mlsanityData to 7 Oct 2026

Denoising Diffusion Samplers

arXiv 2302.13834 ↗First posted 27 Feb 2023cs.LG stat.MLcited by 144

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution. Samples from the generative model are then obtained by simulating an approximation of the time-reversal of this diffusion initialized by Gaussian samples. Practically, the intractable score terms appearing in the time-reversed process are approximated using score matching techniques. We explore here a similar idea to sample approximately from unnormalized probability density functions and estimate their normalizing constants. We consider a process where the target density diffuses towards a Gaussian. Denoising Diffusion Samplers (DDS) are obtained by approximating the corresponding time-reversal. While score matching is not applicable in this context, we can leverage many of the ideas introduced in generative modeling for Monte Carlo sampling. Existing theoretical results from denoising diffusion models also provide theoretical guarantees for DDS. We discuss the connections between DDS, optimal control and Schr"odinger bridges and finally demonstrate DDS experimentally on a variety of challenging sampling tasks.

Key facts. Cited by 144 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 36 of its 66 references that are in the map. First posted on arXiv 27 Feb 2023.

Builds on

36 of 66 references.

Closest ancestors · 12

Same direction, newest first

  1. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  2. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  3. 2022Blurring Diffusion Models12 Sep
  4. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  5. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  6. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  7. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  8. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  9. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Implicit Models6 Oct
  12. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  5. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  6. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  7. 2019Multi-Object Representation Learning with Iterative Variational Inferencecited by 359
  8. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  9. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  10. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  11. 2020Stochastic Normalizing Flowscited by 156
  12. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
12 more
  1. 2021Annealed Flow Transport Monte Carlocited by 90
  2. 2019PIPPS: Flexible Model-Based Policy Search Robust to the Curse of Chaoscited by 56
  3. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  4. 2021Unbiased Gradient Estimation in Unrolled Computation Graphs with Persistent Evolution Strategiescited by 52
  5. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  6. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
  7. 2021Monte Carlo Variational Auto-Encoderscited by 36
  8. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  9. 2020Using a thousand optimization tasks to learn hyperparameter search strategiescited by 29
  10. 2022Langevin Diffusion Variational Inferencecited by 26
  11. 2015Adaptive importance sampling for control and inferencecited by 23
  12. 2020Adaptive Smoothing Path Integral Controlcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 11; 2024: 40; 2025: 58; 2026: 35.

144 papers.

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  1. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  2. 2023Improved sampling via learned diffusionscited by 103
  3. 2024DGE: Direct Gaussian 3D Editing by Consistent Multi-view Editingcited by 92
  4. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 92
  5. 2025Test-time Alignment of Diffusion Models without Reward Over-optimizationcited by 89
  6. 2024Physics-Informed Diffusion Modelscited by 88
  7. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  8. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  9. 2024Amortizing intractable inference in diffusion models for vision, language, and controlcited by 70
  10. 2024NETS: A Non-Equilibrium Transport Samplercited by 67
  11. 2024Particle Denoising Diffusion Samplercited by 63
  12. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 59
38 more
  1. 2024A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimizationcited by 58
  2. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  3. 2024Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Samplingcited by 55
  4. 2024Symbolic Music Generation with Non-Differentiable Rule Guided Diffusioncited by 52
  5. 2025DIME:Diffusion-Based Maximum Entropy Reinforcement Learningcited by 52
  6. 2024Improved off-policy training of diffusion samplerscited by 47
  7. 2024Sequential Controlled Langevin Diffusionscited by 47
  8. 2024Target Score Matchingcited by 46
  9. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 44
  10. 2023Reverse Diffusion Monte Carlocited by 41
  11. 2023Stochastic Optimal Control Matchingcited by 39
  12. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  13. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 36
  14. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 30
  15. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlocited by 29
  16. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 28
  17. 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 28
  18. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  19. 2024Stochastic Localization via Iterative Posterior Samplingcited by 27
  20. 2025Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densitiescited by 26
  21. 2024Liouville Flow Importance Samplercited by 25
  22. 2025No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplerscited by 25
  23. 2024Bridging Model-Based Optimization and Generative Modeling via Conservative Fine-Tuning of Diffusion Modelscited by 24
  24. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  25. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
  26. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  27. 2024Training Neural Samplers with Reverse Diffusive KL Divergencecited by 21
  28. 2025DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Modelscited by 21
  29. 2025Adjoint Schr"odinger Bridge Samplercited by 20
  30. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 20
  31. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  32. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 19
  33. 2023Scaling Riemannian Diffusion Modelscited by 18
  34. 2024Conditional sampling within generative diffusion modelscited by 18
  35. 2025From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster trainingcited by 17
  36. 2024Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inferencecited by 16
  37. 2025Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative modelscited by 16
  38. 2025RNE: plug-and-play diffusion inference-time control and energy-based trainingcited by 16

50 most cited of 144 All 144 (JSON)

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  1. 2022From Denoising Diffusions to Denoising Markov Models
  2. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  3. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  4. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation
  5. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  6. 2022Denoising MCMC for Accelerating Diffusion-Based Generative Models
  7. 2023Score-based Diffusion Models in Function Space
  8. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models