# Generative Flows with Matrix Exponential

arXiv: https://arxiv.org/abs/2007.09651 · HTML: https://mlsanity.com/paper/2007.09651/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2020.

## Built on by (most cited first, 6 of 6)

- [Equivariant Finite Normalizing Flows](https://mlsanity.com/paper/2110.08649/) (2021)
- [Multi-Resolution Continuous Normalizing Flows](https://mlsanity.com/paper/2106.08462/) (2021)
- [CFASL: Composite Factor-Aligned Symmetry Learning for Disentanglement in Variational AutoEncoder](https://mlsanity.com/paper/2401.08897/) (2024)
- [Gradients of Functions of Large Matrices](https://mlsanity.com/paper/2405.17277/) (2024)
- [Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs](https://mlsanity.com/paper/2502.03740/) (2025)
- [Improving Matrix Exponential for Generative AI Flows: A Taylor-Based Approach Beyond Paterson--Stockmeyer](https://mlsanity.com/paper/2512.20777/) (2025)

## Abstract (arXiv)

Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix exponential is a map from matrices to invertible matrices, this property is suitable for generative flows. Based on matrix exponential, we propose matrix exponential coupling layers that are a general case of affine coupling layers and matrix exponential invertible 1 x 1 convolutions that do not collapse during training. And we modify the networks architecture to make trainingstable andsignificantly speed up the training process. Our experiments show that our model achieves great performance on density estimation amongst generative flows models.