The Geometry of Generative Latents: Navigability and Invertibility

Latent diffusion models depend critically on the geometry of the space in which generation is performed. A persistent challenge in VAE- and RAE-based systems is that detail-rich latents improve inversion but can make diffusion dynamics harder to model. We study this reconstruction–generation tension through two geometric properties: invertibility, which measures how faithfully images can be decoded, and navigability, which measures how smoothly diffusion can transport mass in latent space. We introduce a tangent-projected transport complexity that isolates score-field variation along data-manifold directions and highlights intrinsic dimension, curvature, reach, and enrichment direction as geometry-side factors in diffusion difficulty. This analysis yields the Normal Projection Principle: when enriching a navigable base latent, added detail should lie in the normal space so that the base coordinate is preserved under tubular projection, whereas tangential residuals shift that coordinate at first order. Motivated by this principle, we introduce NormFuse, an RAE-based text-to-image model that fuses frozen multi-layer DINOv3 features through normal-space projection. Controlled and large-scale matched comparisons show that NormFuse preserves reconstruction benefits while avoiding the generation degradation of unconstrained fusion, supporting latent geometry as both an explanatory lens and a practical design rule.