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Synthesizing high-quality 3D head textures is crucial for gaming, virtual reality, and digital humans. Achieving seamless 360° textures typically requires expensive multi-view datasets with precise tracking. However, traditional methods struggle without back-view data or precise geometry, especially for human heads, where even minor inconsistencies disrupt realism. We introduce HairFree, an unsupervised texturing framework guided by textual descriptions and 2D diffusion priors, producing high-consistency 360° bald head textures—including non-human skin with fine details—without any texture, back-view, bald, non-human, or synthetic training data. We fine-tune a diffusion prior on a dataset of mostly frontal faces, conditioned on predicted 3D head geometry and face parsing. During inference, HairFree uses precise skin masks and 3D FLAME geometry as input conditioning, ensuring high 3D consistency and alignment. We synthesize the full 360° texture by first generating a frontal RGB image aligned to the 3D FLAME pose and mapping it to UV space. As the virtual camera moves, we inpaint and merge missing regions. A built-in semantic prior enables precise region separation—particularly for isolating and removing hair—allowing seamless integration with various assets like customizable 3D hair, eyeglasses, jewelry, etc. We evaluate HairFree quantitatively and qualitatively, demonstrating its superiority over state-of-the-art 3D head avatar generation methods. https://hairfree.is.tue.mpg.de/