# Transport f divergences

arXiv: https://arxiv.org/abs/2504.15515 · HTML: https://mlsanity.com/paper/2504.15515/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 21 references that are in the map.
- First posted on arXiv 22 Apr 2025.

## Builds on (most cited first, 2 of 2)

- [Relaxed Wasserstein with Applications to GANs](https://mlsanity.com/paper/1705.07164/) (2017)
- [Transport information Bregman divergences](https://mlsanity.com/paper/2101.01162/) (2021)

## Abstract (arXiv)

We define a class of divergences to measure differences between probability density functions in one-dimensional sample space. The construction is based on the convex function with the Jacobi operator of mapping function that pushforwards one density to the other. We call these information measures transport f-divergences. We present several properties of transport f-divergences, including invariances, convexities, variational formulations, and Taylor expansions in terms of mapping functions. Examples of transport f-divergences in generative models are provided.