mlsanityData to 14 Oct 2026

A Flexible Diffusion Model

arXiv 2206.10365 ↗First posted 17 Jun 2022cs.LG cs.AI cs.CVcited by 10

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been revealed, and several new variants of SDEs are proposed (e.g., sub-VP, critically-damped Langevin) along this line. Despite the empirical success of the hand-crafted fixed forward SDEs, a great quantity of proper forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing the diffusion model, especially the spatial part of the forward SDE. An abstract formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. We demonstrate the theoretical advantage of our method from an optimization perspective. Numerical experiments on synthetic datasets, MINIST and CIFAR10 are also presented to validate the effectiveness of our framework.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 36 of its 66 references that are in the map. First posted on arXiv 17 Jun 2022.

Builds on

36 of 66 references.

Closest ancestors · 15

Same direction, newest first

  1. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality11 Feb
  2. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  4. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  5. 2021Diffusion Normalizing Flow14 Oct
  6. 2021Variational Diffusion Models1 Jul
  7. 2021Score-based Generative Modeling in Latent Space10 Jun
  8. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  9. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  10. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  11. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  12. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
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 · 21

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2016Density estimation using Real NVPcited by 2,042
  4. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  5. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  6. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 735
  7. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 677
  8. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 637
  9. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  10. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 516
  11. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 384
  12. 2019Residual Flows for Invertible Generative Modelingcited by 257
9 more
  1. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  2. 2017A Conceptual Introduction to Hamiltonian Monte Carlocited by 209
  3. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 164
  4. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 163
  5. 2020OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transportcited by 143
  6. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 76
  7. 2021DiffSVC: A Diffusion Probabilistic Model for Singing Voice Conversioncited by 39
  8. 2021Learning Disentangled Representation by Exploiting Pretrained Generative Models: A Contrastive Learning Viewcited by 34
  9. 2021Towards Building A Group-based Unsupervised Representation Disentanglement Frameworkcited by 22

Built on by

Cited by year

Citing papers per year: 2023: 5; 2024: 4; 2025: 1.

10 papers.

  1. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  2. 2023Diffusion Models With Learned Adaptive Noisecited by 51
  3. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 45
  4. 2024Diffusion Models as Constrained Samplers for Optimization with Unknown Constraintscited by 35
  5. 2023A Group Symmetric Stochastic Differential Equation Model for Molecule Multi-modal Pretrainingcited by 32
  6. 2023A Complete Recipe for Diffusion Generative Modelscited by 17
  7. 2023Molecule Joint Auto-Encoding: Trajectory Pretraining with 2D and 3D Diffusioncited by 10
  8. 2024What's the score? Automated Denoising Score Matching for Nonlinear Diffusionscited by 7
  9. 2025Flow Along the K-Amplitude for Generative Modelingcited by 3
  10. 2024Sculpting Molecules in Text-3D Space: A Flexible Substructure Aware Framework for Text-Oriented Molecular Optimizationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  2. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models
  3. 2023Closing the ODE-SDE gap in score-based diffusion models through the Fokker-Planck equation
  4. 2023Score-based Generative Modeling Through Backward Stochastic Differential Equations: Inversion and Generation
  5. 2025Generative diffusion models from a PDE perspective
  6. 2023Reflected Diffusion Models
  7. 2025Diffusion Models under Alternative Noise: Simplified Analysis and Sensitivity
  8. 2022An optimal control perspective on diffusion-based generative modeling