# Optimal transport maps for distribution preserving operations on latent spaces of Generative Models

arXiv: https://arxiv.org/abs/1711.01970 · HTML: https://mlsanity.com/paper/1711.01970/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2017.

## Built on by (most cited first, 13 of 13)

- [VTAE: Variational Transformer Autoencoder with Manifolds Learning](https://mlsanity.com/paper/2304.00948/) (2023)
- [Model Extraction and Defenses on Generative Adversarial Networks](https://mlsanity.com/paper/2101.02069/) (2021)
- [Revisiting Latent-Space Interpolation via a Quantitative Evaluation Framework](https://mlsanity.com/paper/2110.06421/) (2021)
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- [Spider GAN: Leveraging Friendly Neighbors to Accelerate GAN Training](https://mlsanity.com/paper/2305.07613/) (2023)
- [Variational Auto Encoder Gradient Clustering](https://mlsanity.com/paper/2105.06246/) (2021)
- [Synthetic data enables faster annotation and robust segmentation for multi-object grasping in clutter](https://mlsanity.com/paper/2401.13405/) (2024)
- [Search at the Cost of Sampling: Nearly-Instant Latent Space Bayesian Optimization](https://mlsanity.com/paper/2609.19476/) (2026)
- [Particle Filter Bridge Interpolation](https://mlsanity.com/paper/2103.14963/) (2021)
- [Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias](https://mlsanity.com/paper/2606.30821/) (2026)
- [Play Like Champions: Counterfactual Feedback Generation in Latent Space](https://mlsanity.com/paper/2607.00190/) (2026)
- [Texture Interpolation as Texton Matching](https://mlsanity.com/paper/2610.18655/) (2026)

## Abstract (arXiv)

Generative models such as Variational Auto Encoders (VAEs) and Generative Adversarial Networks (GANs) are typically trained for a fixed prior distribution in the latent space, such as uniform or Gaussian. After a trained model is obtained, one can sample the Generator in various forms for exploration and understanding, such as interpolating between two samples, sampling in the vicinity of a sample or exploring differences between a pair of samples applied to a third sample. In this paper, we show that the latent space operations used in the literature so far induce a distribution mismatch between the resulting outputs and the prior distribution the model was trained on. To address this, we propose to use distribution matching transport maps to ensure that such latent space operations preserve the prior distribution, while minimally modifying the original operation. Our experimental results validate that the proposed operations give higher quality samples compared to the original operations.