What Secrets Do Your Manifolds Hold? Towards Self-Assessment of Generative Models

As the capabilities of Deep Generative Models improve, thorough evaluation of their generation performance and biases become crucial. Human evaluation remains the gold standard but its cost makes assessing generative models, particularly text-to-image foundation models like Stable Diffusion, prohibitively expensive.
In this paper, we explore the feasibility of using geometric descriptors of the data manifold for self-assessment, therefore, requiring only the network architecture and its weights. We propose three theoretically inspired geometric descriptors – local scaling (ψ), local rank (ν) and local complexity (δ) – that can characterize the local properties of the learned data manifold for a given latent vector. Our proposed measures can be used to quantify (i) uncertainty, (ii) local dimensionality of the manifold as well as (iii) smoothness of the learned generative model manifold. We demonstrate the relationship of our manifold descriptors with generation quality and diversity. Further, we present evidence of geometric bias between sub-populations under the generated distribution for Beta-VAE and Stable Diffusion. We believe that our proposed framework will allow future research into understanding how bias manifests through the learned data manifold of foundation models.