# All Roads Lead to Rome? Exploring Representational Similarities Between Latent Spaces of Generative Image Models

arXiv: https://arxiv.org/abs/2407.13449 · HTML: https://mlsanity.com/paper/2407.13449/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Diffusion Models already have a Semantic Latent Space](https://mlsanity.com/paper/2210.10960/) (2022)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Diffusion-GAN: Training GANs with Diffusion](https://mlsanity.com/paper/2206.02262/) (2022)
- [Comparing the latent space of generative models](https://mlsanity.com/paper/2207.06812/) (2022)

## Built on by (most cited first, 2 of 2)

- [The Universal Normal Embedding](https://mlsanity.com/paper/2603.21786/) (2026)
- [InstantFusion: A Shared Latent Interface for Heterogeneous Image Generators](https://mlsanity.com/paper/2610.13944/) (2026)

## Abstract (arXiv)

Do different generative image models secretly learn similar underlying representations? We investigate this by measuring the latent space similarity of four different models: VAEs, GANs, Normalizing Flows (NFs), and Diffusion Models (DMs). Our methodology involves training linear maps between frozen latent spaces to "stitch" arbitrary pairs of encoders and decoders and measuring output-based and probe-based metrics on the resulting "stitched'' models. Our main findings are that linear maps between latent spaces of performant models preserve most visual information even when latent sizes differ; for CelebA models, gender is the most similarly represented probe-able attribute. Finally we show on an NF that latent space representations converge early in training.