited by 29
  2. 2025Open Materials Generation with Stochastic Interpolantscited by 28
  3. 2024Flowing from Words to Pixels: A Noise-Free Framework for Cross-Modality Evolutioncited by 26
  4. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 25
  5. 2025Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaoscited by 21
  6. 2024FrameBridge: Improving Image-to-Video Generation with Bridge Modelscited by 19
  7. 2023Gaussian Interpolation Flowscited by 17
  8. 2024EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolantscited by 16
  9. 2025VCT: Training Consistency Models with Variational Noise Couplingcited by 15
  10. 2025Flow Matching for Efficient and Scalable Data Assimilationcited by 12
  11. 2025All that structure matches does not glittercited by 12
  12. 2024Extended Flow Matching: a Method of Conditional Generation with Generalized Continuity Equationcited by 11
  13. 2024Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier mapscited by 9
  14. 2025One-Step Offline Distillation of Diffusion-based Models via Koopman Modelingcited by 9
  15. 2025STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulationcited by 8
  16. 2025Learning Straight Flows: Variational Flow Matching for Efficient Generationcited by 8
  17. 2025LADB: Latent Aligned Diffusion Bridges for Semi-Supervised Domain Translationcited by 7
  18. 2025Stochastic Interpolants via Conditional Dependent Couplingcited by 7
  19. 2025Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolantscited by 6
  20. 2025Boltzmann generators for amorphous particle systemscited by 6
  21. 2026Flow-DPPO: Divergence Proximal Policy Optimization for Flow Matching Modelscited by 6
  22. 2024Stochastic Flow Matching for Resolving Small-Scale Physicscited by 5
  23. 2025Good Things Come in Pairs: Paired Autoencoders for Inverse Problemscited by 5
  24. 2026Scalable Maximum Entropy Reinforcement Learning for Diffusion Policies via Adjoint Matchingcited by 5
  25. 2025Finite-Time Analysis of Discrete-Time Stochastic Interpolantscited by 4
  26. 2025In-Context Parametric Inference: Point or Distribution Estimators?cited by 4
  27. 2025Topological Schr"odinger Bridge Matchingcited by 4
  28. 2026Prior-Informed Flow Matching for Graph Reconstructioncited by 4
  29. 2026Cascaded Flow Matching for Heterogeneous Tabular Data with Mixed-Type Featurescited by 4
  30. 2024Exploring the Design Space of Diffusion Bridge Modelscited by 3
  31. 2024Diverse capability and scaling of diffusion and auto-regressive models when learning abstract rulescited by 3
  32. 2025On the Contractivity of Stochastic Interpolation Flowcited by 3
  33. 2025HazeMatching: Dehazing Light Microscopy Images with Guided Conditional Flow Matchingcited by 3
  34. 2025CoVAE: Consistency Training of Variational Autoencoderscited by 3
  35. 2025Multitask Learning with Stochastic Interpolantscited by 3
  36. 2025Distilling LLM Prior to Flow Model for Generalizable Agent's Imagination in Object Goal Navigationcited by 3
  37. 2025Incomplete Data, Complete Dynamics: A Diffusion Approachcited by 3
  38. 2025Split-Flows: Measure Transport and Information Loss Across Molecular Resolutionscited by 3

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