# Geometrical Insights for Implicit Generative Modeling

arXiv: https://arxiv.org/abs/1712.07822 · HTML: https://mlsanity.com/paper/1712.07822/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2017.

## Built on by (most cited first, 7 of 7)

- [KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Support](https://mlsanity.com/paper/2106.08929/) (2021)
- [Survival Mixture Density Networks](https://mlsanity.com/paper/2208.10759/) (2022)
- [Learning Energy Networks with Generalized Fenchel-Young Losses](https://mlsanity.com/paper/2205.09589/) (2022)
- [Theoretical Analysis of Engression and Reverse Markov Engression](https://mlsanity.com/paper/2606.01002/) (2026)
- [Resistance Distance and Linearized Optimal Transport on Graphs](https://mlsanity.com/paper/2404.15261/) (2024)
- [On The Energy Statistics of Feature Maps in Pruning of Neural Networks with Skip-Connections](https://mlsanity.com/paper/2201.11209/) (2022)
- [Touring sampling with pushforward maps](https://mlsanity.com/paper/2311.13845/) (2023)

## Abstract (arXiv)

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by these distances on the space of probability measures reveals interesting differences. In particular, we can establish surprising approximate global convergence guarantees for the 1-Wasserstein distance,even when the parametric generator has a nonconvex parametrization.