mlsanityData to 7 Oct 2026

Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization

arXiv 2402.01965 ↗First posted 3 Feb 2024cs.LG math.OCcited by 7

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models are gaining widespread use in cutting-edge image, video, and audio generation. Score-based diffusion models stand out among these methods, necessitating the estimation of score function of the input data distribution. In this study, we present a theoretical framework to analyze two-layer neural network-based diffusion models by reframing score matching and denoising score matching as convex optimization. We prove that training shallow neural networks for score prediction can be done by solving a single convex program. Although most analyses of diffusion models operate in the asymptotic setting or rely on approximations, we characterize the exact predicted score function and establish convergence results for neural network-based diffusion models with finite data. Our results provide a precise characterization of what neural network-based diffusion models learn in non-asymptotic settings.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 21 of its 32 references that are in the map. First posted on arXiv 3 Feb 2024.

Builds on

21 of 32 references.

Closest ancestors · 4

Same direction, newest first

  1. 2023On the Generalization of Diffusion Model24 May
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  3. 2020Denoising Diffusion Implicit Models6 Oct
  4. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 17

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 633
  3. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  4. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  5. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  6. 2020Neural Networks are Convex Regularizers: Exact Polynomial-time Convex Optimization Formulations for Two-layer Networkscited by 96
  7. 2023A Survey on Audio Diffusion Models: Text To Speech Synthesis and Enhancement in Generative AIcited by 68
  8. 2020Revealing the Structure of Deep Neural Networks via Convex Dualitycited by 54
  9. 2020Vector-output ReLU Neural Network Problems are Copositive Programs: Convex Analysis of Two Layer Networks and Polynomial-time Algorithmscited by 33
  10. 2022Fast Convex Optimization for Two-Layer ReLU Networks: Equivalent Model Classes and Cone Decompositionscited by 31
  11. 2015Estimation of High-Dimensional Graphical Models Using Regularized Score Matchingcited by 20
  12. 2023The Implicit Bias of Minima Stability in Multivariate Shallow ReLU Networkscited by 15
5 more
  1. 2021Path Regularization: A Convexity and Sparsity Inducing Regularization for Parallel ReLU Networkscited by 14
  2. 2021The Convex Geometry of Backpropagation: Neural Network Gradient Flows Converge to Extreme Points of the Dual Convex Programcited by 11
  3. 2021Parallel Deep Neural Networks Have Zero Duality Gapcited by 9
  4. 2023Globally Optimal Training of Neural Networks with Threshold Activation Functionscited by 9
  5. 2023How do Minimum-Norm Shallow Denoisers Look in Function Space?cited by 9

Built on by

Cited by year (2026 to 7 Oct)

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

7 papers.

  1. 2025On the Interpolation Effect of Score Smoothing in Diffusion Modelscited by 15
  2. 2025A Survey on Diffusion Models for Anomaly Detectioncited by 13
  3. 2025When Diffusion Models Memorize: Inductive Biases in Probability Flow of Minimum-Norm Shallow Neural Netscited by 6
  4. 2025Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Accesscited by 2
  5. 2024Active Learning of Deep Neural Networks via Gradient-Free Cutting Planescited by 1
  6. 2025Realistic Image-to-Image Machine Unlearning via Decoupling and Knowledge Retentioncited by 1
  7. 2026Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refinecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization
  2. 2026Where the Score Lives: A Wavelet View of Diffusion
  3. 2021Conditional Image Generation with Score-Based Diffusion Models
  4. 2024Efficient Denoising using Score Embedding in Score-based Diffusion Models
  5. 2022Understanding Diffusion Models: A Unified Perspective
  6. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data
  7. 2023Closed-Form Diffusion Models
  8. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models