HEART: Hyperspherical Embedding Alignment via Kent-Representation Traversal in Diffusion Models
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arXiv
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| Natura: | Preprint |
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2026
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| author | Roy, Arani Biswas, Shristi Das Roy, Kaushik |
| author_facet | Roy, Arani Biswas, Shristi Das Roy, Kaushik |
| contents | 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 control 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. 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 spherical, can unlock fast, and controllable image generation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07973 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | HEART: Hyperspherical Embedding Alignment via Kent-Representation Traversal in Diffusion Models Roy, Arani Biswas, Shristi Das Roy, Kaushik Computer Vision and Pattern Recognition 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 control 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. 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 spherical, can unlock fast, and controllable image generation. |
| title | HEART: Hyperspherical Embedding Alignment via Kent-Representation Traversal in Diffusion Models |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2605.07973 |