mlsanityData to 7 Oct 2026

Evaluating the design space of diffusion-based generative models

arXiv 2406.12839 ↗First posted 18 Jun 2024cs.LG math.DS math.OCcited by 25

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation. This article instead provides a first quantitative understanding of the whole generation process, i.e., both training and sampling. More precisely, it conducts a non-asymptotic convergence analysis of denoising score matching under gradient descent. In addition, a refined sampling error analysis for variance exploding models is also provided. The combination of these two results yields a full error analysis, which elucidates (again, but this time theoretically) how to design the training and sampling processes for effective generation. For instance, our theory implies a preference toward noise distribution and loss weighting in training that qualitatively agree with the ones used in [Karras et al., 2022]. It also provides perspectives on the choices of time and variance schedules in sampling: when the score is well trained, the design in [Song et al., 2021] is more preferable, but when it is less trained, the design in [Karras et al., 2022] becomes more preferable.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 54 of its 65 references that are in the map. First posted on arXiv 18 Jun 2024.

Builds on

54 of 65 references.

Closest ancestors · 26

Same direction, newest first

  1. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization11 Apr
  2. 2024Quantum State Generation with Structure-Preserving Diffusion Model9 Apr
  3. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion27 Feb
  4. 2024Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization12 Feb
  5. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances31 Jan
  6. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization28 Jan
  7. 2023Analyzing and Improving the Training Dynamics of Diffusion Models5 Dec
  8. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  9. 2023Learning Mixtures of Gaussians Using the DDPM Objective3 Jul
  10. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  11. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  12. 2022Scalable Diffusion Models with Transformers19 Dec
14 more
  1. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  2. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  3. 2022A Survey on Generative Diffusion Model6 Sep
  4. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  5. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  6. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  8. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  9. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  10. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  11. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  12. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  13. 2020Denoising Diffusion Probabilistic Models19 Jun
  14. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 28

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2022Video Diffusion Modelscited by 2,280
  6. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
  7. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  8. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 784
  9. 2018Gradient Descent Provably Optimizes Over-parameterized Neural Networkscited by 655
  10. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  11. 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 572
  12. 2019Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networkscited by 562
16 more
  1. 2021Label-Efficient Semantic Segmentation with Diffusion Modelscited by 495
  2. 2021Score-based diffusion models for accelerated MRIcited by 308
  3. 2018Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Datacited by 260
  4. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
  5. 2019Universal Approximation with Deep Narrow Networkscited by 198
  6. 2022MedSegDiff: Medical Image Segmentation with Diffusion Probabilistic Modelcited by 180
  7. 2017Convergence Analysis of Two-layer Neural Networks with ReLU Activationcited by 137
  8. 2021Adversarial purification with Score-based generative modelscited by 132
  9. 2019An Improved Analysis of Training Over-parameterized Deep Neural Networkscited by 120
  10. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
  11. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Modelscited by 97
  12. 2018On the Convergence Rate of Training Recurrent Neural Networkscited by 82
  13. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  14. 2019Quadratic Suffices for Over-parametrization via Matrix Chernoff Boundcited by 58
  15. 2023Accurate transition state generation with an object-aware equivariant elementary reaction diffusion modelcited by 30
  16. 2021Provable Convergence of Nesterov's Accelerated Gradient Method for Over-Parameterized Neural Networkscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 11; 2026: 9.

25 papers.

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  1. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionalitycited by 44
  2. 2025Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curvescited by 20
  3. 2024On the Feature Learning in Diffusion Modelscited by 19
  4. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  5. 2025A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspectivecited by 18
  6. 2024Presto! Distilling Steps and Layers for Accelerating Music Generationcited by 16
  7. 2025On the Interpolation Effect of Score Smoothing in Diffusion Modelscited by 15
  8. 2025Lipschitz-Guided Design of Interpolation Schedules in Generative Modelscited by 15
  9. 2024Differential Privacy Mechanisms in Neural Tangent Kernel Regressioncited by 14
  10. 2025A solvable model of learning generative diffusion: theory and insightscited by 14
  11. 2024Shallow diffusion networks provably learn hidden low-dimensional structurecited by 12
  12. 2025Generalization of Diffusion Models Arises with a Balanced Representation Spacecited by 10
13 more
  1. 2026Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approachcited by 10
  2. 2025Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domainscited by 8
  3. 2025Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Financecited by 3
  4. 2026Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Datacited by 3
  5. 2025Convergence Dynamics of Over-Parameterized Score Matching for a Single Gaussiancited by 2
  6. 2026Provably Reliable Classifier Guidance via Cross-Entropy Controlcited by 1
  7. 2026NoiseRater: Meta-Learned Noise Valuation for Diffusion Model Trainingcited by 1
  8. 2026Optimizing Visual Generative Models via Distribution-wise Rewardscited by 1
  9. 2025DiffPace: Diffusion-based Plug-and-play Augmented Channel Estimation in mmWave and Terahertz Ultra-Massive MIMO Systemscited by 0
  10. 2026Transformers Learn the Optimal DDPM Denoiser for Multi-Token GMMscited by 0
  11. 2026Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landingcited by 0
  12. 2026Understanding and Accelerating the Training of Masked Diffusion Language Modelscited by 0
  13. 2026Universal Local Error and Realized Amplification for the First-Order EDM Predictorcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models
  2. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  3. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models
  4. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation
  5. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models
  6. 2024Theoretical research on generative diffusion models: an overview
  7. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent
  8. 2024GUD: Generation with Unified Diffusion