# Generative Flows with Invertible Attentions

arXiv: https://arxiv.org/abs/2106.03959 · HTML: https://mlsanity.com/paper/2106.03959/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 64 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [AttnGAN: Fine-Grained Text to Image Generation with Attentional Generative Adversarial Networks](https://mlsanity.com/paper/1711.10485/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)

## Built on by (most cited first, 13 of 13)

- [On the Robustness of Normalizing Flows for Inverse Problems in Imaging](https://mlsanity.com/paper/2212.04319/) (2022)
- [Concurrent Misclassification and Out-of-Distribution Detection for Semantic Segmentation via Energy-Based Normalizing Flow](https://mlsanity.com/paper/2305.09610/) (2023)
- [Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction](https://mlsanity.com/paper/2405.18527/) (2024)
- [MANGO: Multimodal Attention-based Normalizing Flow Approach to Fusion Learning](https://mlsanity.com/paper/2508.10133/) (2025)
- [Neural Diffeomorphic Non-uniform B-spline Flows](https://mlsanity.com/paper/2304.04555/) (2023)
- [Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems](https://mlsanity.com/paper/2505.09528/) (2025)
- [Hierarchical Disentangled Representation for Invertible Image Denoising and Beyond](https://mlsanity.com/paper/2301.13358/) (2023)
- [Probabilistic Forecasting of Irregular Time Series via Conditional Flows](https://mlsanity.com/paper/2402.06293/) (2024)
- [How Image Generation Helps Visible-to-Infrared Person Re-Identification?](https://mlsanity.com/paper/2210.01585/) (2022)
- [MixerFlow: MLP-Mixer meets Normalising Flows](https://mlsanity.com/paper/2310.16777/) (2023)
- [Dimension Mixer: Group Mixing of Input Dimensions for Efficient Function Approximation](https://mlsanity.com/paper/2311.18735/) (2023)
- [Generalizing Dynamics Modeling More Easily from Representation Perspective](https://mlsanity.com/paper/2603.22655/) (2026)
- [α-Graph: Attention-Infused Normalizing Flow Approach to Tractable Graph Modeling](https://mlsanity.com/paper/2609.07961/) (2026)

## Abstract (arXiv)

Flow-based generative models have shown an excellent ability to explicitly learn the probability density function of data via a sequence of invertible transformations. Yet, learning attentions in generative flows remains understudied, while it has made breakthroughs in other domains. To fill the gap, this paper introduces two types of invertible attention mechanisms, i.e., map-based and transformer-based attentions, for both unconditional and conditional generative flows. The key idea is to exploit a masked scheme of these two attentions to learn long-range data dependencies in the context of generative flows. The masked scheme allows for invertible attention modules with tractable Jacobian determinants, enabling its seamless integration at any positions of the flow-based models. The proposed attention mechanisms lead to more efficient generative flows, due to their capability of modeling the long-term data dependencies. Evaluation on multiple image synthesis tasks shows that the proposed attention flows result in efficient models and compare favorably against the state-of-the-art unconditional and conditional generative flows.