mlsanityData to 7 Oct 2026

Interpreting and Improving Diffusion Models from an Optimization Perspective

arXiv 2306.04848 ↗First posted 8 Jun 2023cs.LG cs.CV math.OCcited by 19

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this paper, we use this observation to interpret denoising diffusion models as approximate gradient descent applied to the Euclidean distance function. We then provide straight-forward convergence analysis of the DDIM sampler under simple assumptions on the projection error of the denoiser. Finally, we propose a new gradient-estimation sampler, generalizing DDIM using insights from our theoretical results. In as few as 5-10 function evaluations, our sampler achieves state-of-the-art FID scores on pretrained CIFAR-10 and CelebA models and can generate high quality samples on latent diffusion models.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 37 of its 51 references that are in the map. First posted on arXiv 8 Jun 2023.

Builds on

37 of 51 references.

Closest ancestors · 15

Same direction, newest first

  1. 2023Consistency Models2 Mar
  2. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models9 Feb
  3. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  4. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  5. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  7. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  8. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  9. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  10. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  11. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  12. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
3 more
  1. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  2. 2020Denoising Diffusion Implicit Models6 Oct
  3. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 22

  1. 2014Microsoft COCO: Common Objects in Contextcited by 17,498
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  4. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  5. 2022Flow Matching for Generative Modelingcited by 5,426
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  8. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  9. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusioncited by 2,730
  10. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  11. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
  12. 2023Zero-1-to-3: Zero-shot One Image to 3D Objectcited by 1,483
10 more
  1. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  2. 2022Human Motion Diffusion Modelcited by 1,062
  3. 2022Denoising Diffusion Restoration Modelscited by 951
  4. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  5. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 307
  6. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  7. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 78
  8. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
  9. 2019Deep Eikonal Solverscited by 9
  10. 2021Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restorationcited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 7; 2026: 7.

19 papers.

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  1. 2024Diffusion Policy Policy Optimizationcited by 255
  2. 2025Much Ado About Noising: Dispelling the Myths of Generative Robotic Controlcited by 35
  3. 2025Locality in Image Diffusion Models Emerges from Data Statisticscited by 25
  4. 2025Accelerating Residual Reinforcement Learning with Uncertainty Estimationcited by 6
  5. 2024The Duality of Generative AI and Reinforcement Learning in Robotics: A Reviewcited by 5
  6. 2024Enhancing Sample Generation of Diffusion Models using Noise Level Correctioncited by 4
  7. 2026Any-OPD: Heterogeneous On-Policy Distillation for Flow-Matching Models via Representation-Space Bridgingcited by 4
  8. 2025How Well do Diffusion Policies Learn Kinematic Constraint Manifolds?cited by 3
  9. 2026Improving Classifier-Free Guidance of Flow Matching via Manifold Projectioncited by 3
  10. 2025Delta Sampling: Data-Free Knowledge Transfer Across Diffusion Modelscited by 2
  11. 2025Is Your Conditional Diffusion Model Actually Denoising?cited by 1
  12. 2025Residual Prior Diffusion: A Probabilistic Framework Integrating Coarse Latent Priors with Diffusion Modelscited by 1
7 more
  1. 2024VisDiff: SDF-Guided Polygon Generation for Visibility Reconstruction and Recognitioncited by 0
  2. 2024A Probabilistic Formulation of Offset Noise in Diffusion Modelscited by 0
  3. 2026Distance Marching for Generative Modelingcited by 0
  4. 2026Geometry-Preserving Neural Architectures on Manifolds with Boundarycited by 0
  5. 2026Sampling sea state using a diffusion modelcited by 0
  6. 2026Asymptotic Preservation and Uniform Accuracy of Diffusion and Flow-Matching Samplerscited by 0
  7. 2026Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusioncited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation
  2. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  3. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models
  4. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models
  5. 2024On the Asymptotic Mean Square Error Optimality of Diffusion Models
  6. 2023Denoising Diffusion Samplers
  7. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality
  8. 2026Blind denoising diffusion models and the blessings of dimensionality