# Hybrid Generative Models for Two-Dimensional Datasets

arXiv: https://arxiv.org/abs/2106.00203 · HTML: https://mlsanity.com/paper/2106.00203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 1 Jun 2021.

## Builds on (most cited first, 13 of 13)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [Generative Adversarial Networks for Extreme Learned Image Compression](https://mlsanity.com/paper/1804.02958/) (2018)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/1809.09087/) (2018)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [Non-Adversarial Image Synthesis with Generative Latent Nearest Neighbors](https://mlsanity.com/paper/1812.08985/) (2018)
- [SWAGAN: A Style-based Wavelet-driven Generative Model](https://mlsanity.com/paper/2102.06108/) (2021)

## Abstract (arXiv)

Two-dimensional array-based datasets are pervasive in a variety of domains. Current approaches for generative modeling have typically been limited to conventional image datasets and performed in the pixel domain which do not explicitly capture the correlation between pixels. Additionally, these approaches do not extend to scientific and other applications where each element value is continuous and is not limited to a fixed range. In this paper, we propose a novel approach for generating two-dimensional datasets by moving the computations to the space of representation bases and show its usefulness for two different datasets, one from imaging and another from scientific computing. The proposed approach is general and can be applied to any dataset, representation basis, or generative model. We provide a comprehensive performance comparison of various combinations of generative models and representation basis spaces. We also propose a new evaluation metric which captures the deficiency of generating images in pixel space.