# GMapLatent: Geometric Mapping in Latent Space

arXiv: https://arxiv.org/abs/2503.23407 · HTML: https://mlsanity.com/paper/2503.23407/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 30 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Unsupervised Image-to-Image Translation Networks](https://mlsanity.com/paper/1703.00848/) (2017)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [Wasserstein-2 Generative Networks](https://mlsanity.com/paper/1909.13082/) (2019)
- [Transformation Consistency Regularization- A Semi-Supervised Paradigm for Image-to-Image Translation](https://mlsanity.com/paper/2007.07867/) (2020)
- [GLASS: Geometric Latent Augmentation for Shape Spaces](https://mlsanity.com/paper/2108.03225/) (2021)
- [Deep Learning Autoencoder Approach for Handwritten Arabic Digits Recognition](https://mlsanity.com/paper/1706.06720/) (2017)
- [Prototypical Partial Optimal Transport for Universal Domain Adaptation](https://mlsanity.com/paper/2408.01089/) (2024)

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

- [Complex variational autoencoders admit K"ahler structure](https://mlsanity.com/paper/2511.15172/) (2025)

## Abstract (arXiv)

Cross-domain generative models based on encoder-decoder AI architectures have attracted much attention in generating realistic images, where domain alignment is crucial for generation accuracy. Domain alignment methods usually deal directly with the initial distribution; however, mismatched or mixed clusters can lead to mode collapse and mixture problems in the decoder, compromising model generalization capabilities. In this work, we innovate a cross-domain alignment and generation model that introduces a canonical latent space representation based on geometric mapping to align the cross-domain latent spaces in a rigorous and precise manner, thus avoiding mode collapse and mixture in the encoder-decoder generation architectures. We name this model GMapLatent. The core of the method is to seamlessly align latent spaces with strict cluster correspondence constraints using the canonical parameterizations of cluster-decorated latent spaces. We first (1) transform the latent space to a canonical parameter domain by composing barycenter translation, optimal transport merging and constrained harmonic mapping, and then (2) compute geometric registration with cluster constraints over the canonical parameter domains. This process realizes a bijective (one-to-one and onto) mapping between newly transformed latent spaces and generates a precise alignment of cluster pairs. Cross-domain generation is then achieved through the aligned latent spaces embedded in the encoder-decoder pipeline. Experiments on gray-scale and color images validate the efficiency, efficacy and applicability of GMapLatent, and demonstrate that the proposed model has superior performance over existing models.