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.
@article{arxiv.2407.13449,
title = {All Roads Lead to Rome? Exploring Representational Similarities Between Latent Spaces of Generative Image Models},
author = {Charumathi Badrinath and Usha Bhalla and Alex Oesterling and Suraj Srinivas and Himabindu Lakkaraju},
journal= {arXiv preprint arXiv:2407.13449},
year = {2024}
}