# Discond-VAE: Disentangling Continuous Factors from the Discrete

arXiv: https://arxiv.org/abs/2009.08039 · HTML: https://mlsanity.com/paper/2009.08039/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2020.

## Built on by (most cited first, 4 of 4)

- [Disentanglement of Correlated Factors via Hausdorff Factorized Support](https://mlsanity.com/paper/2210.07347/) (2022)
- [Benchmarks, Algorithms, and Metrics for Hierarchical Disentanglement](https://mlsanity.com/paper/2102.05185/) (2021)
- [Unsupervised Causal Binary Concepts Discovery with VAE for Black-box Model Explanation](https://mlsanity.com/paper/2109.04518/) (2021)
- [Rethinking Disentanglement under Dependent Factors of Variation](https://mlsanity.com/paper/2408.07016/) (2024)

## Abstract (arXiv)

In the real-world data, there are common variations shared by all classes (e.g. category label) and exclusive variations of each class. We propose a variant of VAE capable of disentangling both of these variations. To represent these generative factors of data, we introduce two sets of continuous latent variables, private variable and public variable. Our proposed framework models the private variable as a Mixture of Gaussian and the public variable as a Gaussian, respectively. Each mode of the private variable is responsible for a class of the discrete variable. Most of the previous attempts to integrate the discrete generative factors to disentanglement assume statistical independence between the continuous and discrete variables. Our proposed model, which we call Discond-VAE, DISentangles the class-dependent CONtinuous factors from the Discrete factors by introducing the private variables. The experiments show that Discond-VAE can discover the private and public factors from data. Moreover, even under the dataset with only public factors, Discond-VAE does not fail and adapts the private variables to represent the public factors.