mlsanityData to 7 Oct 2026

Maximum Likelihood Training of Implicit Nonlinear Diffusion Models

arXiv 2205.13699 ↗First posted 27 May 2022cs.LGcited by 42

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Whereas diverse variations of diffusion models exist, extending the linear diffusion into a nonlinear diffusion process is investigated by very few works. The nonlinearity effect has been hardly understood, but intuitively, there would be promising diffusion patterns to efficiently train the generative distribution towards the data distribution. This paper introduces a data-adaptive nonlinear diffusion process for score-based diffusion models. The proposed Implicit Nonlinear Diffusion Model (INDM) learns by combining a normalizing flow and a diffusion process. Specifically, INDM implicitly constructs a nonlinear diffusion on the textitdata space by leveraging a linear diffusion on the textitlatent space through a flow network. This flow network is key to forming a nonlinear diffusion, as the nonlinearity depends on the flow network. This flexible nonlinearity improves the learning curve of INDM to nearly Maximum Likelihood Estimation (MLE) against the non-MLE curve of DDPM++, which turns out to be an inflexible version of INDM with the flow fixed as an identity mapping. Also, the discretization of INDM shows the sampling robustness. In experiments, INDM achieves the state-of-the-art FID of 1.75 on CelebA. We release our code at https://github.com/byeonghu-na/INDM.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 55 of its 88 references that are in the map. First posted on arXiv 27 May 2022.

Builds on

55 of 88 references.

Closest ancestors · 18

Same direction, newest first

  1. 2022Understanding DDPM Latent Codes Through Optimal Transport14 Feb
  2. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  3. 2021Diffusion Normalizing Flow14 Oct
  4. 2021Denoising Diffusion Gamma Models10 Oct
  5. 2021Variational Diffusion Models1 Jul
  6. 2021Non Gaussian Denoising Diffusion Models14 Jun
  7. 2021Score-based Generative Modeling in Latent Space10 Jun
  8. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation10 Jun
  9. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  11. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  12. 2021UNIT-DDPM: UNpaired Image Translation with Denoising Diffusion Probabilistic Models12 Apr
6 more
  1. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  2. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Implicit Models6 Oct
  5. 2020Denoising Diffusion Probabilistic Models19 Jun
  6. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 37

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25 more
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  10. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 13; 2024: 13; 2025: 8; 2026: 1.

42 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2022Diffusion Models in Vision: A Surveycited by 1,008
  3. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
  4. 2022A Survey on Generative Diffusion Modelcited by 238
  5. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 171
  6. 2023DiffiT: Diffusion Vision Transformers for Image Generationcited by 104
  7. 2022Refining Generative Process with Discriminator Guidance in Score-based Diffusion Modelscited by 98
  8. 2022Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidancecited by 67
  9. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 59
  10. 2022Efficient Diffusion Models for Vision: A Surveycited by 50
  11. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 43
  12. 2023Mirror Diffusion Models for Constrained and Watermarked Generationcited by 38
30 more
  1. 2023Neural Diffusion Modelscited by 20
  2. 2024Diffusion Models as Cartoonists: The Curious Case of High Density Regionscited by 19
  3. 2023Stage-by-stage Wavelet Optimization Refinement Diffusion Model for Sparse-View CT Reconstructioncited by 18
  4. 2023DiffEnc: Variational Diffusion with a Learned Encodercited by 16
  5. 2024Label-Noise Robust Diffusion Modelscited by 16
  6. 2023Star-Shaped Denoising Diffusion Probabilistic Modelscited by 13
  7. 2023Generative Fractional Diffusion Modelscited by 12
  8. 2025Nonisotropic Gaussian Diffusion for Realistic 3D Human Motion Predictioncited by 12
  9. 2024Structure-Guided Adversarial Training of Diffusion Modelscited by 11
  10. 2024Diffusion Rejection Samplingcited by 11
  11. 2024Safe-SD: Safe and Traceable Stable Diffusion with Text Prompt Trigger for Invisible Generative Watermarkingcited by 11
  12. 2024Neural Residual Diffusion Models for Deep Scalable Vision Generationcited by 9
  13. 2025Flexible Language Modeling in Continuous Space with Transformer-based Autoregressive Flowscited by 8
  14. 2022Applying Regularized Schr"odinger-Bridge-Based Stochastic Process in Generative Modelingcited by 7
  15. 2023Diffusion Models with Deterministic Normalizing Flow Priorscited by 7
  16. 2024What's the score? Automated Denoising Score Matching for Nonlinear Diffusionscited by 7
  17. 2023Preconditioned Score-based Generative Modelscited by 6
  18. 2024Diffusion Bridge AutoEncoders for Unsupervised Representation Learningcited by 6
  19. 2025Diffusion Generative Modeling on Lie Group Representationscited by 6
  20. 2025Diffusion-Sharpening: Fine-tuning Diffusion Models with Denoising Trajectory Sharpeningcited by 6
  21. 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
  22. 2024Variational Flow Models: Flowing in Your Stylecited by 3
  23. 2025Fractional Diffusion Bridge Modelscited by 3
  24. 2026Lookahead Sample Reward Guidance for Test-Time Scaling of Diffusion Modelscited by 3
  25. 2023Mitigating Exposure Bias in Discriminator Guided Diffusion Modelscited by 2
  26. 2025Likelihood Training of Cascaded Diffusion Models via Hierarchical Volume-preserving Mapscited by 2
  27. 2024Contextualized Diffusion Models for Text-Guided Image and Video Generationcited by 1
  28. 2024Hardware-Friendly Diffusion Models with Fixed-Size Reusable Structures for On-Device Image Generationcited by 0
  29. 2024Local Curvature Smoothing with Stein's Identity for Efficient Score Matchingcited by 0
  30. 2025Ordered-subsets Multi-diffusion Model for Sparse-view CT Reconstructioncited by 0

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  5. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions
  6. 2024Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization
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