mlsanityData to 7 Oct 2026

DDIM Redux: Mathematical Foundation and Some Extension

arXiv 2408.07285 ↗First posted 3 Aug 2024cs.LGcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

This note provides a critical review of the mathematical concepts underlying the generalized diffusion denoising implicit model (gDDIM) and the exponential integrator (EI) scheme. We present enhanced mathematical results, including an exact expression for the reverse trajectory in the probability flow ODE and an exact expression for the covariance matrix in the gDDIM scheme. Furthermore, we offer an improved understanding of the EI scheme's efficiency in terms of the change of variables. The noising process in DDIM is analyzed from the perspective of non-equilibrium statistical physics. Additionally, we propose a new scheme for DDIM, called the principal-axis DDIM (paDDIM).

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 9 of its 18 references that are in the map. First posted on arXiv 3 Aug 2024.

Builds on

9 of 18 references.

Closest ancestors · 6

Same direction, newest first

  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  2. 2022gDDIM: Generalized denoising diffusion implicit models11 Jun
  3. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  4. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 3

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2021Fluctuation-dissipation Type Theorem in Stochastic Linear Learningcited by 3

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Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025NatADiff: Adversarial Boundary Guidance for Natural Adversarial Diffusioncited by 5

Similar, not cited

Close in wording, no citation either way

  1. 2020Denoising Diffusion Implicit Models
  2. 2024Diffusion Bridge Implicit Models
  3. 2026Connections between the F"ollmer process and the denoising diffusion probabilistic model
  4. 2023Interpreting and Improving Diffusion Models from an Optimization Perspective
  5. 2024Structural and Convergence Analysis of Discrete-Time Denoising Diffusion Probabilistic Models
  6. 2023Improved DDIM Sampling with Moment Matching Gaussian Mixtures
  7. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers
  8. 2024Denoising Diffusion Probabilistic Models in Six Simple Steps