# Atlas flow : compatible local structures on the manifold

arXiv: https://arxiv.org/abs/2210.14149 · HTML: https://mlsanity.com/paper/2210.14149/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 24 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection](https://mlsanity.com/paper/1607.00148/) (2016)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Riemannian Continuous Normalizing Flows](https://mlsanity.com/paper/2006.10605/) (2020)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Normalizing Flows on Tori and Spheres](https://mlsanity.com/paper/2002.02428/) (2020)
- [Normalizing Flows on Riemannian Manifolds](https://mlsanity.com/paper/1611.02304/) (2016)
- [Topologically-Informed Atlas Learning](https://mlsanity.com/paper/2110.00429/) (2021)

## Built on by (most cited first, 1 of 1)

- [Atlas Gaussian processes on restricted domains and point clouds](https://mlsanity.com/paper/2511.15822/) (2025)

## Abstract (arXiv)

In this paper, we focus on the intersections of a manifold's local structures to analyze the global structure of a manifold. We obtain local regions on data manifolds such as the latent space of StyleGAN2, using Mapper, a tool from topological data analysis. We impose gluing compatibility conditions on overlapping local regions, which guarantee that the local structures can be glued together to the global structure of a manifold. We propose a novel generative flow model called Atlas flow that uses compatibility to reattach the local regions. Our model shows that the generating processes perform well on synthetic dataset samples of well-known manifolds with noise. Furthermore, we investigate the style vector manifold of StyleGAN2 using our model.