mlsanityData to 7 Oct 2026

Contractive Diffusion Probabilistic Models

arXiv 2401.13115 ↗First posted 23 Jan 2024cs.LGcited by 29

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed score matching, we propose a new criterion -- the contraction property of backward sampling in the design of DPMs, leading to a novel class of contractive DPMs (CDPMs). Our key insight is that, the contraction property can provably narrow score matching errors and discretization errors, thus our proposed CDPMs are robust to both sources of error. For practical use, we show that CDPM can leverage weights of pretrained DPMs by a simple transformation, and does not need retraining. We corroborated our approach by experiments on synthetic 1-dim examples, Swiss Roll, MNIST, CIFAR-10 32×32 and AFHQ 64×64 dataset. Notably, CDPM steadily improves the performance of baseline score-based diffusion models.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 46 of its 61 references that are in the map. First posted on arXiv 23 Jan 2024.

Builds on

46 of 61 references.

Closest ancestors · 32

Same direction, newest first

  1. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  2. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models20 Sep
  3. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  4. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
  5. 2023Error Bounds for Flow Matching Methods26 May
  6. 2023The probability flow ODE is provably fast19 May
  7. 2023Diffusion Models for Constrained Domains11 Apr
  8. 2023Reflected Diffusion Models10 Apr
  9. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers6 Mar
  10. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  11. 2023Consistency Models2 Mar
  12. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
20 more
  1. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance13 Dec
  2. 2022Categorical SDEs with Simplex Diffusion26 Oct
  3. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  4. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  5. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  6. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  7. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  8. 2022Score-Based Generative Models Detect Manifolds2 Jun
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  10. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  11. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  12. 2021Variational Diffusion Models1 Jul
  13. 2021Score-based Generative Modeling in Latent Space10 Jun
  14. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  15. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  16. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  17. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  18. 2020Denoising Diffusion Implicit Models6 Oct
  19. 2020Denoising Diffusion Probabilistic Models19 Jun
  20. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 14

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  5. 2020Training Generative Adversarial Networks with Limited Datacited by 1,184
  6. 2016Conditional Image Generation with PixelCNN Decoderscited by 859
  7. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  8. 2018Pros and Cons of GAN Evaluation Measurescited by 224
  9. 2022Continuous diffusion for categorical datacited by 202
  10. 2020Improved Contrastive Divergence Training of Energy Based Modelscited by 127
  11. 2021ViTGAN: Training GANs with Vision Transformerscited by 110
  12. 2022Poisson Flow Generative Modelscited by 95
2 more
  1. 2022Statistical Efficiency of Score Matching: The View from Isoperimetrycited by 63
  2. 2023Policy Optimization for Continuous Reinforcement Learningcited by 30

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 10; 2025: 13; 2026: 6.

29 papers.

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  1. 2024Accelerating Convergence of Score-Based Diffusion Models, Provablycited by 74
  2. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  3. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 64
  4. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorialcited by 60
  5. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Modelscited by 56
  6. 2024Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Modelscited by 46
  7. 2024Fine-tuning of diffusion models via stochastic control: entropy regularization and beyondcited by 42
  8. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalizationcited by 39
  9. 2024PaGoDA: Progressive Growing of a One-Step Generator from a Low-Resolution Diffusion Teachercited by 27
  10. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 27
  11. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distancecited by 20
  12. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Accelerationcited by 17
17 more
  1. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  2. 2025Provable Maximum Entropy Manifold Exploration via Diffusion Modelscited by 12
  3. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Modelscited by 9
  4. 2025Diffusion Models in Simulation-Based Inference: A Tutorial Reviewcited by 8
  5. 2025Understanding Sampler Stochasticity in Training Diffusion Models for RLHFcited by 7
  6. 2024Parallel Simulation for Log-concave Sampling and Score-based Diffusion Modelscited by 6
  7. 2025Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Financecited by 3
  8. 2025The Ensemble Schr"odinger Bridge filter for Nonlinear Data Assimilationcited by 3
  9. 2026On Forgetting and Stability of Score-based Generative modelscited by 3
  10. 2025Non-asymptotic convergence bound of conditional diffusion modelscited by 1
  11. 2025Generating solution paths of Markovian stochastic differential equations using diffusion modelscited by 1
  12. 2026Contractive Diffusion Policies: Robust Action Diffusion via Contractive Score-Based Sampling with Differential Equationscited by 1
  13. 2026Diffusion Models for Adaptive Sequential Data Generationcited by 1
  14. 2026Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Samplingcited by 1
  15. 2025Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimizationcited by 0
  16. 2026From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Modelscited by 0
  17. 2026Leveraging Inference-Time Compute for Diffusion Models via Global Scheduling of Denoising Trajectoriescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Fast Diffusion Probabilistic Model Sampling through the lens of Backward Error Analysis
  2. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models
  3. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps
  4. 2023On Calibrating Diffusion Probabilistic Models
  5. 2021Improved Denoising Diffusion Probabilistic Models
  6. 2024Denoising Diffusion Probabilistic Models in Six Simple Steps
  7. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models
  8. 2024Towards Faster Training of Diffusion Models: An Inspiration of A Consistency Phenomenon