mlsanityData to 7 Oct 2026

Manifold Diffusion Fields

arXiv 2305.15586 ↗First posted 24 May 2023cs.LGcited by 11

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We present Manifold Diffusion Fields (MDF), an approach that unlocks learning of diffusion models of data in general non-Euclidean geometries. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. In addition, we show that MDF generalizes to the case where the training set contains functions on different manifolds. Empirical results on multiple datasets and manifolds including challenging scientific problems like weather prediction or molecular conformation show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 45 of its 78 references that are in the map. First posted on arXiv 24 May 2023.

Builds on

45 of 78 references.

Closest ancestors · 8

Same direction, newest first

  1. 2023∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States31 Mar
  2. 2023Diffusion Probabilistic Fields1 Mar
  3. 2022Riemannian Score-Based Generative Modelling6 Feb
  4. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  5. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Implicit Models6 Oct
  8. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 37

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Language Models are Few-Shot Learnerscited by 32,199
  3. 2022FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awarenesscited by 3,611
  4. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  5. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  6. 2022Video Diffusion Modelscited by 2,280
  7. 2021MLP-Mixer: An all-MLP Architecture for Visioncited by 1,441
  8. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  9. 2016HyperNetworkscited by 1,003
  10. 2020Benchmarking Graph Neural Networkscited by 672
  11. 2021Perceiver IO: A General Architecture for Structured Inputs & Outputscited by 616
  12. 2021Neural Fields in Visual Computing and Beyondcited by 539
25 more
  1. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  2. 2018Neural Processescited by 307
  3. 2019Attentive Neural Processescited by 280
  4. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  5. 2023Flow Matching on General Geometriescited by 260
  6. 2020The Creation and Detection of Deepfakes: A Surveycited by 246
  7. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 163
  8. 2021An Attention Free Transformercited by 111
  9. 2021GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensemblescited by 106
  10. 2022A Generalization of ViT/MLP-Mixer to Graphscited by 93
  11. 2021Generative Models as Distributions of Functionscited by 89
  12. 2021Learning Neural Generative Dynamics for Molecular Conformation Generationcited by 87
  13. 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
  14. 2016Normalizing Flows on Riemannian Manifoldscited by 68
  15. 2021Moser Flow: Divergence-based Generative Modeling on Manifoldscited by 67
  16. 2023Spatial Functa: Scaling Functa to ImageNet Classification and Generationcited by 55
  17. 2022Neural Diffusion Processescited by 50
  18. 2021Learning Signal-Agnostic Manifolds of Neural Fieldscited by 45
  19. 2020This Face Does Not Exist ... But It Might Be Yours! Identity Leakage in Generative Modelscited by 33
  20. 2022Generalised Implicit Neural Representationscited by 31
  21. 2020Imperfect ImaGANation: Implications of GANs Exacerbating Biases on Facial Data Augmentation and Snapchat Selfie Lensescited by 27
  22. 2022Generalized Laplacian Positional Encoding for Graph Representation Learningcited by 21
  23. 2022Intrinsic Neural Fields: Learning Functions on Manifoldscited by 20
  24. 2021Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernelscited by 19
  25. 2021Ethics and Creativity in Computer Visioncited by 15

Built on by

Cited by year (2026 to 7 Oct)

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

11 papers.

  1. 2023Single Mesh Diffusion Models with Field Latents for Texture Generationcited by 11
  2. 2023Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fieldscited by 7
  3. 2024CaFA: Global Weather Forecasting with Factorized Attention on Spherecited by 6
  4. 2024UV-free Texture Generation with Denoising and Geodesic Heat Diffusionscited by 3
  5. 2025Physically Valid Biomolecular Interaction Modeling with Gauss-Seidel Projectioncited by 3
  6. 2025A Malliavin-Gamma calculus approach to Score Based Diffusion Generative models for random fieldscited by 2
  7. 2026Divergence-Free Diffusion Models for Incompressible Fluid Flowscited by 2
  8. 2026Manifold-Aware Perturbations for Constrained Generative Modelingcited by 2
  9. 2025DoubleDiffusion: Combining Heat Diffusion with Denoising Diffusion for Texture Generation on 3D Meshescited by 1
  10. 2024MING: A Functional Approach to Learning Molecular Generative Modelscited by 0
  11. 2026Manifold Diffusion for Structure Generation of Transition Metal Complexescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity
  2. 2023Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes
  3. 2025Efficient Diffusion Models for Symmetric Manifolds
  4. 2026Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networks
  5. 2025Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity
  6. 2025What's Inside Your Diffusion Model? A Score-Based Riemannian Metric to Explore the Data Manifold
  7. 2023Learning Distributions on Manifolds with Free-Form Flows
  8. 2025Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Models