mlsanityData to 7 Oct 2026

Generative Models as Distributions of Functions

arXiv 2102.04776 ↗First posted 9 Feb 2021cs.LG cs.CV stat.MLcited by 89

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Abstract (arXiv)

Generative models are typically trained on grid-like data such as images. As a result, the size of these models usually scales directly with the underlying grid resolution. In this paper, we abandon discretized grids and instead parameterize individual data points by continuous functions. We then build generative models by learning distributions over such functions. By treating data points as functions, we can abstract away from the specific type of data we train on and construct models that are agnostic to discretization. To train our model, we use an adversarial approach with a discriminator that acts on continuous signals. Through experiments on a wide variety of data modalities including images, 3D shapes and climate data, we demonstrate that our model can learn rich distributions of functions independently of data type and resolution.

Key facts. Cited by 89 papers in the map (data through 7 Oct 2026). Builds on 63 of its 84 references that are in the map. First posted on arXiv 9 Feb 2021.

Builds on

63 of 84 references.

References · 63

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38 more
  1. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
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  17. 2020Implicit Geometric Regularization for Learning Shapescited by 707
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  19. 2020GRAF: Generative Radiance Fields for 3D-Aware Image Synthesiscited by 688
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50 most cited of 63 All 63 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 10; 2022: 17; 2023: 26; 2024: 15; 2025: 13; 2026: 8.

89 papers.

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  1. 2021StyleGAN-V: A Continuous Video Generator with the Price, Image Quality and Perks of StyleGAN2cited by 300
  2. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  3. 2021COIN: COmpression with Implicit Neural representationscited by 232
  4. 2022Generating Videos with Dynamics-aware Implicit Generative Adversarial Networkscited by 186
  5. 2022From data to functa: Your data point is a function and you can treat it like onecited by 183
  6. 2023HyperDiffusion: Generating Implicit Neural Fields with Weight-Space Diffusioncited by 152
  7. 2021A Structured Dictionary Perspective on Implicit Neural Representationscited by 100
  8. 2023Implicit Neural Representation for Cooperative Low-light Image Enhancementcited by 92
  9. 2022COIN++: Neural Compression Across Modalitiescited by 81
  10. 2023Score-based Diffusion Models in Function Spacecited by 80
  11. 2023Permutation Equivariant Neural Functionalscited by 69
  12. 2021CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assemblycited by 62
38 more
  1. 2023Deep Learning on Implicit Neural Representations of Shapescited by 62
  2. 2021Improved Transformer for High-Resolution GANscited by 59
  3. 2023Spatial Functa: Scaling Functa to ImageNet Classification and Generationcited by 55
  4. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 55
  5. 2022Generative Adversarial Neural Operatorscited by 51
  6. 2023Neural Functional Transformerscited by 50
  7. 2022Diffusion Generative Models in Infinite Dimensionscited by 49
  8. 2021Learning Signal-Agnostic Manifolds of Neural Fieldscited by 45
  9. 2022Low-Rank Tensor Function Representation for Multi-Dimensional Data Recoverycited by 45
  10. 2023Sphere2Vec: A General-Purpose Location Representation Learning over a Spherical Surface for Large-Scale Geospatial Predictionscited by 38
  11. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generationcited by 37
  12. 2022Learning Continuous Grasping Function with a Dexterous Hand from Human Demonstrationscited by 34
  13. 2023Diffusion Probabilistic Fieldscited by 28
  14. 2023A Unified Framework for U-Net Design and Analysiscited by 27
  15. 2021Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmscited by 24
  16. 2023Variational Autoencoding Neural Operatorscited by 22
  17. 2023∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified Statescited by 21
  18. 2022SeamlessGAN: Self-Supervised Synthesis of Tileable Texture Mapscited by 19
  19. 2022UncertaINR: Uncertainty Quantification of End-to-End Implicit Neural Representations for Computed Tomographycited by 19
  20. 2024Grounding Continuous Representations in Geometry: Equivariant Neural Fieldscited by 19
  21. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 19
  22. 2022Learning Deep Time-index Models for Time Series Forecastingcited by 18
  23. 2024DDMI: Domain-Agnostic Latent Diffusion Models for Synthesizing High-Quality Implicit Neural Representationscited by 16
  24. 2024Quantum Implicit Neural Representationscited by 16
  25. 2024Monomial Matrix Group Equivariant Neural Functional Networkscited by 15
  26. 2025Stochastic Process Learning via Operator Flow Matchingcited by 14
  27. 2023Globally injective and bijective neural operatorscited by 13
  28. 2022Points2NeRF: Generating Neural Radiance Fields from 3D point cloudcited by 11
  29. 2023Manifold Diffusion Fieldscited by 11
  30. 2025Mesh-Informed Neural Operator : A Transformer Generative Approachcited by 11
  31. 2023Generative Neural Fields by Mixtures of Neural Implicit Functionscited by 10
  32. 2023Neural Field Convolutions by Repeated Differentiationcited by 9
  33. 2024Universal Functional Regression with Neural Operator Flowscited by 9
  34. 2023Revisiting Implicit Neural Representations in Low-Level Visioncited by 8
  35. 2023Tracing Hyperparameter Dependencies for Model Parsing via Learnable Graph Pooling Networkcited by 8
  36. 2024Hyperspectral and multispectral image fusion with arbitrary resolution through self-supervised representationscited by 8
  37. 2023HyperNeRFGAN: Hypernetwork approach to 3D NeRF GANcited by 7
  38. 2023Deep Stochastic Processes via Functional Markov Transition Operatorscited by 7

50 most cited of 89 All 89 (JSON)