HEART: Hyperspherical Embedding Alignment via Kent-Representation Traversal in Diffusion Models

Text-to-image diffusion models can generate visually stunning images, yet controlling what appears and how it appears- remains surprisingly difficult, especially when operating solely within the constraints of the text-conditioning space. For example, changing a subject or adjusting an attribute often leads to unintended side effects, such as altered backgrounds or distorted details. This is because most existing text-based editing methods treat the embedding space as Euclidean and apply simple linear transformations, which do not reflect how semantic concepts are actually organized. In this work, we take a step back and ask: what is the true geometry of these embeddings? We find that text encoder representations lie on a hypersphere, where concepts are not linear directions but structured, anisotropic distributions better captured by Kent distributions. This geometric perspective reveals why linear edits lead to entanglement and loss of control. Building on this insight, we propose HEART, a training-free framework that performs Kent-aware geodesic transformations directly on the hypersphere. By respecting the underlying geometry, HEART enables intuitive and precise edits - such as consistent subject replacement and fine-grained attribute control - while preserving the original scene. Importantly, HEART requires no finetuning, inversion, or optimization, and generalizes across diffusion model architectures. Our results show that a simple shift in perspective, from linear to geometric, can unlock fast, reliable, and controllable image generation.