mlsanityData to 14 Oct 2026

Emerging Convolutions for Generative Normalizing Flows

arXiv 1901.11137 ↗First posted 30 Jan 2019cs.LG stat.MLcited by 31

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Abstract (arXiv)

Generative flows are attractive because they admit exact likelihood optimization and efficient image synthesis. Recently, Kingma & Dhariwal (2018) demonstrated with Glow that generative flows are capable of generating high quality images. We generalize the 1 x 1 convolutions proposed in Glow to invertible d x d convolutions, which are more flexible since they operate on both channel and spatial axes. We propose two methods to produce invertible convolutions that have receptive fields identical to standard convolutions: Emerging convolutions are obtained by chaining specific autoregressive convolutions, and periodic convolutions are decoupled in the frequency domain. Our experiments show that the flexibility of d x d convolutions significantly improves the performance of generative flow models on galaxy images, CIFAR10 and ImageNet.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). First posted on arXiv 30 Jan 2019.

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Citing papers per year: 2021: 12; 2022: 5; 2023: 5; 2024: 5; 2025: 4.

31 papers.

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  1. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 252
  2. 2023A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPTcited by 224
  3. 2022Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Seriescited by 42
  4. 2021Implicit Normalizing Flowscited by 28
  5. 2024Maximum Entropy Reinforcement Learning via Energy-Based Normalizing Flowcited by 26
  6. 2021MolGrow: A Graph Normalizing Flow for Hierarchical Molecular Generationcited by 22
  7. 2021Generative Flows with Invertible Attentionscited by 13
  8. 2022ButterflyFlow: Building Invertible Layers with Butterfly Matricescited by 12
  9. 2024Jet: A Modern Transformer-Based Normalizing Flowcited by 12
  10. 2023Training Energy-Based Normalizing Flow with Score-Matching Objectivescited by 6
  11. 2021Invertible Attentioncited by 5
  12. 2022Flowification: Everything is a Normalizing Flowcited by 5
19 more
  1. 2021Multi-Resolution Continuous Normalizing Flowscited by 4
  2. 2021CInC Flow: Characterizable Invertible 3x3 Convolutioncited by 4
  3. 2021Funnels: Exact maximum likelihood with dimensionality reductioncited by 4
  4. 2022Transformer-Based Speech Synthesizer Attribution in an Open Set Scenariocited by 4
  5. 2021Flow-based Spatio-Temporal Structured Prediction of Motion Dynamicscited by 3
  6. 2024Segment-Level Road Obstacle Detection Using Visual Foundation Model Priors and Likelihood Ratioscited by 3
  7. 2022Orthonormal Convolutions for the Rotation Based Iterative Gaussianizationcited by 2
  8. 2023FInC Flow: Fast and Invertible k × k Convolutions for Normalizing Flowscited by 2
  9. 2021PixelPyramids: Exact Inference Models from Lossless Image Pyramidscited by 1
  10. 2021Characteristic Neural Ordinary Differential Equationscited by 1
  11. 2024VeriFlow: Modeling Distributions for Neural Network Verificationcited by 1
  12. 2025CDFlow: Building Invertible Layers with Circulant and Diagonal Matricescited by 1
  13. 2021Delta-GAN-Encoder: Encoding Semantic Changes for Explicit Image Editing, using Few Synthetic Samplescited by 0
  14. 2023Invertible Convolution with Symmetric Paddingscited by 0
  15. 2023MixerFlow: MLP-Mixer meets Normalising Flowscited by 0
  16. 2024Parallel Backpropagation for Inverse of a Convolution with Application to Normalizing Flowscited by 0
  17. 2025On Uniformly Scaling Flows: A Density-Aligned Approach to Deep One-Class Classificationcited by 0
  18. 2025MAGIC-Flow: Multiscale Adaptive Conditional Flows for Generation and Interpretable Classificationcited by 0
  19. 2025Amortized Inference of Multi-Modal Posteriors using Likelihood-Weighted Normalizing Flowscited by 0