mlsanityData to 7 Oct 2026

Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matching

arXiv 2406.10808 ↗First posted 16 Jun 2024cs.LGcited by 13

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or learned covariances. In this paper, we leverage the recently proposed covariance moment matching technique and introduce a novel method for learning the diagonal covariance. Unlike traditional data-driven diagonal covariance approximation approaches, our method involves directly regressing the optimal diagonal analytic covariance using a new, unbiased objective named Optimal Covariance Matching (OCM). This approach can significantly reduce the approximation error in covariance prediction. We demonstrate how our method can substantially enhance the sampling efficiency, recall rate and likelihood of commonly used diffusion models.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 52 of its 72 references that are in the map. First posted on arXiv 16 Jun 2024.

Builds on

52 of 72 references.

Closest ancestors · 27

Same direction, newest first

  1. 2024Multistep Distillation of Diffusion Models via Moment Matching6 Jun
  2. 2024EM Distillation for One-step Diffusion Models27 May
  3. 2024Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation5 Apr
  4. 2024Bidirectional Consistency Models26 Mar
  5. 2024Multistep Consistency Models11 Mar
  6. 2023Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Acceleration26 Oct
  7. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion1 Oct
  8. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models29 May
  9. 2023TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation7 Mar
  10. 2023Consistency Models2 Mar
  11. 2023Denoising Diffusion Samplers27 Feb
  12. 2022Scalable Diffusion Models with Transformers19 Dec
15 more
  1. 2022Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models15 Jun
  2. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  4. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  5. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  6. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  7. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  8. 2021Variational Diffusion Models1 Jul
  9. 2021Score-based Generative Modeling in Latent Space10 Jun
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  11. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  12. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  13. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  14. 2020Denoising Diffusion Implicit Models6 Oct
  15. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  5. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  6. 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,526
  7. 2022Video Diffusion Modelscited by 2,280
  8. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  9. 2023ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillationcited by 1,207
  10. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  11. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  12. 2023AudioLDM: Text-to-Audio Generation with Latent Diffusion Modelscited by 592
13 more
  1. 2023VideoCrafter1: Open Diffusion Models for High-Quality Video Generationcited by 530
  2. 2018Assessing Generative Models via Precision and Recallcited by 401
  3. 2022Diffusion-GAN: Training GANs with Diffusioncited by 203
  4. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  5. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  6. 2019Practical Lossless Compression with Latent Variables using Bits Back Codingcited by 85
  7. 2021Estimating High Order Gradients of the Data Distribution by Denoisingcited by 63
  8. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 60
  9. 2021On the Out-of-distribution Generalization of Probabilistic Image Modellingcited by 32
  10. 2018Spread Divergencecited by 23
  11. 2024Diffusive Gibbs Samplingcited by 21
  12. 2019Variational f-divergence Minimizationcited by 16
  13. 2023Moment Matching Denoising Gibbs Samplingcited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 9.

13 papers.

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  1. 2025Diffusion and Flow-based Copulas: Forgetting and Remembering Dependenciescited by 7
  2. 2025Improved probabilistic regression using diffusion modelscited by 2
  3. 2026Few-Step Boltzmann Generators via Scalable Likelihood Flow Mapscited by 2
  4. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
  5. 2026Diffusion Alignment Beyond KL: Variance Minimisation as Effective Policy Optimisercited by 1
  6. 2026Covariance-aware sampling for Diffusion Modelscited by 1
  7. 2026Spatially Adaptive Noise Injectioncited by 1
  8. 2026Improved Distributional Diffusion Modelscited by 1
  9. 2025Likelihood Matching for Diffusion Modelscited by 0
  10. 2025Demystifying Transition Matching: When and Why It Can Beat Flow Matchingcited by 0
  11. 2026The Value of Covariance Matching in Gaussian DDPMs and the Lanczos Samplercited by 0
  12. 2026Localizing Memorized Regions in Diffusion Models via Coordinate-Wise Curvature Differencescited by 0
1 more
  1. 2026Is your uncertainty map wrong, or is its target? Exact diagnostics for the Tweedie diagonal, and a gradient-free alternativecited by 0

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  1. 2024Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costs
  2. 2026Improved denoising diffusion probabilistic models with efficient non-diagonal covariance modeling
  3. 2025Diffusion Models: A Mathematical Introduction
  4. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance
  5. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions
  6. 2025Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noise
  7. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling
  8. 2025Generalization through variance: how noise shapes inductive biases in diffusion models