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

arXiv: https://arxiv.org/abs/2605.07973 · HTML: https://mlsanity.com/paper/2605.07973/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 16 of its 22 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 16 of 16)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Concept Sliders: LoRA Adaptors for Precise Control in Diffusion Models](https://mlsanity.com/paper/2311.12092/) (2023)
- [LEDITS++: Limitless Image Editing using Text-to-Image Models](https://mlsanity.com/paper/2311.16711/) (2023)
- [The Double-Ellipsoid Geometry of CLIP](https://mlsanity.com/paper/2411.14517/) (2024)
- [Continuous, Subject-Specific Attribute Control in T2I Models by Identifying Semantic Directions](https://mlsanity.com/paper/2403.17064/) (2024)
- [CURE: Concept Unlearning via Orthogonal Representation Editing in Diffusion Models](https://mlsanity.com/paper/2505.12677/) (2025)
- [Prompt Sliders for Fine-Grained Control, Editing and Erasing of Concepts in Diffusion Models](https://mlsanity.com/paper/2409.16535/) (2024)
- [Text Slider: Efficient and Plug-and-Play Continuous Concept Control for Image/Video Synthesis via LoRA Adapters](https://mlsanity.com/paper/2509.18831/) (2025)
- [Now You See It, Now You Don't - Instant Concept Erasure for Safe Text-to-Image and Video Generation](https://mlsanity.com/paper/2511.18684/) (2025)
- [Modelling of directional data using Kent distributions](https://mlsanity.com/paper/1506.08105/) (2015)

## Abstract (arXiv)

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.