mlsanityData to 7 Oct 2026

Reflected Diffusion Models

arXiv 2304.04740 ↗First posted 10 Apr 2023stat.ML cs.LGcited by 81

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Key facts. Cited by 81 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 43 of its 65 references that are in the map. First posted on arXiv 10 Apr 2023.

Builds on

43 of 65 references.

Closest ancestors · 14

Same direction, newest first

  1. 2022Categorical SDEs with Simplex Diffusion26 Oct
  2. 2022Classifier-Free Diffusion Guidance26 Jul
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  4. 2022Subspace Diffusion Generative Models3 May
  5. 2022Riemannian Score-Based Generative Modelling6 Feb
  6. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  7. 2021Variational Diffusion Models1 Jul
  8. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation10 Jun
  9. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  10. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  11. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  12. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
2 more
  1. 2020Denoising Diffusion Implicit Models6 Oct
  2. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 29

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  5. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  6. 2016Layer Normalizationcited by 5,579
  7. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,451
  8. 2014Going Deeper with Convolutionscited by 4,231
  9. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  10. 2018Neural Ordinary Differential Equationscited by 3,733
  11. 2016Improved Techniques for Training GANscited by 2,938
  12. 2022Video Diffusion Modelscited by 2,280
17 more
  1. 2019Generating Long Sequences with Sparse Transformerscited by 1,523
  2. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  3. 2016Pixel Recurrent Neural Networkscited by 814
  4. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  5. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  6. 2017PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modificationscited by 415
  7. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  8. 2017A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasetscited by 374
  9. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  10. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  11. 2021Autoregressive Diffusion Modelscited by 208
  12. 2022Continuous diffusion for categorical datacited by 202
  13. 2021ViTGAN: Training GANs with Vision Transformerscited by 110
  14. 2020Adversarial score matching and improved sampling for image generationcited by 95
  15. 2022Statistical Efficiency of Score Matching: The View from Isoperimetrycited by 63
  16. 2021Styleformer: Transformer based Generative Adversarial Networks with Style Vectorcited by 27
  17. 2020Generalized Score Matching for General Domainscited by 13

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 20; 2024: 22; 2025: 18; 2026: 21.

81 papers.

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By area:

  1. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 712
  2. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 180
  3. 2025LLaDA-V: Large Language Diffusion Models with Visual Instruction Tuningcited by 145
  4. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 105
  5. 2024Constrained Synthesis with Projected Diffusion Modelscited by 83
  6. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  7. 2023Bayesian Flow Networkscited by 62
  8. 2023Diffusion Models for Constrained Domainscited by 60
  9. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorialcited by 60
  10. 2023Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimizationcited by 56
  11. 2023Diffusion Models With Learned Adaptive Noisecited by 50
  12. 2023Mirror Diffusion Models for Constrained and Watermarked Generationcited by 38
38 more
  1. 2024Diffusion Models as Constrained Samplers for Optimization with Unknown Constraintscited by 33
  2. 2025Attention Is All You Need for KV Cache in Diffusion LLMscited by 32
  3. 2024Contractive Diffusion Probabilistic Modelscited by 29
  4. 2023Metropolis Sampling for Constrained Diffusion Modelscited by 28
  5. 2024Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equationscited by 28
  6. 2023Score-Based Generative Models for PET Image Reconstructioncited by 22
  7. 2024Constrained Diffusion Models via Dual Trainingcited by 19
  8. 2023Scaling Riemannian Diffusion Modelscited by 18
  9. 2023Beta Diffusioncited by 17
  10. 2024Generative Modelling of Structurally Constrained Graphscited by 17
  11. 2023DiffEnc: Variational Diffusion with a Learned Encodercited by 16
  12. 2025DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectoriescited by 14
  13. 2024Reflected Flow Matchingcited by 13
  14. 2023Generative Fractional Diffusion Modelscited by 12
  15. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  16. 2024Context-Guided Diffusion for Out-of-Distribution Molecular and Protein Designcited by 11
  17. 2023Geometric Neural Diffusion Processescited by 10
  18. 2023Unbalanced Diffusion Schr"odinger Bridgecited by 9
  19. 2025Watermarking Diffusion Language Modelscited by 9
  20. 2024Quantum State Generation with Structure-Preserving Diffusion Modelcited by 8
  21. 2025Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domainscited by 8
  22. 2024Neural Approximate Mirror Maps for Constrained Diffusion Modelscited by 7
  23. 2023Don't be so negative! Score-based Generative Modeling with Oracle-assisted Guidancecited by 6
  24. 2023A High-Quality Robust Diffusion Framework for Corrupted Datasetcited by 6
  25. 2024Statistical guarantees for denoising reflected diffusion modelscited by 6
  26. 2025Projected Coupled Diffusion for Test-Time Constrained Joint Generationcited by 6
  27. 2025The Rise of Generative AI for Metal-Organic Framework Design and Synthesiscited by 6
  28. 2023The Missing U for Efficient Diffusion Modelscited by 5
  29. 2024Equality Constrained Diffusion for Direct Trajectory Optimizationcited by 5
  30. 2026Membership Inference Attacks Against Fine-tuned Diffusion Language Modelscited by 5
  31. 2023Structured Voronoi Samplingcited by 4
  32. 2024Towards diffusion models for large-scale sea-ice modellingcited by 4
  33. 2025Improved Diffusion-based Generative Model with Better Adversarial Robustnesscited by 3
  34. 2025Fractional Diffusion Bridge Modelscited by 3
  35. 2024Neural Shr"odinger Bridge Matching for Pansharpeningcited by 2
  36. 2025Diffusion-based Planning with Learned Viability Filterscited by 2
  37. 2025Flexibility-Conditioned Protein Structure Design with Flow Matchingcited by 2
  38. 2026Logic-Guided Vector Fields for Constrained Generative Modelingcited by 2

50 most cited of 81 All 81 (JSON)

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  1. 2024Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models
  2. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  3. 2025Diffusion Models: A Mathematical Introduction
  4. 2022A Flexible Diffusion Model
  5. 2022Understanding Diffusion Models: A Unified Perspective
  6. 2024Non-Normal Diffusion Models
  7. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models
  8. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models