mlsanityData to 7 Oct 2026

Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers

arXiv 2303.03384 ↗First posted 6 Mar 2023cs.LG math.ST stat.MLcited by 73

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 35 of its 46 references that are in the map. First posted on arXiv 6 Mar 2023.

Builds on

35 of 46 references.

Closest ancestors · 22

Same direction, newest first

  1. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  2. 2022Diffusion Models already have a Semantic Latent Space20 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. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models31 Aug
  7. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise19 Aug
  8. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  9. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  10. 2022gDDIM: Generalized denoising diffusion implicit models11 Jun
  11. 2022Score-Based Generative Models Detect Manifolds2 Jun
  12. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
10 more
  1. 2022Generating High Fidelity Data from Low-density Regions using Diffusion Models31 Mar
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  3. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation10 Jun
  4. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  5. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  6. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  7. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  8. 2020Denoising Diffusion Implicit Models6 Oct
  9. 2020Denoising Diffusion Probabilistic Models19 Jun
  10. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 13

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  3. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  6. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  7. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  8. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  9. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  10. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
  11. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
  12. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Modelscited by 97
1 more
  1. 2022Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problemscited by 11

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 14; 2024: 36; 2025: 18; 2026: 5.

73 papers.

Sort:

By area:

  1. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  2. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 387
  3. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 230
  4. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 156
  5. 2023The probability flow ODE is provably fastcited by 145
  6. 2023Error Bounds for Flow Matching Methodscited by 88
  7. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Modelscited by 84
  8. 2023White-Box Transformers via Sparse Rate Reductioncited by 77
  9. 2024Accelerating Convergence of Score-Based Diffusion Models, Provablycited by 74
  10. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  11. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  12. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 64
38 more
  1. 2023The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editingcited by 61
  2. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorialcited by 60
  3. 2024Gradient Guidance for Diffusion Models: An Optimization Perspectivecited by 59
  4. 2023Learning Mixtures of Gaussians Using the DDPM Objectivecited by 56
  5. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distancescited by 56
  6. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Modelscited by 56
  7. 2024On the Trajectory Regularity of ODE-based Diffusion Samplingcited by 51
  8. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptionscited by 48
  9. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  10. 2024Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Modelscited by 46
  11. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionalitycited by 44
  12. 2024Learning general Gaussian mixtures with efficient score matchingcited by 43
  13. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  14. 2024Critical windows: non-asymptotic theory for feature emergence in diffusion modelscited by 41
  15. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Modelscited by 39
  16. 2023Analysis of learning a flow-based generative model from limited sample complexitycited by 38
  17. 2025Low-dimensional adaptation of diffusion models: Convergence in total variationcited by 38
  18. 2024A Good Score Does not Lead to A Good Generative Modelcited by 36
  19. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Modelscited by 35
  20. 2023Convergence of flow-based generative models via proximal gradient descent in Wasserstein spacecited by 34
  21. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Datacited by 32
  22. 2024Contractive Diffusion Probabilistic Modelscited by 29
  23. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallelcited by 29
  24. 2024Provable Acceleration for Diffusion Models under Minimal Assumptionscited by 27
  25. 2024Towards a mathematical theory for consistency training in diffusion modelscited by 25
  26. 2024Diffusion Model for Data-Driven Black-Box Optimizationcited by 24
  27. 2024Unraveling the Smoothness Properties of Diffusion Models: A Gaussian Mixture Perspectivecited by 24
  28. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distancecited by 20
  29. 2025Discrete Diffusion Models: Novel Analysis and New Sampler Guaranteescited by 20
  30. 2024How much is a noisy image worth? Data Scaling Laws for Ambient Diffusioncited by 18
  31. 2025Ambient Diffusion Omni: Training Good Models with Bad Datacited by 18
  32. 2024U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Modelscited by 17
  33. 2025Faster Diffusion Models via Higher-Order Approximationcited by 16
  34. 2024The Silent Assistant: NoiseQuery as Implicit Guidance for Goal-Driven Image Generationcited by 14
  35. 2024Shallow diffusion networks provably learn hidden low-dimensional structurecited by 12
  36. 2024On the Asymptotic Mean Square Error Optimality of Diffusion Modelscited by 10
  37. 2025SADA: Stability-guided Adaptive Diffusion Accelerationcited by 9
  38. 2023Conditional Stochastic Interpolation for Generative Learningcited by 8

50 most cited of 73 All 73 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2024Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat
  2. 2024Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers
  3. 2025Information-Theoretic Proofs for Diffusion Sampling
  4. 2023Denoising Diffusion Samplers
  5. 2025On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Models
  6. 2023A Geometric Perspective on Diffusion Models
  7. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  8. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Models