mlsanityData to 7 Oct 2026

Diffusion Probabilistic Fields

arXiv 2303.00165 ↗First posted 1 Mar 2023cs.CV cs.AIcited by 28

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be carefully designed for each domain independently, oftentimes under the assumption that data lives in a Euclidean grid. In this paper we introduce Diffusion Probabilistic Fields (DPF), a diffusion model that can learn distributions over continuous functions defined over metric spaces, commonly known as fields. We extend the formulation of diffusion probabilistic models to deal with this field parametrization in an explicit way, enabling us to define an end-to-end learning algorithm that side-steps the requirement of representing fields with latent vectors as in previous approaches (Dupont et al., 2022a; Du et al., 2021). We empirically show that, while using the same denoising network, DPF effectively deals with different modalities like 2D images and 3D geometry, in addition to modeling distributions over fields defined on non-Euclidean metric spaces.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 49 of its 71 references that are in the map. First posted on arXiv 1 Mar 2023.

Builds on

49 of 71 references.

Closest ancestors · 10

Same direction, newest first

  1. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise19 Aug
  2. 2022Riemannian Score-Based Generative Modelling6 Feb
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  4. 2021Score-based Generative Modeling in Latent Space10 Jun
  5. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  6. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  7. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  8. 2020Denoising Diffusion Implicit Models6 Oct
  9. 2020Denoising Diffusion Probabilistic Models19 Jun
  10. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 39

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  6. 2013Auto-Encoding Variational Bayescited by 3,980
  7. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,580
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  10. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  11. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  12. 2022Video Diffusion Modelscited by 2,280
27 more
  1. 2021MLP-Mixer: An all-MLP Architecture for Visioncited by 1,441
  2. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
  3. 2020Training Generative Adversarial Networks with Limited Datacited by 1,184
  4. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  5. 2018Learning Implicit Fields for Generative Shape Modelingcited by 1,060
  6. 2016HyperNetworkscited by 1,003
  7. 2016Least Squares Generative Adversarial Networkscited by 1,000
  8. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  9. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
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  18. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  19. 2021An Attention Free Transformercited by 111
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  21. 2016Normalizing Flows on Riemannian Manifoldscited by 68
  22. 2021Moser Flow: Divergence-based Generative Modeling on Manifoldscited by 67
  23. 2021Learning Signal-Agnostic Manifolds of Neural Fieldscited by 45
  24. 2020This Face Does Not Exist ... But It Might Be Yours! Identity Leakage in Generative Modelscited by 33
  25. 2018Autoregressive Quantile Networks for Generative Modelingcited by 31
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 12; 2024: 7; 2025: 7; 2026: 2.

28 papers.

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By area:

  1. 2023HyperDiffusion: Generating Implicit Neural Fields with Weight-Space Diffusioncited by 152
  2. 2023HiFA: High-fidelity Text-to-3D Generation with Advanced Diffusion Guidancecited by 109
  3. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 59
  4. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 55
  5. 2024ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generationcited by 41
  6. 2023∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified Statescited by 21
  7. 2024Grounding Continuous Representations in Geometry: Equivariant Neural Fieldscited by 19
  8. 2024DDMI: Domain-Agnostic Latent Diffusion Models for Synthesizing High-Quality Implicit Neural Representationscited by 16
  9. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spacescited by 16
  10. 2023Functional Diffusioncited by 13
  11. 2023Manifold Diffusion Fieldscited by 11
  12. 2023Single Mesh Diffusion Models with Field Latents for Texture Generationcited by 11
16 more
  1. 2023Generative Neural Fields by Mixtures of Neural Implicit Functionscited by 10
  2. 20243D Shape Tokenization via Latent Flow Matchingcited by 10
  3. 2023Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fieldscited by 7
  4. 2023Latent Field Discovery In Interacting Dynamical Systems With Neural Fieldscited by 7
  5. 2024E(3)-equivariant models cannot learn chirality: Field-based molecular generationcited by 6
  6. 2025MedFuncta: A Unified Framework for Learning Efficient Medical Neural Fieldscited by 6
  7. 2025Flow Straight and Fast in Hilbert Space: Functional Rectified Flowcited by 5
  8. 2025Functional Mean Flow in Hilbert Spacecited by 5
  9. 2025LIFT: Latent Implicit Functions for Task- and Data-Agnostic Encodingcited by 2
  10. 2025Incomplete Data, Complete Dynamics: A Diffusion Approachcited by 2
  11. 2026Trajectory Consistency for One-Step Generation on Euler Mean Flowscited by 2
  12. 2023T1: Scaling Diffusion Probabilistic Fields to High-Resolution on Unified Visual Modalitiescited by 1
  13. 2025DoubleDiffusion: Combining Heat Diffusion with Denoising Diffusion for Texture Generation on 3D Meshescited by 1
  14. 2026Neural Field Tokenizations with Hierarchy and Spatial Locality Priorscited by 1
  15. 2024MING: A Functional Approach to Learning Molecular Generative Modelscited by 0
  16. 2025A standard transformer and attention with linear biases for molecular conformer generationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024An overview of diffusion models for generative artificial intelligence
  2. 2022Diffusion Models in Vision: A Survey
  3. 2023Generalised Diffusion Probabilistic Scale-Spaces
  4. 2025Diffusion Models: A Mathematical Introduction
  5. 2021Structured Denoising Diffusion Models in Discrete State-Spaces
  6. 2023Diffusion Probabilistic Models for Scene-Scale 3D Categorical Data
  7. 2024Learning to Discretize Denoising Diffusion ODEs
  8. 2023Diffusion with Forward Models: Solving Stochastic Inverse Problems Without Direct Supervision