mlsanityData to 7 Oct 2026

Neural Diffusion Models

arXiv 2310.08337 ↗First posted 12 Oct 2023cs.LG stat.MLcited by 20

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can potentially help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs with learnable transformations through experiments on standard image generation benchmarks, including CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood and produce high-quality samples.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 40 of its 62 references that are in the map. First posted on arXiv 12 Oct 2023.

Builds on

40 of 62 references.

Closest ancestors · 19

Same direction, newest first

  1. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions14 Feb
  2. 2023Minimizing Trajectory Curvature of ODE-based Generative Models27 Jan
  3. 2022f-DM: A Multi-stage Diffusion Model via Progressive Signal Transformation10 Oct
  4. 2022Blurring Diffusion Models12 Sep
  5. 2022Soft Diffusion: Score Matching for General Corruptions12 Sep
  6. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  7. 2022Maximum Likelihood Training of Implicit Nonlinear Diffusion Models27 May
  8. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  9. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  10. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  11. 2021Variational Diffusion Models1 Jul
  12. 2021Score-based Generative Modeling in Latent Space10 Jun
7 more
  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  2. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  3. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  4. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Denoising Diffusion Implicit Models6 Oct
  7. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 21

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Flow Matching for Generative Modelingcited by 5,426
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  5. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  6. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  7. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  8. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  9. 2016Pixel Recurrent Neural Networkscited by 814
  10. 2017Generative Adversarial Networks: An Overviewcited by 588
  11. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  12. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 445
9 more
  1. 2017A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasetscited by 374
  2. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transportcited by 277
  3. 2017PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examplescited by 243
  4. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  5. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  6. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  7. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  8. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  9. 2017Good Semi-supervised Learning that Requires a Bad GANcited by 85

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 11; 2026: 4.

20 papers.

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  1. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
  2. 2023Diffusion Models With Learned Adaptive Noisecited by 50
  3. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 43
  4. 2025Continuously Augmented Discrete Diffusion model for Categorical Generative Modelingcited by 32
  5. 2025SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equationscited by 19
  6. 2025Beyond Masked and Unmasked: Discrete Diffusion Models via Partial Maskingcited by 19
  7. 2023DiffEnc: Variational Diffusion with a Learned Encodercited by 16
  8. 2025VCT: Training Consistency Models with Variational Noise Couplingcited by 15
  9. 2025Equivariant Neural Diffusion for Molecule Generationcited by 13
  10. 2025Modular MeanFlow: Towards Stable and Scalable One-Step Generative Modelingcited by 8
  11. 2025Adaptive Destruction Processes for Diffusion Samplerscited by 6
  12. 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
8 more
  1. 2025CoVAE: Consistency Training of Variational Autoencoderscited by 3
  2. 2026A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimationcited by 3
  3. 2024Takin-VC: Expressive Zero-Shot Voice Conversion via Adaptive Hybrid Content Encoding and Enhanced Timbre Modelingcited by 1
  4. 2025A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarioscited by 1
  5. 2026VQ-SAD: Vector Quantized Structure Aware Diffusion For Molecule Generationcited by 1
  6. 2025Breaking the Likelihood-Quality Trade-off in Diffusion Models by Merging Pretrained Expertscited by 0
  7. 2026Simulation-free and finite-time diffusion modelcited by 0
  8. 2026Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolioscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2022Understanding Diffusion Models: A Unified Perspective
  2. 2025Diffusion Models: A Mathematical Introduction
  3. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models
  4. 2022Diffusion Models in Vision: A Survey
  5. 2025Sparse-to-Sparse Training of Diffusion Models
  6. 2024Diffusion Models in Low-Level Vision: A Survey
  7. 2024Scalable Diffusion Models with State Space Backbone
  8. 2025Residual Prior Diffusion: A Probabilistic Framework Integrating Coarse Latent Priors with Diffusion Models