mlsanityData to 7 Oct 2026

To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models

arXiv 2305.09605 ↗First posted 16 May 2023stat.ML cs.LGcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into a Gaussian. Samples from the generative model are then obtained by simulating an approximation of the time reversal of this diffusion initialized by Gaussian samples. Recent research has explored adapting diffusion models for sampling and inference tasks. In this paper, we leverage known connections to stochastic control akin to the F"ollmer drift to extend established neural network approximation results for the F"ollmer drift to denoising diffusion models and samplers.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 29 of its 52 references that are in the map. First posted on arXiv 16 May 2023.

Builds on

29 of 52 references.

Closest ancestors · 13

Same direction, newest first

  1. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  2. 2023Denoising Diffusion Samplers27 Feb
  3. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  4. 2023I2SB: Image-to-Image Schr"odinger Bridge12 Feb
  5. 2022An optimal control perspective on diffusion-based generative modeling2 Nov
  6. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  7. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  8. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  9. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  10. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  11. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  12. 2020Denoising Diffusion Implicit Models6 Oct
1 more
  1. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 16

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2016Variational Inference: A Review for Statisticianscited by 1,466
  3. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  4. 2019Deep Double Descent: Where Bigger Models and More Data Hurtcited by 667
  5. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  6. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  7. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  8. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  9. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
  10. 2020Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regimecited by 95
  11. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 80
  12. 2018Sampling Can Be Faster Than Optimizationcited by 68
4 more
  1. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  2. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  3. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  4. 2017Many Paths to Equilibrium: GANs Do Not Need to Decrease a Divergence At Every Stepcited by 45

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Cited by year

Citing papers per year: 2023: 1.

1 paper.

  1. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57

Similar, not cited

Close in wording, no citation either way

  1. 2022From Denoising Diffusions to Denoising Markov Models
  2. 2025Diffusion Models: A Mathematical Introduction
  3. 2024Particle Denoising Diffusion Sampler
  4. 2025Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions
  5. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation
  6. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  7. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  8. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions