mlsanityData to 14 Oct 2026

Functional Diffusion

arXiv 2311.15435 ↗First posted 26 Nov 2023cs.CV cs.GR cs.LGcited by 13

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. Functional diffusion is very versatile as images, videos, audio, 3D shapes, deformations, etc, can be handled by the same framework with minimal changes. In addition, functional diffusion is especially suited for irregular data or data defined in non-standard domains. In our work, we derive the necessary foundations for functional diffusion and propose a first implementation based on the transformer architecture. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 40 of its 49 references that are in the map. First posted on arXiv 26 Nov 2023.

Builds on

40 of 49 references.

Closest ancestors · 16

Same direction, newest first

  1. 2023State of the Art on Diffusion Models for Visual Computing11 Oct
  2. 2023Geometric Neural Diffusion Processes11 Jul
  3. 2023∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States31 Mar
  4. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation8 Mar
  5. 2023Continuous-Time Functional Diffusion Processes1 Mar
  6. 2023Diffusion Probabilistic Fields1 Mar
  7. 2023Score-based Diffusion Models in Function Space14 Feb
  8. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  9. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise19 Aug
  10. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  11. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  12. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
4 more
  1. 2021Variational Diffusion Models1 Jul
  2. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  3. 2020Denoising Diffusion Implicit Models6 Oct
  4. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 24

  1. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  2. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,689
  3. 2022Video Diffusion Modelscited by 2,305
  4. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,041
  5. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,778
  6. 2020Convolutional Occupancy Networkscited by 761
  7. 2021Neural Fields in Visual Computing and Beyondcited by 540
  8. 20233DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Modelscited by 458
  9. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
  10. 2022SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generationcited by 288
  11. 2022DiffRF: Rendering-Guided 3D Radiance Field Diffusioncited by 204
  12. 2023Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstructioncited by 180
12 more
  1. 2019CvxNet: Learnable Convex Decompositioncited by 174
  2. 2022Generative Modelling With Inverse Heat Dissipationcited by 167
  3. 2023DiffuScene: Denoising Diffusion Models for Generative Indoor Scene Synthesiscited by 166
  4. 2022Neural Wavelet-domain Diffusion for 3D Shape Generationcited by 132
  5. 2023Locally Attentional SDF Diffusion for Controllable 3D Shape Generationcited by 130
  6. 2022ShapeFormer: Transformer-based Shape Completion via Sparse Representationcited by 106
  7. 20223DILG: Irregular Latent Grids for 3D Generative Modelingcited by 93
  8. 2023Functional Flow Matchingcited by 67
  9. 2021SA-ConvONet: Sign-Agnostic Optimization of Convolutional Occupancy Networkscited by 59
  10. 2022Neural Diffusion Processescited by 50
  11. 2022Learning Deep Implicit Functions for 3D Shapes with Dynamic Code Cloudscited by 42
  12. 2022Neural Shape Deformation Priorscited by 27

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 5; 2025: 4; 2026: 3.

13 papers.

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  1. 2025MagicArticulate: Make Your 3D Models Articulation-Readycited by 43
  2. 2025Puppeteer: Rig and Animate Your 3D Modelscited by 43
  3. 2024Motion2VecSets: 4D Latent Vector Set Diffusion for Non-rigid Shape Reconstruction and Trackingcited by 29
  4. 2024LaGeM: A Large Geometry Model for 3D Representation Learning and Diffusioncited by 16
  5. 2024NeuSDFusion: A Spatial-Aware Generative Model for 3D Shape Completion, Reconstruction, and Generationcited by 13
  6. 2025iFlame: Interleaving Full and Linear Attention for Efficient Mesh Generationcited by 13
  7. 2023DPHMs: Diffusion Parametric Head Models for Depth-based Trackingcited by 10
  8. 2025Functional Mean Flow in Hilbert Spacecited by 5
  9. 2024Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulationcited by 4
  10. 2026Trajectory Consistency for One-Step Generation on Euler Mean Flowscited by 2
  11. 2026Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Spacecited by 1
  12. 2026ViP-Rig: Visual-Prompted Controllable Riggingcited by 1
1 more
  1. 2024Geometry Distributionscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2022Diffusion Generative Models in Infinite Dimensions
  2. 2023Infinite-Dimensional Diffusion Models
  3. 2024Fixed Point Diffusion Models
  4. 2022f-DM: A Multi-stage Diffusion Model via Progressive Signal Transformation
  5. 2025FRIDU: Functional Map Refinement with Guided Image Diffusion
  6. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models
  7. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications
  8. 2023HoloDiffusion: Training a 3D Diffusion Model using 2D Images