mlsanityData to 14 Oct 2026

Bayesian Learning via Neural Schr"odinger-F"ollmer Flows

arXiv 2111.10510 ↗First posted 20 Nov 2021stat.ML cs.LGcited by 56

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Cited by 24 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schr"odinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular steady-state methods such as stochastic gradient Langevin dynamics (SGLD). Furthermore, we discuss and adapt the existing theoretical guarantees of this framework and establish connections to already existing VI routines in SDE-based models.

Key facts. Cited by 56 papers in the map (data through 14 Oct 2026). Builds on 36 of its 95 references that are in the map. First posted on arXiv 20 Nov 2021.

Builds on

36 of 95 references.

References · 36

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
  4. 2017On Calibration of Modern Neural Networkscited by 4,960
  5. 2013Auto-Encoding Variational Bayescited by 4,053
  6. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  7. 2021Variational Diffusion Modelscited by 1,153
  8. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 927
  9. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  10. 2013Gaussian Processes for Big Datacited by 383
  11. 2021What Are Bayesian Neural Network Posteriors Really Like?cited by 308
  12. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 292
24 more
  1. 2017Advances in Variational Inferencecited by 236
  2. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 219
  3. 2018Bayesian Model-Agnostic Meta-Learningcited by 194
  4. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 176
  5. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 141
  6. 2016Towards a Neural Statisticiancited by 121
  7. 2018Meta-Learning Probabilistic Inference For Predictioncited by 110
  8. 2021Deep Generative Learning via Schr"odinger Bridgecited by 104
  9. 2021The Bayesian Learning Rulecited by 99
  10. 2017Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inferencecited by 98
  11. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
  12. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 82
  13. 2021Diffusion Normalizing Flowcited by 77
  14. 2020VarGrad: A Low-Variance Gradient Estimator for Variational Inferencecited by 75
  15. 2018Mirrored Langevin Dynamicscited by 61
  16. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  17. 2019Bayesian Variational Autoencoders for Unsupervised Out-of-Distribution Detectioncited by 35
  18. 2018The data-driven Schroedinger bridgecited by 26
  19. 2014Structured Stochastic Variational Inferencecited by 22
  20. 2019Schr"odinger Bridge Samplerscited by 14
  21. 2014Path Integral Control and State Dependent Feedbackcited by 12
  22. 2019From Reinforcement Learning to Optimal Control: A unified framework for sequential decisionscited by 12
  23. 2021On the Effects of Quantisation on Model Uncertainty in Bayesian Neural Networkscited by 8
  24. 2021Deterministic particle flows for constraining SDEscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 9; 2024: 19; 2025: 15; 2026: 12.

56 papers.

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  1. 2023Denoising Diffusion Samplerscited by 149
  2. 2022An optimal control perspective on diffusion-based generative modelingcited by 147
  3. 2023Improved sampling via learned diffusionscited by 104
  4. 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 66
  5. 2025DIME:Diffusion-Based Maximum Entropy Reinforcement Learningcited by 58
  6. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  7. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 56
  8. 2024Target Score Matchingcited by 50
  9. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 46
  10. 2023Reverse Diffusion Monte Carlocited by 41
  11. 2026Meta Flow Maps enable scalable reward alignmentcited by 37
  12. 2023Blackout Diffusion: Generative Diffusion Models in Discrete-State Spacescited by 30
38 more
  1. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 29
  2. 2024Stochastic Localization via Iterative Posterior Samplingcited by 28
  3. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 28
  4. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 23
  5. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  6. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  7. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 21
  8. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  9. 2025Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative modelscited by 17
  10. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spacescited by 16
  11. 2024BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matchingcited by 15
  12. 2024Schr"odinger Bridge with Quadratic State Cost is Exactly Solvablecited by 12
  13. 2024Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Seriescited by 10
  14. 2026Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matchingcited by 10
  15. 2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flowscited by 9
  16. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  17. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  18. 2025InfoBridge: Mutual Information estimation via Bridge Matchingcited by 7
  19. 2026Reward Score Matching: Unifying Reward-based Fine-tuning for Flow and Diffusion Modelscited by 7
  20. 2024Partially Stochastic Infinitely Deep Bayesian Neural Networkscited by 6
  21. 2025Iterative Importance Fine-tuning of Diffusion Modelscited by 6
  22. 2025Adaptive Destruction Processes for Diffusion Samplerscited by 6
  23. 2025Reinforced sequential Monte Carlo for amortised samplingcited by 6
  24. 2026Scalable Maximum Entropy Reinforcement Learning for Diffusion Policies via Adjoint Matchingcited by 5
  25. 2024Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusioncited by 4
  26. 2025End-To-End Learning of Gaussian Mixture Priors for Diffusion Samplercited by 4
  27. 2025Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spacescited by 4
  28. 2026Ito maps for any-step SDEscited by 4
  29. 2024Weyl Calculus and Exactly Solvable Schr"odinger Bridges with Quadratic State Costcited by 3
  30. 2024Schr"odinger bridge based deep conditional generative learningcited by 3
  31. 2026Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spacescited by 2
  32. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 2
  33. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Modelscited by 1
  34. 2024Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Modelscited by 1
  35. 2025Causal Posterior Estimationcited by 1
  36. 2025Path Integral Optimiser: Global Optimisation via Neural Schr"odinger-F"ollmer Diffusioncited by 1
  37. 2026Pathwise Learning of Stochastic Dynamical Systems with Partial Observationscited by 1
  38. 2026Discrete Bridges for Mutual Information Estimationcited by 1

50 most cited of 56 All 56 (JSON)