mlsanityData to 7 Oct 2026

Improved sampling via learned diffusions

arXiv 2307.01198 ↗First posted 3 Jul 2023cs.LG math.OC math.PRcited by 103

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Cited by 47 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on previous work, we identify these approaches as special cases of a generalized Schr"odinger bridge problem, seeking a stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.

Key facts. Cited by 103 papers in the map (data through 7 Oct 2026). Builds on 33 of its 83 references that are in the map. First posted on arXiv 3 Jul 2023.

Builds on

33 of 83 references.

References · 33

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  4. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  6. 2021Variational Diffusion Modelscited by 1,145
  7. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  8. 2021Score-based Generative Modeling in Latent Spacecited by 634
  9. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  10. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  11. 2022Trajectory balance: Improved credit assignment in GFlowNetscited by 244
  12. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
21 more
  1. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 182
  2. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  3. 2020Stochastic Normalizing Flowscited by 156
  4. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  5. 2023Denoising Diffusion Samplerscited by 144
  6. 2022Flow Annealed Importance Sampling Bootstrapcited by 124
  7. 2022GFlowNets and variational inferencecited by 103
  8. 2017Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inferencecited by 97
  9. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
  10. 2021Annealed Flow Transport Monte Carlocited by 90
  11. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 80
  12. 2020VarGrad: A Low-Variance Gradient Estimator for Variational Inferencecited by 73
  13. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  14. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  15. 2019Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Driftcited by 50
  16. 2022Deep Generalized Schr"odinger Bridgecited by 47
  17. 2021Resampling Base Distributions of Normalizing Flowscited by 42
  18. 2019Schr"odinger Bridge Samplerscited by 14
  19. 2022Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learningcited by 13
  20. 2022Neural Lagrangian Schr"odinger Bridge: Diffusion Modeling for Population Dynamicscited by 7
  21. 2022On local entropy, stochastic control and deep neural networkscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 31; 2025: 43; 2026: 27.

103 papers.

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  1. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  2. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  3. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  4. 2024Amortizing intractable inference in diffusion models for vision, language, and controlcited by 70
  5. 2024Particle Denoising Diffusion Samplercited by 63
  6. 2024A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimizationcited by 58
  7. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  8. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 55
  9. 2025DIME:Diffusion-Based Maximum Entropy Reinforcement Learningcited by 52
  10. 2024Improved off-policy training of diffusion samplerscited by 47
  11. 2024Sequential Controlled Langevin Diffusionscited by 47
  12. 2024Target Score Matchingcited by 46
38 more
  1. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 44
  2. 2023Stochastic Optimal Control Matchingcited by 39
  3. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 36
  4. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 30
  5. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 28
  6. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 28
  7. 2024Stochastic Localization via Iterative Posterior Samplingcited by 27
  8. 2025Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densitiescited by 26
  9. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 25
  10. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  11. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
  12. 2025DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Modelscited by 21
  13. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  14. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  15. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 19
  16. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 17
  17. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spacescited by 16
  18. 2025Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative modelscited by 16
  19. 2025Proximal Diffusion Neural Samplercited by 16
  20. 2024BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matchingcited by 14
  21. 2025Temperature-Annealed Boltzmann Generatorscited by 14
  22. 2025Accelerated Parallel Tempering via Neural Transportscited by 13
  23. 2025Discrete Neural Flow Samplers with Locally Equivariant Transformercited by 13
  24. 2025Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Designcited by 12
  25. 2024Harmonic Path Integral Diffusioncited by 11
  26. 2025Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyondcited by 11
  27. 2025Amortized Sampling with Transferable Normalizing Flowscited by 11
  28. 2024Transition Path Sampling with Improved Off-Policy Training of Diffusion Path Samplerscited by 10
  29. 2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flowscited by 9
  30. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  31. 2025Improving the evaluation of samplers on multi-modal targetscited by 9
  32. 2024PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimationcited by 8
  33. 2024Soft-constrained Schrodinger Bridge: a Stochastic Control Approachcited by 8
  34. 2025Non-equilibrium Annealed Adjoint Samplercited by 8
  35. 2024Energy based diffusion generator for efficient sampling of Boltzmann distributionscited by 7
  36. 2024Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion modelscited by 7
  37. 2024Importance Corrected Neural JKO Samplingcited by 7
  38. 2025Rethinking Losses for Diffusion Bridge Samplerscited by 7

50 most cited of 103 All 103 (JSON)