mlsanityData to 7 Oct 2026

A Note on the Convergence of Denoising Diffusion Probabilistic Models

arXiv 2312.05989 ↗First posted 10 Dec 2023cs.LGcited by 9

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models are one of the most important families of deep generative models. In this note, we derive a quantitative upper bound on the Wasserstein distance between the data-generating distribution and the distribution learned by a diffusion model. Unlike previous works in this field, our result does not make assumptions on the learned score function. Moreover, our bound holds for arbitrary data-generating distributions on bounded instance spaces, even those without a density w.r.t. the Lebesgue measure, and the upper bound does not suffer from exponential dependencies. Our main result builds upon the recent work of Mbacke et al. (2023) and our proofs are elementary.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 28 of its 36 references that are in the map. First posted on arXiv 10 Dec 2023.

Builds on

28 of 36 references.

Closest ancestors · 16

Same direction, newest first

  1. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  2. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
  3. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance13 Dec
  4. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  5. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  6. 2022Understanding Diffusion Models: A Unified Perspective25 Aug
  7. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  8. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  9. 2022Score-Based Generative Models Detect Manifolds2 Jun
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  11. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  12. 2021Diffusion Models Beat GANs on Image Synthesis11 May
4 more
  1. 2021UNIT-DDPM: UNpaired Image Translation with Denoising Diffusion Probabilistic Models12 Apr
  2. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 12

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Generative Adversarial Networkscited by 5,603
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  5. 20213D Shape Generation and Completion through Point-Voxel Diffusioncited by 516
  6. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 445
  7. 2021SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Modelscited by 415
  8. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 307
  9. 2023Effective Data Augmentation With Diffusion Modelscited by 282
  10. 2021User-friendly introduction to PAC-Bayes boundscited by 234
  11. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
  12. 2023Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theorycited by 16

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 1; 2026: 3.

9 papers.

  1. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 64
  2. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  3. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionalitycited by 44
  4. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  5. 2025Dimension-free error estimate for diffusion model and optimal schedulingcited by 3
  6. 2026Bound to Disagree: Generalization Bounds via Certifiable Surrogatescited by 2
  7. 2024Structural and Convergence Analysis of Discrete-Time Denoising Diffusion Probabilistic Modelscited by 1
  8. 2026PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoderscited by 1
  9. 2026Error Bounds for a Diffusion Model-Based Drift Estimatorcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  2. 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer process
  3. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
  4. 2024Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat
  5. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
  6. 2024Wasserstein Bounds for generative diffusion models with Gaussian tail targets
  7. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  8. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data