mlsanityData to 7 Oct 2026

Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces

arXiv 2205.14627 ↗First posted 29 May 2022stat.ML cs.LGcited by 6

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Abstract (arXiv)

In this work, we present and study Continuous Generative Neural Networks (CGNNs), namely, generative models in the continuous setting: the output of a CGNN belongs to an infinite-dimensional function space. The architecture is inspired by DCGAN, with one fully connected layer, several convolutional layers and nonlinear activation functions. In the continuous L2 setting, the dimensions of the spaces of each layer are replaced by the scales of a multiresolution analysis of a compactly supported wavelet. We present conditions on the convolutional filters and on the nonlinearity that guarantee that a CGNN is injective. This theory finds applications to inverse problems, and allows for deriving Lipschitz stability estimates for (possibly nonlinear) infinite-dimensional inverse problems with unknowns belonging to the manifold generated by a CGNN. Several numerical simulations, including signal deblurring, illustrate and validate this approach.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 33 of its 90 references that are in the map. First posted on arXiv 29 May 2022.

Builds on

33 of 90 references.

References · 33

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21 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 1; 2025: 0; 2026: 1.

6 papers.

  1. 2023Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learningcited by 57
  2. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generationcited by 37
  3. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 16
  4. 2023Globally injective and bijective neural operatorscited by 13
  5. 2024Can neural operators always be continuously discretized?cited by 2
  6. 2026Infinite dimensional generative sensingcited by 0