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

TL;DR

This paper investigates whether different generative image models learn similar underlying representations by measuring latent space similarities across VAEs, GANs, NFs, and DMs, revealing that these models often preserve visual information and share representations.

Contribution

The study introduces a methodology to compare latent spaces of various generative models using linear mappings and output-based metrics, revealing commonalities in their learned representations.

Findings

Linear maps preserve visual information across models.

Gender is a consistently similar attribute in CelebA models.

Latent representations in NFs converge early in training.

Abstract

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.