Stable Diffusion's intrinsic dimension tracks prompt perplexity in bottleneck layers

Kvinge et al. estimate the intrinsic dimension of Stable Diffusion's internal representations at bottleneck and latent layers across denoising steps and prompts, finding prompt choice substantially shifts the measured ID [kvinge-etal-2023-exploring-representation-manifolds-of-stable-diffusion] In certain bottleneck layers ID correlates with prompt perplexity (via a surrogate language model), but this correlation vanishes in the latent layers [kvinge-etal-2023-exploring-representation-manifolds-of-stable-diffusion] The representation manifold thus responds to linguistic complexity differently depending on where along the architecture it is measured [kvinge-etal-2023-exploring-representation-manifolds-of-stable-diffusion]