mlsanityData to 14 Oct 2026

CARD: Classification and Regression Diffusion Models

arXiv 2206.07275 ↗First posted 15 Jun 2022stat.ML cs.LG stat.COcited by 103

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Learning the distribution of a continuous or categorical response variable boldsymbol y given its covariates boldsymbol x is a fundamental problem in statistics and machine learning. Deep neural network-based supervised learning algorithms have made great progress in predicting the mean of boldsymbol y given boldsymbol x, but they are often criticized for their ability to accurately capture the uncertainty of their predictions. In this paper, we introduce classification and regression diffusion (CARD) models, which combine a denoising diffusion-based conditional generative model and a pre-trained conditional mean estimator, to accurately predict the distribution of boldsymbol y given boldsymbol x. We demonstrate the outstanding ability of CARD in conditional distribution prediction with both toy examples and real-world datasets, the experimental results on which show that CARD in general outperforms state-of-the-art methods, including Bayesian neural network-based ones that are designed for uncertainty estimation, especially when the conditional distribution of boldsymbol y given boldsymbol x is multi-modal. In addition, we utilize the stochastic nature of the generative model outputs to obtain a finer granularity in model confidence assessment at the instance level for classification tasks.

Key facts. Cited by 103 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 47 of its 85 references that are in the map. First posted on arXiv 15 Jun 2022.

Builds on

47 of 85 references.

Closest ancestors · 11

Same direction, newest first

  1. 2022Truncated Diffusion Probabilistic Models and Diffusion-based Adversarial Auto-Encoders19 Feb
  2. 2022DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents2 Jan
  3. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  4. 2021Score-Based Generative Classifiers1 Oct
  5. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  6. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  7. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  8. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  9. 2020Denoising Diffusion Implicit Models6 Oct
  10. 2020Denoising Diffusion Probabilistic Models19 Jun
  11. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 36

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  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2019Momentum Contrast for Unsupervised Visual Representation Learningcited by 7,513
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
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  10. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  11. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,614
  12. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,352
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  3. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  4. 2015Variational Dropout and the Local Reparameterization Trickcited by 490
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  19. 2019Understanding the Limitations of Conditional Generative Modelscited by 28
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  21. 2021Wasserstein Generative Learning of Conditional Distributioncited by 24
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 5; 2023: 25; 2024: 31; 2025: 25; 2026: 17.

103 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  2. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 395
  3. 2022A Survey on Generative Diffusion Modelcited by 240
  4. 2023In-Context Learning Unlocked for Diffusion Modelscited by 104
  5. 2023HumanMAC: Masked Motion Completion for Human Motion Predictioncited by 81
  6. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  7. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 67
  8. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 60
  9. 2022JPEG Artifact Correction using Denoising Diffusion Restoration Modelscited by 47
  10. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 46
  11. 2022Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidancecited by 33
  12. 2023DiffMIC: Dual-Guidance Diffusion Network for Medical Image Classificationcited by 32
38 more
  1. 2023Contrastive Conditional Latent Diffusion for Audio-visual Segmentationcited by 31
  2. 2022Spot the fake lungs: Generating Synthetic Medical Images using Neural Diffusion Modelscited by 27
  3. 2024Towards Aligned Layout Generation via Diffusion Model with Aesthetic Constraintscited by 26
  4. 2023Add and Thin: Diffusion for Temporal Point Processescited by 23
  5. 2023FedDiff: Diffusion Model Driven Federated Learning for Multi-Modal and Multi-Clientscited by 23
  6. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  7. 2023Label-Retrieval-Augmented Diffusion Models for Learning from Noisy Labelscited by 20
  8. 2023Learning to Jump: Thinning and Thickening Latent Counts for Generative Modelingcited by 18
  9. 2024DiffusionMTL: Learning Multi-Task Denoising Diffusion Model from Partially Annotated Datacited by 18
  10. 2023DiffBFR: Bootstrapping Diffusion Model Towards Blind Face Restorationcited by 17
  11. 2023Beta Diffusioncited by 17
  12. 2023Towards Generative Modeling of Urban Flow through Knowledge-enhanced Denoising Diffusioncited by 17
  13. 2024Adding Conditional Control to Diffusion Models with Reinforcement Learningcited by 16
  14. 2023NPCL: Neural Processes for Uncertainty-Aware Continual Learningcited by 14
  15. 2025MapDiffusion: Generative Diffusion for Vectorized Online HD Map Construction and Uncertainty Estimation in Autonomous Drivingcited by 13
  16. 2024Annealed Multiple Choice Learning: Overcoming limitations of Winner-takes-all with annealingcited by 12
  17. 2024Diffusion Models For Multi-Modal Generative Modelingcited by 9
  18. 2026Thinking with Looped Flowscited by 9
  19. 2023MDFL: Multi-domain Diffusion-driven Feature Learningcited by 8
  20. 2024Simulation-Free Training of Neural ODEs on Paired Datacited by 8
  21. 2025NoProp: Training Neural Networks without Full Back-propagation or Full Forward-propagationcited by 8
  22. 2024DiffSF: Diffusion Models for Scene Flow Estimationcited by 6
  23. 2024TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generationcited by 6
  24. 2024Timeline and Boundary Guided Diffusion Network for Video Shadow Detectioncited by 6
  25. 2024ROIC-DM: Robust Text Inference and Classification via Diffusion Modelcited by 5
  26. 2024Treeffuser: Probabilistic Predictions via Conditional Diffusions with Gradient-Boosted Treescited by 5
  27. 2025TFG-Flow: Training-free Guidance in Multimodal Generative Flowcited by 5
  28. 2025An Image-like Diffusion Method for Human-Object Interaction Detectioncited by 5
  29. 2023ACT-Net: Anchor-context Action Detection in Surgery Videoscited by 4
  30. 2023Investigating the Adversarial Robustness of Density Estimation Using the Probability Flow ODEcited by 4
  31. 2023Improving Robustness and Reliability in Medical Image Classification with Latent-Guided Diffusion and Nested-Ensemblescited by 4
  32. 2024A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Modelscited by 4
  33. 2025Calibrating Pre-trained Language Classifiers on LLM-generated Noisy Labels via Iterative Refinementcited by 4
  34. 2025Torch-Uncertainty: A Deep Learning Framework for Uncertainty Quantificationcited by 4
  35. 2026Theoretical Analysis of Engression and Reverse Markov Engressioncited by 4
  36. 2023Imitation Learning from Purified Demonstrationscited by 3
  37. 2023Learning to Simulate: Generative Metamodeling via Quantile Regressioncited by 3
  38. 2024Diffusion Cross-domain Recommendationcited by 3

50 most cited of 103 All 103 (JSON)

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  2. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory
  3. 2024On the Feature Learning in Diffusion Models
  4. 2025Beyond Linear Diffusions: Improved Representations for Rare Conditional Generative Modeling
  5. 2023Conditional Generation from Unconditional Diffusion Models using Denoiser Representations
  6. 2026Deep Bootstrap
  7. 2024Model Free Prediction with Uncertainty Assessment
  8. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization