Title: 3DGH: 3D Head Generation with Composable Hair and Face

URL Source: https://arxiv.org/html/2506.20875

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###### Abstract.

We present 3DGH, an unconditional generative model for 3D human heads with composable hair and face components. Unlike previous work that entangles the modeling of hair and face, we propose to separate them using a novel data representation with template-based 3D Gaussian Splatting, in which deformable hair geometry is introduced to capture the geometric variations across different hairstyles. Based on this data representation, we design a 3D GAN-based architecture with dual generators and employ a cross-attention mechanism to model the inherent correlation between hair and face. The model is trained on synthetic renderings using carefully designed objectives to stabilize training and facilitate hair-face separation. We conduct extensive experiments to validate the design choice of 3DGH, and evaluate it both qualitatively and quantitatively by comparing with several state-of-the-art 3D GAN methods, demonstrating its effectiveness in unconditional full-head image synthesis and composable 3D hairstyle editing. More details will be available on our project page: [https://c-he.github.io/projects/3dgh/](https://c-he.github.io/projects/3dgh/).

Facial Modeling, Hair Modeling, Generative 3D Modeling

††copyright: cc††journal: TOG††journalyear: 2025††journalvolume: 44††journalnumber: 4††publicationmonth: 8††price: ††doi: 10.1145/3731211††ccs: Computing methodologies Shape representations††ccs: Computing methodologies Appearance and texture representations![Image 1: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/teaser.png)

Figure 1. 3DGH: Our method generates 3D head representations that can be rendered at 360∘superscript 360 360^{\circ}360 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT with photorealistic rendering quality and high-fidelity geometry based on 3D Gaussian Splatting. The generated heads include composable hair and face components, enabling 3D hairstyle editing with multi-view consistency.

1. Introduction
---------------

The generation of high-quality 3D human heads has broad applications in digital avatars, telepresence, immersive gaming, and so on. Recently, many generative models have been proposed to facilitate 3D head generation by integrating geometry-aware representations with well-studied 2D image generative models[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4); Li et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib25); Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8); Kirschstein et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib24)].

Despite their advancements, existing methods often overlook the inherent diversity difference between hair and face, where faces of different identities still share a similarity in facial features while hairstyles are significantly more diverse. As a result, most prior 3D head generative models, which entangle the modeling of hair and face, are unsuitable for finer-grained editing tasks such as hair transfer. Although some approaches enable editability for 2D images[Nikolaev et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib33); Richardson et al., [2021](https://arxiv.org/html/2506.20875v1#bib.bib39)] or geometry-aware representations like tri-plane[Sun et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib45); Gao et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib12)], they either suffer from view inconsistency in 3D applications or are inadequate for modeling 3D hair, particularly in back-of-head regions. To address these limitations, we introduce 3DGH, a generative model for 3D full-head synthesis that supports composable hair and face components.

To train a generative model that supports compositionality, there are two key issues we need to address: (1) first, we need to ensure a clear separation between hair and face to disentangle these components, and meanwhile, (2) we need to respect their inherent correlation, as observed in real-world patterns where male faces are predominantly associated with short hairstyles, while female faces typically feature medium to long hairstyles. To tackle these challenges, we propose a novel data representation with template-based 3D Gaussian Splatting (3DGS), in which two separate mesh templates are involved to model the overall structure of hair and face with 3D Gaussians spawned on their 2D u⁢v 𝑢 𝑣 uv italic_u italic_v texture maps. To capture the geometric variations among different hairstyles, we make the hair geometry itself deformable through PCA-based linear blend shapes fitted from multi-view facial capture data. This data representation then drives the design of our network architecture, which employs dual branches of StyleGAN2[Karras et al., [2020](https://arxiv.org/html/2506.20875v1#bib.bib21)] generators to independently generate hair and face Gaussians. A cross-attention mechanism[Vaswani et al., [2017](https://arxiv.org/html/2506.20875v1#bib.bib46)] is introduced to carefully model the inherent correlation between hair and face, ensuring coherent and realistic outputs. The model is trained using a comprehensive objective that combines adversarial loss, reconstruction terms, and regularization terms, all carefully designed to stabilize training and facilitate effective hair-face separation.

We train our model using synthetic renderings from PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)]. After training on 25⁢m 25 𝑚 25m 25 italic_m images, we obtain a 3D generative model capable of producing diverse 3D heads with composable hair and face components. We evaluate the model both qualitatively and quantitatively, demonstrating its effectiveness in unconditional full-head image synthesis and composable 3D hairstyle editing through comparisons with several state-of-the-art 3D GAN methods.

In summary, our contributions are as follows:

*   •
We propose 3DGH, a Gaussian-based 3D GAN for human heads that supports composable hair and face components.

*   •
We introduce a novel data representation that utilizes separate template meshes for hair and face, with deformable hair geometry to capture diverse hairstyles.

*   •
We design network architectures and training objectives to model hair-face separation and correlation, demonstrating their effectiveness through qualitative and quantitative comparisons with state-of-the-art 3D GAN methods.

2. Related Work
---------------

In this section, we review prior work in 3D head generative models, conditional image editing methods, and 3D hair modeling approaches.

### 2.1. 3D Generative Adversarial Networks

3D Generative Adversarial Networks (GANs) are able to leverage adversarial training to develop generative models for 3D representations from 2D image collections. Early approaches primarily employed implicit 3D representations, such as NeRF[Mildenhall et al., [2020](https://arxiv.org/html/2506.20875v1#bib.bib31)], to render either raw pixels[Chan et al., [2021](https://arxiv.org/html/2506.20875v1#bib.bib9); Schwarz et al., [2020](https://arxiv.org/html/2506.20875v1#bib.bib42)] or features subsequently decoded by a CNN-based neural renderer[Niemeyer and Geiger, [2021](https://arxiv.org/html/2506.20875v1#bib.bib32); Xue et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib54)]. However, the high computational cost for volume rendering posed challenges for training high-resolution GANs. To address these limitations, more recent works have adapted successful 2D GAN architectures to generate compact intermediate representations, which can then be lifted to 3D[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8); Gu et al., [2021](https://arxiv.org/html/2506.20875v1#bib.bib14); Or-El et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib34)]. Among these approaches, the tri-plane representation introduced in EG3D[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8)] has proven to be the most effective for generating diverse and realistic geometry-aware portrait images. Building on this foundation, subsequent works, such as PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)] and SphereHead[Li et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib25)], extend the tri-plane representation for full-head synthesis including back-view head images.

Despite the use of compact intermediate representations, the aforementioned methods typically rely on a 2D super-resolution network to enhance efficiency during training and inference, which may introduce unwanted artifacts in the form of 3D inconsistencies as well as low-resolution geometry. 3D Gaussian Splatting (3DGS) by Kerbl et al.[[2023](https://arxiv.org/html/2506.20875v1#bib.bib22)] provided an alternative direction by utilizing an explicit representation, where a set of 3D Gaussians is optimized from multi-view images using volume splatting[Zwicker et al., [2001](https://arxiv.org/html/2506.20875v1#bib.bib63)]. Although the original 3DGS representation is unstructured, subsequent works such as Gaussian Shell Maps[Abdal et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib2)] and GGHead[Kirschstein et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib24)] have demonstrated strategies to rig Gaussians in an organized manner relative to an underlying template mesh, thereby enabling the training of Gaussian-based 3D GANs for human body and head generations. In this work, we aim at training a similar Gaussian-based 3D GAN for human head generation, while focusing on disentangling the generation of hair and face to enable a composable model through the introduction of novel data representations, network architectures, and training strategies.

### 2.2. Conditional Image Editing

Beyond unconditional generation, GANs are extensively employed to learn mappings from a reference in a source domain to a target domain. Examples include translating semantic masks[Park et al., [2019](https://arxiv.org/html/2506.20875v1#bib.bib37); Zhu et al., [2020](https://arxiv.org/html/2506.20875v1#bib.bib62)] or hand-drawn sketches[Chen et al., [2020](https://arxiv.org/html/2506.20875v1#bib.bib10)] into photorealistic images. A common approach involves using a pre-trained StyleGAN[Karras et al., [2019](https://arxiv.org/html/2506.20875v1#bib.bib20)] generator as a decoder while training customized encoders for different input modalities[Richardson et al., [2021](https://arxiv.org/html/2506.20875v1#bib.bib39)]. Specifically for hairstyle editing, works like[Wei et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib49), [2023](https://arxiv.org/html/2506.20875v1#bib.bib50); Nikolaev et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib33); Zhu et al., [2021](https://arxiv.org/html/2506.20875v1#bib.bib61)] take this approach to train customized encoders to map the input conditions to the latent space of StyleGAN, thereby achieving hairstyle editing with conditions such as reference images and text. While these methods achieve impressive results in 2D image editing, they often struggle to edit geometry-aware content due to the lack of mechanisms for preserving multi-view consistency in the synthesized outputs. To address this limitation, geometry-aware editing approaches such as IDE-3D[Sun et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib45)] and SketchFaceNeRF[Gao et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib12)] train 3D GANs from scratch with additional intermediate 3D representations for conditions such as semantic masks or sketches, thereby ensuring multi-view consistency during editing. A concurrent work by Bilecen et al.[[2024](https://arxiv.org/html/2506.20875v1#bib.bib5)] solves a similar 3D hairstyle editing problem through tri-plane editing. In this work, we adopt a similar approach by rendering hair-face segmentation as additional supervision. Furthermore, we carefully model the correlation between hair and face to enhance editing fidelity while respecting plausible conditional hairstyle distributions observed in the real world.

### 2.3. 3D Hair Modeling

Given the complexity and variability of hair, high-quality 3D hair modeling has remained a persistent challenge for decades, as summarized in the comprehensive survey by Ward et al.[[2007](https://arxiv.org/html/2506.20875v1#bib.bib48)]. To capture high-quality 3D hair models, existing methods typically require high-end capture systems[Paris et al., [2004](https://arxiv.org/html/2506.20875v1#bib.bib36); Jakob et al., [2009](https://arxiv.org/html/2506.20875v1#bib.bib19); Xu et al., [2014](https://arxiv.org/html/2506.20875v1#bib.bib53)] or even CT scanners[Shen et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib43)] to fully recover strand-level details, leaving them inaccessible to most users. With the availability of synthetic 3D hair datasets[Hu et al., [2015](https://arxiv.org/html/2506.20875v1#bib.bib18)], deep learning-based methods have emerged to regress 3D hair models from single-view[Chai et al., [2016](https://arxiv.org/html/2506.20875v1#bib.bib7); Saito et al., [2018](https://arxiv.org/html/2506.20875v1#bib.bib40); Zhou et al., [2018](https://arxiv.org/html/2506.20875v1#bib.bib60); Zheng et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib57); Wu et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib51)] or sparse-view[Zhang et al., [2017](https://arxiv.org/html/2506.20875v1#bib.bib56)] image input, thereby reducing the hardware requirement for 3D hair reconstruction. However, the performance of these data-driven methods is inherently constrained by the quality of their synthetic training datasets, which often lack realism and fail to represent intricate hairstyles, such as afro-textured hair. Recently, more advanced hair capture techniques have been proposed to jointly reconstruct hair geometry and appearance by incorporating neural volumetric primitives[Wang et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib47)] or strand-aligned Gaussians[Luo et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib29); Zakharov et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib55)]. While these methods produce impressive results, creating a large-scale 3D hair dataset with them remains tedious. Consequently, current hair generative models[Zhou et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib59); Sklyarova et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib44); He et al., [2025](https://arxiv.org/html/2506.20875v1#bib.bib15)] continue to rely on synthetic data with augmentations and primarily focus on modeling hair geometry without appearance. In this work, we introduce a hair generative model trained on 2D image collections, capable of modeling both hair geometry and appearance with our deformable hair geometry representation and 3DGS-based rendering framework.

3. Methodology
--------------

![Image 2: Refer to caption](https://arxiv.org/html/2506.20875v1/x1.png)

Figure 2. Overview of 3DGH, which takes a randomly sampled Gaussian noise vector 𝐳 𝐳\mathbf{z}bold_z and camera pose Π Π\Pi roman_Π as input and outputs disentangled 3D head and hair representations, which are modeled as 3D Gaussians spawned on the 2D u⁢v 𝑢 𝑣 uv italic_u italic_v textures of the underlying 3D meshes. The generated 3D Gaussians are rasterized and supervised by the discriminator, with additional reconstruction supervision provided by inferring PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)] using the same noise 𝐳 𝐳\mathbf{z}bold_z and camera pose Π Π\Pi roman_Π. In 3DGH, the hair geometric variation is modeled with a separate geometry mapping network f geom subscript 𝑓 geom f_{\text{geom}}italic_f start_POSTSUBSCRIPT geom end_POSTSUBSCRIPT that produces PCA coefficients for our pre-computed linear blend shapes, and the hair-face correlation is modeled using cross-attention layers to integrate the information from 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT.

An overview of our method is presented in[Fig.2](https://arxiv.org/html/2506.20875v1#S3.F2 "In 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), which integrates 3D Gaussian Splatting with the well-studied 3D GAN formulation. Our approach comprises three key components: a novel data representation that incorporates 3DGS and deformable hair geometry ([Section 3.1](https://arxiv.org/html/2506.20875v1#S3.SS1 "3.1. Data Representation ‣ 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face")), a newly designed network architecture that simultaneously models hair-face separation and correlation ([Section 3.2](https://arxiv.org/html/2506.20875v1#S3.SS2 "3.2. Network Architecture ‣ 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face")), and training objectives specifically crafted to stabilize GAN training and enhance hair-face separation ([Section 3.3](https://arxiv.org/html/2506.20875v1#S3.SS3 "3.3. 3D GAN Training ‣ 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face")).

### 3.1. Data Representation

#### 3.1.1. Template-Based 3D Gaussian Splatting

Since the emergence of 3D Gaussian Splatting[Kerbl et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib22)], it has shown outstanding expressivity in 3D scene representation, in which the scene is represented as a collection of 3D Gaussians, with each Gaussian denoted as 𝐠 i={𝐩 i,𝐪 i,𝐬 i,𝐜 i,o i}∈ℝ 14 subscript 𝐠 𝑖 subscript 𝐩 𝑖 subscript 𝐪 𝑖 subscript 𝐬 𝑖 subscript 𝐜 𝑖 subscript 𝑜 𝑖 superscript ℝ 14\mathbf{g}_{i}=\{\mathbf{p}_{i},\mathbf{q}_{i},\mathbf{s}_{i},\mathbf{c}_{i},o% _{i}\}\in\mathbb{R}^{14}bold_g start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT = { bold_p start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT , bold_q start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT , bold_s start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT , bold_c start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT , italic_o start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT } ∈ blackboard_R start_POSTSUPERSCRIPT 14 end_POSTSUPERSCRIPT, characterized by a set of parameters. These parameters include its center position 𝐩 i∈ℝ 3 subscript 𝐩 𝑖 superscript ℝ 3\mathbf{p}_{i}\in\mathbb{R}^{3}bold_p start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT, rotation parameterized by a unit quaternion 𝐪 i∈ℝ 4 subscript 𝐪 𝑖 superscript ℝ 4\mathbf{q}_{i}\in\mathbb{R}^{4}bold_q start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT, scale factor 𝐬 i∈ℝ 3 subscript 𝐬 𝑖 superscript ℝ 3\mathbf{s}_{i}\in\mathbb{R}^{3}bold_s start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT along each axis, color 𝐜 i∈ℝ 3 subscript 𝐜 𝑖 superscript ℝ 3\mathbf{c}_{i}\in\mathbb{R}^{3}bold_c start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT, and opacity value o i∈ℝ subscript 𝑜 𝑖 ℝ o_{i}\in\mathbb{R}italic_o start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∈ blackboard_R. This collection of 3D Gaussians can then be efficiently rendered through its differentiable tile-based rasterizer given the camera pose Π Π\Pi roman_Π.

Considering the highly unstructured nature of the original 3DGS, we follow previous works[Kirschstein et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib24); Abdal et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib2); Saito et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib41)] and associate each 3D Gaussian with a template mesh with corresponding u⁢v 𝑢 𝑣 uv italic_u italic_v layout. In this way, 3D Gaussians are represented as a 2D texture map 𝐓∈ℝ 256×256×14 𝐓 superscript ℝ 256 256 14\mathbf{T}\in\mathbb{R}^{256\times 256\times 14}bold_T ∈ blackboard_R start_POSTSUPERSCRIPT 256 × 256 × 14 end_POSTSUPERSCRIPT, where each texel stores the parameters for a single 3D Gaussian primitive. In our 3D head representation, we adopt two different meshes and texture maps for hair and face, respectively, resulting in ∼131⁢K similar-to absent 131 𝐾{\sim}131K∼ 131 italic_K Gaussians in total for the final rendering.

#### 3.1.2. Deformable Hair Geometry

Even with our template-based 3DGS representation, there is an inherent difference between hair and face remaining unsolved, that is, hair contains much more geometric variation than different faces, which always share some commonalities among facial features such as eyes and mouth. For hair, there are many different hairstyles in the real world, ranging from short to long, fluffy to flat, making it hard to find a single template mesh to cover all these variations. To solve this problem, we learn a hair geometry prior that allows to produce deformable hair geometry to fit different hairstyles.

To learn the prior, we first fit hair geometries from multi-view facial capture data that are similar to the Multiface dataset[Wuu et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib52)], which provides calibrated camera parameters and semantic segmentations for each captured image. Given a template hair mesh, we formulate its deformation as an optimization problem, in which we differentiably render the segmentation of the deformed hair mesh using DRTK[Pidhorskyi et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib38)], and compute the L 1 subscript 𝐿 1 L_{1}italic_L start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT loss over the provided calibration. To suppress artifacts such as flipped and folded faces during deformation, we adopt an idea similar to Neural Jacobian Fields[Aigerman et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib3)], where we optimize for Jacobians 𝐉∈ℝ F×3×3 𝐉 superscript ℝ 𝐹 3 3\mathbf{J}\in\mathbb{R}^{F\times 3\times 3}bold_J ∈ blackboard_R start_POSTSUPERSCRIPT italic_F × 3 × 3 end_POSTSUPERSCRIPT (F 𝐹 F italic_F refers to the number of faces of the template mesh) and centroid translation 𝐭∈ℝ 3 𝐭 superscript ℝ 3\mathbf{t}\in\mathbb{R}^{3}bold_t ∈ blackboard_R start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT of the template mesh, rather than vertex offsets directly. Vertex positions can be computed efficiently with a differentiable Poisson solver, and this process can thus be formally defined as:

(1)𝐉∗,𝐭∗≔arg⁢min 𝐉,𝐭⁡‖ℛ⁢(PoissonSolve⁢(𝐉)+𝐭;Π)−𝐈 seg‖1,≔superscript 𝐉∗superscript 𝐭∗subscript arg min 𝐉 𝐭 subscript norm ℛ PoissonSolve 𝐉 𝐭 Π subscript 𝐈 seg 1\mathbf{J}^{\ast},\mathbf{t}^{\ast}\coloneqq\operatorname*{arg\,min}_{\mathbf{% J},\mathbf{t}}\|\mathcal{R}\big{(}\text{PoissonSolve}(\mathbf{J})+\mathbf{t};% \Pi\big{)}-\mathbf{I}_{\text{seg}}\|_{1},bold_J start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT , bold_t start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ≔ start_OPERATOR roman_arg roman_min end_OPERATOR start_POSTSUBSCRIPT bold_J , bold_t end_POSTSUBSCRIPT ∥ caligraphic_R ( PoissonSolve ( bold_J ) + bold_t ; roman_Π ) - bold_I start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ,

where ℛ⁢(⋅;Π)ℛ⋅Π\mathcal{R}(\cdot;\Pi)caligraphic_R ( ⋅ ; roman_Π ) is the differentiable rendering operator of DRTK given the camera pose Π Π\Pi roman_Π, PoissonSolve⁢(⋅)PoissonSolve⋅\text{PoissonSolve}(\cdot)PoissonSolve ( ⋅ ) is the differentiable Poisson solver in Neural Jacobian Fields, and 𝐈 seg subscript 𝐈 seg\mathbf{I}_{\text{seg}}bold_I start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT is the pre-calibrated ground truth segmentation. Our experiments show that this optimization process converges within 500 500 500 500 iterations, and in [Fig.3](https://arxiv.org/html/2506.20875v1#S3.F3 "In 3.1.2. Deformable Hair Geometry ‣ 3.1. Data Representation ‣ 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face") we visualize 10 10 10 10 hair meshes fitted from this process.

![Image 3: Refer to caption](https://arxiv.org/html/2506.20875v1/x2.png)

Figure 3. Examples of hair meshes fitted by our algorithm. Since all examples are deformed from the same template, they share a consistent topology, as illustrated by their wireframe visualization.

In total, we collect 283 283 283 283 different hair meshes, and then learn their prior using the conventional PCA-based methods in digital humans[Blanz and Vetter, [1999](https://arxiv.org/html/2506.20875v1#bib.bib6); Loper et al., [2015](https://arxiv.org/html/2506.20875v1#bib.bib28)]. Specifically, we solve a set of linear blend shapes by performing PCA on the normalized hair meshes, and different deformed hair meshes can thus be obtained from the linear function ℳ⁢(θ→)ℳ→𝜃\mathcal{M}(\vec{\theta})caligraphic_M ( over→ start_ARG italic_θ end_ARG ):

(2)ℳ⁢(θ→;𝐗)=𝐌¯+σ⁢∑n=1|θ→|θ→n⁢𝐗 n,ℳ→𝜃 𝐗¯𝐌 𝜎 superscript subscript 𝑛 1→𝜃 subscript→𝜃 𝑛 subscript 𝐗 𝑛\mathcal{M}(\vec{\theta};\mathbf{X})=\bar{\mathbf{M}}+\sigma\sum_{n=1}^{|\vec{% \theta}|}\vec{\theta}_{n}\mathbf{X}_{n},caligraphic_M ( over→ start_ARG italic_θ end_ARG ; bold_X ) = over¯ start_ARG bold_M end_ARG + italic_σ ∑ start_POSTSUBSCRIPT italic_n = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT | over→ start_ARG italic_θ end_ARG | end_POSTSUPERSCRIPT over→ start_ARG italic_θ end_ARG start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT bold_X start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ,

where θ→=[θ 1,…,θ|θ→|]⊤→𝜃 superscript subscript 𝜃 1…subscript 𝜃→𝜃 top\vec{\theta}=[\theta_{1},\dots,\theta_{|\vec{\theta}|}]^{\top}over→ start_ARG italic_θ end_ARG = [ italic_θ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_θ start_POSTSUBSCRIPT | over→ start_ARG italic_θ end_ARG | end_POSTSUBSCRIPT ] start_POSTSUPERSCRIPT ⊤ end_POSTSUPERSCRIPT is a vector of blend shape coefficients, and 𝐗=[𝐗 1,…,𝐗|θ→|]⊤∈ℝ|θ→|×3⁢V 𝐗 superscript subscript 𝐗 1…subscript 𝐗→𝜃 top superscript ℝ→𝜃 3 𝑉\mathbf{X}=[\mathbf{X}_{1},\dots,\mathbf{X}_{|\vec{\theta}|}]^{\top}\in\mathbb% {R}^{|\vec{\theta}|\times 3V}bold_X = [ bold_X start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , bold_X start_POSTSUBSCRIPT | over→ start_ARG italic_θ end_ARG | end_POSTSUBSCRIPT ] start_POSTSUPERSCRIPT ⊤ end_POSTSUPERSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT | over→ start_ARG italic_θ end_ARG | × 3 italic_V end_POSTSUPERSCRIPT forms a matrix of orthogonal principal components of shape displacements, with V 𝑉 V italic_V referring to the number of vertices of the template mesh, and 𝐌¯∈ℝ 3⁢V¯𝐌 superscript ℝ 3 𝑉\bar{\mathbf{M}}\in\mathbb{R}^{3V}over¯ start_ARG bold_M end_ARG ∈ blackboard_R start_POSTSUPERSCRIPT 3 italic_V end_POSTSUPERSCRIPT and σ∈ℝ 𝜎 ℝ\sigma\in\mathbb{R}italic_σ ∈ blackboard_R denote the mean shape and standard variation computed from the original fitted hair meshes. We set the number of blend shape coefficients |θ→|=32→𝜃 32|\vec{\theta}|=32| over→ start_ARG italic_θ end_ARG | = 32, which ensures that the deformed mesh is smooth while still covering enough variations.

### 3.2. Network Architecture

To obtain enough training data of frontal and back-of-head images with accurate camera poses, we adopt PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)] as our training data generator and train our generative model following the scheme of StyleGAN2[Karras et al., [2020](https://arxiv.org/html/2506.20875v1#bib.bib21)]. Formally, given a randomly sampled latent code 𝐳∈ℝ 512 𝐳 superscript ℝ 512\mathbf{z}\in\mathbb{R}^{512}bold_z ∈ blackboard_R start_POSTSUPERSCRIPT 512 end_POSTSUPERSCRIPT and camera pose Π∈ℝ 25 Π superscript ℝ 25\Pi\in\mathbb{R}^{25}roman_Π ∈ blackboard_R start_POSTSUPERSCRIPT 25 end_POSTSUPERSCRIPT, they are first passed to PanoHead to obtain a rendered RGB image 𝐈 rgb∈ℝ 512×512×3 subscript 𝐈 rgb superscript ℝ 512 512 3\mathbf{I}_{\text{rgb}}\in\mathbb{R}^{512\times 512\times 3}bold_I start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 512 × 512 × 3 end_POSTSUPERSCRIPT, which is later segmented and parsed to obtain the foreground mask 𝐈 mask∈ℝ 512×512 subscript 𝐈 mask superscript ℝ 512 512\mathbf{I}_{\text{mask}}\in\mathbb{R}^{512\times 512}bold_I start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 512 × 512 end_POSTSUPERSCRIPT and the hair-face segmentation map 𝐈 seg∈ℝ 512×512 subscript 𝐈 seg superscript ℝ 512 512\mathbf{I}_{\text{seg}}\in\mathbb{R}^{512\times 512}bold_I start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 512 × 512 end_POSTSUPERSCRIPT using[Lin et al., [2021](https://arxiv.org/html/2506.20875v1#bib.bib27); Zheng et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib58)]. These images, i.e., 𝐈 rgb subscript 𝐈 rgb\mathbf{I}_{\text{rgb}}bold_I start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT, 𝐈 mask subscript 𝐈 mask\mathbf{I}_{\text{mask}}bold_I start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT, 𝐈 seg subscript 𝐈 seg\mathbf{I}_{\text{seg}}bold_I start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT, serve as supervision signals to train our model.

#### 3.2.1. Dual-Branch 3D GAN

As illustrated in [Fig.2](https://arxiv.org/html/2506.20875v1#S3.F2 "In 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), we design two separate branches to handle the generation of hair and face respectively. Given the same latent code 𝐳 𝐳\mathbf{z}bold_z and camera pose Π Π\Pi roman_Π, the mapping network f:𝒵↦𝒲:𝑓 maps-to 𝒵 𝒲 f:\mathcal{Z}\mapsto\mathcal{W}italic_f : caligraphic_Z ↦ caligraphic_W is first introduced to map them to the intermediate latent space, denoted as 𝐰 hair subscript 𝐰 hair\mathbf{w}_{\text{hair}}bold_w start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT and 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT. For hair, an additional geometry mapping network f geom:𝒲↦θ→:subscript 𝑓 geom maps-to 𝒲→𝜃 f_{\text{geom}}:\mathcal{W}\mapsto\vec{\theta}italic_f start_POSTSUBSCRIPT geom end_POSTSUBSCRIPT : caligraphic_W ↦ over→ start_ARG italic_θ end_ARG is designed, which maps the latent code 𝐰 hair subscript 𝐰 hair\mathbf{w}_{\text{hair}}bold_w start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT to proper blend shape coefficients that can represent the global shape of the hairstyle. These intermediate latent codes are then fed into two separate StyleGAN generators 𝒢 hair subscript 𝒢 hair\mathcal{G}_{\text{hair}}caligraphic_G start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT and 𝒢 face subscript 𝒢 face\mathcal{G}_{\text{face}}caligraphic_G start_POSTSUBSCRIPT face end_POSTSUBSCRIPT, yielding two textures 𝐓 hair subscript 𝐓 hair\mathbf{T}_{\text{hair}}bold_T start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT and 𝐓 face subscript 𝐓 face\mathbf{T}_{\text{face}}bold_T start_POSTSUBSCRIPT face end_POSTSUBSCRIPT that store Gaussian parameters on each texel. We spawn 3D Gaussians from these textures and associate them with the underlying template mesh, combining and rendering them together to obtain the rendered RGB image 𝐈^rgb subscript^𝐈 rgb\hat{\mathbf{I}}_{\text{rgb}}over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT and mask 𝐈^mask subscript^𝐈 mask\hat{\mathbf{I}}_{\text{mask}}over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT from the provided camera pose. We use a similar dual discrimination method as EG3D[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8)], where we concatenate the rendered RGB and mask images and feed them into the discriminator with the camera pose Π Π\Pi roman_Π. Aligning with the findings of Mimic3D[Chen et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib11)], this adversarial training scheme helps increase diversity and maintain high-frequency details in our generated outputs.

#### 3.2.2. Hair-Face Correlation

In reality, the distributions of plausible faces and hairstyles are correlated. For instance, hairstyles often correlate with gender and ethnicity. To encourage our model to learn these correlations, which are commonly observed in the real world, we use cross-attention layers[Vaswani et al., [2017](https://arxiv.org/html/2506.20875v1#bib.bib46)] to inject 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT into each synthesis block of 𝒢 hair subscript 𝒢 hair\mathcal{G}_{\text{hair}}caligraphic_G start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT, thereby influencing the hair generation process at different scales. Specifically, the intermediate feature map 𝐲 l+1 superscript 𝐲 𝑙 1\mathbf{y}^{l+1}bold_y start_POSTSUPERSCRIPT italic_l + 1 end_POSTSUPERSCRIPT generated at layer l+1 𝑙 1 l+1 italic_l + 1 is computed as:

(3)𝐱 l superscript 𝐱 𝑙\displaystyle\mathbf{x}^{l}bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT=Conv⁢(𝐱 l)absent Conv superscript 𝐱 𝑙\displaystyle=\text{Conv}(\mathbf{x}^{l})= Conv ( bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT )
𝐱 l+1 superscript 𝐱 𝑙 1\displaystyle\mathbf{x}^{l+1}bold_x start_POSTSUPERSCRIPT italic_l + 1 end_POSTSUPERSCRIPT=𝐱 l+\mathcolor⁢v⁢e⁢r⁢m⁢i⁢l⁢i⁢o⁢n⁢CrossAttention⁢(𝐐=𝐱 l,𝐊=𝐕=𝐰 face)absent superscript 𝐱 𝑙\mathcolor 𝑣 𝑒 𝑟 𝑚 𝑖 𝑙 𝑖 𝑜 𝑛 CrossAttention formulae-sequence 𝐐 superscript 𝐱 𝑙 𝐊 𝐕 subscript 𝐰 face\displaystyle=\mathbf{x}^{l}+\mathcolor{vermilion}{\text{CrossAttention}(% \mathbf{Q}=\mathbf{x}^{l},\mathbf{K}=\mathbf{V}=\mathbf{w}_{\text{face}})}= bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT + italic_v italic_e italic_r italic_m italic_i italic_l italic_i italic_o italic_n CrossAttention ( bold_Q = bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT , bold_K = bold_V = bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT )
𝐲 l+1 superscript 𝐲 𝑙 1\displaystyle\mathbf{y}^{l+1}bold_y start_POSTSUPERSCRIPT italic_l + 1 end_POSTSUPERSCRIPT=Upsample⁢(𝐲 l)+ToRGB⁢(𝐱 l+1)absent Upsample superscript 𝐲 𝑙 ToRGB superscript 𝐱 𝑙 1\displaystyle=\text{Upsample}(\mathbf{y}^{l})+\text{ToRGB}(\mathbf{x}^{l+1})= Upsample ( bold_y start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT ) + ToRGB ( bold_x start_POSTSUPERSCRIPT italic_l + 1 end_POSTSUPERSCRIPT )

In [Eq.3](https://arxiv.org/html/2506.20875v1#S3.E3 "In 3.2.2. Hair-Face Correlation ‣ 3.2. Network Architecture ‣ 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), 𝐱 l superscript 𝐱 𝑙\mathbf{x}^{l}bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT is the input feature map for convolution from layer l 𝑙 l italic_l, Conv⁢(⋅)Conv⋅\text{Conv}(\cdot)Conv ( ⋅ ) is the modulated convolution layers inside synthesis blocks, Upsample⁢(⋅)Upsample⋅\text{Upsample}(\cdot)Upsample ( ⋅ ) is the spatial upsampling operator to upscale the previous feature map 𝐲 l superscript 𝐲 𝑙\mathbf{y}^{l}bold_y start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT to match the spatial resolution of 𝐱 l+1 superscript 𝐱 𝑙 1\mathbf{x}^{l+1}bold_x start_POSTSUPERSCRIPT italic_l + 1 end_POSTSUPERSCRIPT, ToRGB⁢(⋅)ToRGB⋅\text{ToRGB}(\cdot)ToRGB ( ⋅ ) is the convolution layer that adjusts the number of channels in the convolved feature map 𝐱 l+1 superscript 𝐱 𝑙 1\mathbf{x}^{l+1}bold_x start_POSTSUPERSCRIPT italic_l + 1 end_POSTSUPERSCRIPT to match 𝐲 l superscript 𝐲 𝑙\mathbf{y}^{l}bold_y start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT, and CrossAttention⁢(⋅,⋅)CrossAttention⋅⋅\text{CrossAttention}(\cdot,\cdot)CrossAttention ( ⋅ , ⋅ ) is the cross-attention layers we newly introduced compared to the original synthesis blocks in StyleGAN2. The diagram for our hair-face correlation module is provided in[Fig.4](https://arxiv.org/html/2506.20875v1#S3.F4 "In 3.2.2. Hair-Face Correlation ‣ 3.2. Network Architecture ‣ 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face").

![Image 4: Refer to caption](https://arxiv.org/html/2506.20875v1/x3.png)

Figure 4. Diagram of our hair-face correlation module, which utilizes cross-attention layers to inject 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT into each synthesis block of StyleGAN2.

Inspired by classifier-free guidance[Ho and Salimans, [2022](https://arxiv.org/html/2506.20875v1#bib.bib17)], we design a similar technique by randomly dropping the condition 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT (replacing it with all-zero vectors ∅\varnothing∅) during training with a probability of 10%percent 10 10\%10 %. Then in the inference stage, we blend the conditional feature map 𝐱 l superscript 𝐱 𝑙\mathbf{x}^{l}bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT and unconditional feature map 𝐱∅l subscript superscript 𝐱 𝑙\mathbf{x}^{l}_{\varnothing}bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT ∅ end_POSTSUBSCRIPT with the CFG factor ω 𝜔\omega italic_ω:

(4)𝐱~l=ω⁢𝐱 l+(1−ω)⁢𝐱∅l,superscript~𝐱 𝑙 𝜔 superscript 𝐱 𝑙 1 𝜔 subscript superscript 𝐱 𝑙\tilde{\mathbf{x}}^{l}=\omega\mathbf{x}^{l}+(1-\omega)\mathbf{x}^{l}_{% \varnothing},over~ start_ARG bold_x end_ARG start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT = italic_ω bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT + ( 1 - italic_ω ) bold_x start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT ∅ end_POSTSUBSCRIPT ,

thereby allowing for further control over the hair-face correlation with the CFG factor ω 𝜔\omega italic_ω.

### 3.3. 3D GAN Training

As PanoHead gives us direct supervision during training, our final training objective consists of adversarial loss, reconstruction losses on rendered images, and several regularization terms to stabilize the training and improve the generation quality.

##### Adversarial Loss

Following EG3D[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8)], we incorporate the standard non-saturating GAN loss ℒ adv subscript ℒ adv\mathcal{L}_{\text{adv}}caligraphic_L start_POSTSUBSCRIPT adv end_POSTSUBSCRIPT[Goodfellow et al., [2014](https://arxiv.org/html/2506.20875v1#bib.bib13)] with R 1 subscript 𝑅 1 R_{1}italic_R start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT gradient regularization[Mescheder et al., [2018](https://arxiv.org/html/2506.20875v1#bib.bib30)] on both the RGB and mask images, where the regularization strengths are set to 1 1 1 1 for both of them.

##### RGB and Mask Loss

From Gaussian Splatting we can obtain the rendered RGB image 𝐈^rgb subscript^𝐈 rgb\hat{\mathbf{I}}_{\text{rgb}}over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT and mask 𝐈^mask subscript^𝐈 mask\hat{\mathbf{I}}_{\text{mask}}over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT, on which we compute the L 1 subscript 𝐿 1 L_{1}italic_L start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT loss to measure their reconstruction quality. These loss terms can be expressed as:

(5)ℒ rgb=‖𝐈^rgb−𝐈 rgb‖1,ℒ mask=‖𝐈^mask−𝐈 mask‖1.formulae-sequence subscript ℒ rgb subscript norm subscript^𝐈 rgb subscript 𝐈 rgb 1 subscript ℒ mask subscript norm subscript^𝐈 mask subscript 𝐈 mask 1\mathcal{L}_{\text{rgb}}=\|\hat{\mathbf{I}}_{\text{rgb}}-\mathbf{I}_{\text{rgb% }}\|_{1},\quad\mathcal{L}_{\text{mask}}=\|\hat{\mathbf{I}}_{\text{mask}}-% \mathbf{I}_{\text{mask}}\|_{1}.caligraphic_L start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT = ∥ over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT - bold_I start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , caligraphic_L start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT = ∥ over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT - bold_I start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT .

##### Segmentation Loss

To encourage a clear separation between hair and face, we further assign different one-hot labels to Gaussians spawned from 𝐓 hair subscript 𝐓 hair\mathbf{T}_{\text{hair}}bold_T start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT and 𝐓 face subscript 𝐓 face\mathbf{T}_{\text{face}}bold_T start_POSTSUBSCRIPT face end_POSTSUBSCRIPT ([0,0,1]0 0 1[0,0,1][ 0 , 0 , 1 ] for hair and [0,1,0]0 1 0[0,1,0][ 0 , 1 , 0 ] for face, [1,0,0]1 0 0[1,0,0][ 1 , 0 , 0 ] is left for background), which will be used to render an additional segmentation map 𝐈^seg∈ℝ 512×512×3 subscript^𝐈 seg superscript ℝ 512 512 3\hat{\mathbf{I}}_{\text{seg}}\in\mathbb{R}^{512\times 512\times 3}over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 512 × 512 × 3 end_POSTSUPERSCRIPT with other Gaussian parameters. To ensure that the generated hair mesh faithfully represents the hairstyle in the image, we additionally render the hair mesh segmentation 𝐈^seg mesh∈ℝ 512×512 superscript subscript^𝐈 seg mesh superscript ℝ 512 512\hat{\mathbf{I}}_{\text{seg}}^{\text{mesh}}\in\mathbb{R}^{512\times 512}over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT start_POSTSUPERSCRIPT mesh end_POSTSUPERSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT 512 × 512 end_POSTSUPERSCRIPT with DRTK[Pidhorskyi et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib38)] by assigning different scalar values to vertices of the hair and face meshes (2 2 2 2 for hair and 1 1 1 1 for face, the default value 0 0 is for background). These segmentation maps are supervised with the segmentation map 𝐈 seg subscript 𝐈 seg\mathbf{I}_{\text{seg}}bold_I start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT parsed from 𝐈 rgb subscript 𝐈 rgb\mathbf{I}_{\text{rgb}}bold_I start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT, where the loss terms are defined as:

(6)ℒ seg=CrossEntropy⁢(𝐈^seg,𝐈 seg),ℒ seg mesh=‖𝐈^seg mesh−𝐈 seg‖1.formulae-sequence subscript ℒ seg CrossEntropy subscript^𝐈 seg subscript 𝐈 seg subscript superscript ℒ mesh seg subscript norm subscript superscript^𝐈 mesh seg subscript 𝐈 seg 1\mathcal{L}_{\text{seg}}=\text{CrossEntropy}(\hat{\mathbf{I}}_{\text{seg}},% \mathbf{I}_{\text{seg}}),\quad\mathcal{L}^{\text{mesh}}_{\text{seg}}=\|\hat{% \mathbf{I}}^{\text{mesh}}_{\text{seg}}-\mathbf{I}_{\text{seg}}\|_{1}.caligraphic_L start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT = CrossEntropy ( over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT , bold_I start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT ) , caligraphic_L start_POSTSUPERSCRIPT mesh end_POSTSUPERSCRIPT start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT = ∥ over^ start_ARG bold_I end_ARG start_POSTSUPERSCRIPT mesh end_POSTSUPERSCRIPT start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT - bold_I start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT .

Note that we use the cross-entropy loss rather than L 1 subscript 𝐿 1 L_{1}italic_L start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT loss for the segmentation map 𝐈^seg subscript^𝐈 seg\hat{\mathbf{I}}_{\text{seg}}over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT rendered from Gaussian Splatting, as its α 𝛼\alpha italic_α-blending nature will inevitably change values around the boundary, thus causing mislabeling issues for pixels on the boundary if their labels are scalar.

##### Regularization Terms

As our adversarial training is weakly supervised and 3D Gaussians are quite sensitive to gradient updates during early training stages, unconstrained training will quickly lead to divergence or mode collapse with overly large or extremely small Gaussians in the early stage. Therefore, we apply some regularization terms to stabilize the training. First, based on our hybrid 3DGS representation, the center position 𝐩 i subscript 𝐩 𝑖\mathbf{p}_{i}bold_p start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT of each Gaussian is defined as the sum of the 3D position 𝐯 i subscript 𝐯 𝑖\mathbf{v}_{i}bold_v start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT on the mesh surface and the delta position Δ⁢𝐩 i Δ subscript 𝐩 𝑖\Delta\mathbf{p}_{i}roman_Δ bold_p start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT decoded from the generated texture maps. To ensure that all Gaussians stay within a thin layer around the mesh surface, we first clamp the absolute value of the decoded delta position Δ⁢𝐩 i Δ subscript 𝐩 𝑖\Delta\mathbf{p}_{i}roman_Δ bold_p start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT with a threshold γ 𝛾\gamma italic_γ. We use γ=40 𝛾 40\gamma=40 italic_γ = 40 for face Gaussians, meaning that they can move at most 40 40 40 40 mm away from the surface. As the hair mesh itself is deformable, we reduce γ 𝛾\gamma italic_γ to 20 20 20 20 for hair Gaussians to make sure that different hairstyles are generated with different geometries, rather than similar geometries with largely deviated Gaussians. A regularization term for delta positions is applied:

(7)ℒ reg pos=∑i‖Δ⁢𝐩 i‖2,subscript superscript ℒ pos reg subscript 𝑖 subscript norm Δ subscript 𝐩 𝑖 2\mathcal{L}^{\text{pos}}_{\text{reg}}=\sum_{i}\|\Delta\mathbf{p}_{i}\|_{2},caligraphic_L start_POSTSUPERSCRIPT pos end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT = ∑ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∥ roman_Δ bold_p start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ,

which encourages all predicted Gaussians to stay close to the mesh surface. To constrain the scale of Gaussians to stay within a reasonable range, the most effective regularization term we experimented with can be defined as:

(8)ℒ reg scale={10×|s i−s min|s i<s min(s i−s max)2 s i>s max subscript superscript ℒ scale reg cases 10 subscript 𝑠 𝑖 subscript 𝑠 min subscript 𝑠 𝑖 subscript 𝑠 min superscript subscript 𝑠 𝑖 subscript 𝑠 max 2 subscript 𝑠 𝑖 subscript 𝑠 max\mathcal{L}^{\text{scale}}_{\text{reg}}=\begin{cases}10\times|s_{i}-s_{\text{% min}}|&s_{i}<s_{\text{min}}\\ (s_{i}-s_{\text{max}})^{2}&s_{i}>s_{\text{max}}\\ \end{cases}caligraphic_L start_POSTSUPERSCRIPT scale end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT = { start_ROW start_CELL 10 × | italic_s start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT - italic_s start_POSTSUBSCRIPT min end_POSTSUBSCRIPT | end_CELL start_CELL italic_s start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT < italic_s start_POSTSUBSCRIPT min end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL ( italic_s start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT - italic_s start_POSTSUBSCRIPT max end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_CELL start_CELL italic_s start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT > italic_s start_POSTSUBSCRIPT max end_POSTSUBSCRIPT end_CELL end_ROW

It applies different penalties to constrain the Gaussian scaling along all axes if they are outside of a reasonable range [s min,s max]subscript 𝑠 min subscript 𝑠 max[s_{\text{min}},s_{\text{max}}][ italic_s start_POSTSUBSCRIPT min end_POSTSUBSCRIPT , italic_s start_POSTSUBSCRIPT max end_POSTSUBSCRIPT ], where s min=0.2 subscript 𝑠 min 0.2 s_{\text{min}}=0.2 italic_s start_POSTSUBSCRIPT min end_POSTSUBSCRIPT = 0.2 and s max=5 subscript 𝑠 max 5 s_{\text{max}}=5 italic_s start_POSTSUBSCRIPT max end_POSTSUBSCRIPT = 5. Finally, we also apply the u⁢v 𝑢 𝑣 uv italic_u italic_v total variation loss ℒ reg uv subscript superscript ℒ uv reg\mathcal{L}^{\text{uv}}_{\text{reg}}caligraphic_L start_POSTSUPERSCRIPT uv end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT proposed in GGHead[Kirschstein et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib24)] to prevent Gaussians in the back from shining through to the front.

Combining all the terms discussed above, the final training objective is defined as their weighted sum, expressed as:

(9)ℒ ℒ\displaystyle\mathcal{L}caligraphic_L=ℒ adv+λ rgb⁢ℒ rgb+λ mask⁢ℒ mask+λ seg⁢ℒ seg+λ seg mesh⁢ℒ seg mesh absent subscript ℒ adv subscript 𝜆 rgb subscript ℒ rgb subscript 𝜆 mask subscript ℒ mask subscript 𝜆 seg subscript ℒ seg subscript superscript 𝜆 mesh seg subscript superscript ℒ mesh seg\displaystyle=\mathcal{L}_{\text{adv}}+\lambda_{\text{rgb}}\mathcal{L}_{\text{% rgb}}+\lambda_{\text{mask}}\mathcal{L}_{\text{mask}}+\lambda_{\text{seg}}% \mathcal{L}_{\text{seg}}+\lambda^{\text{mesh}}_{\text{seg}}\mathcal{L}^{\text{% mesh}}_{\text{seg}}= caligraphic_L start_POSTSUBSCRIPT adv end_POSTSUBSCRIPT + italic_λ start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT caligraphic_L start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT + italic_λ start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT caligraphic_L start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT + italic_λ start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT caligraphic_L start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT + italic_λ start_POSTSUPERSCRIPT mesh end_POSTSUPERSCRIPT start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT caligraphic_L start_POSTSUPERSCRIPT mesh end_POSTSUPERSCRIPT start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT
+λ reg pos⁢ℒ reg pos+λ reg scale⁢ℒ reg scale+λ reg uv⁢ℒ reg uv subscript superscript 𝜆 pos reg subscript superscript ℒ pos reg subscript superscript 𝜆 scale reg subscript superscript ℒ scale reg subscript superscript 𝜆 uv reg subscript superscript ℒ uv reg\displaystyle+\lambda^{\text{pos}}_{\text{reg}}\mathcal{L}^{\text{pos}}_{\text% {reg}}+\lambda^{\text{scale}}_{\text{reg}}\mathcal{L}^{\text{scale}}_{\text{% reg}}+\lambda^{\text{uv}}_{\text{reg}}\mathcal{L}^{\text{uv}}_{\text{reg}}+ italic_λ start_POSTSUPERSCRIPT pos end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT caligraphic_L start_POSTSUPERSCRIPT pos end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT + italic_λ start_POSTSUPERSCRIPT scale end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT caligraphic_L start_POSTSUPERSCRIPT scale end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT + italic_λ start_POSTSUPERSCRIPT uv end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT caligraphic_L start_POSTSUPERSCRIPT uv end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT

where we set the weighting factors λ rgb=10 subscript 𝜆 rgb 10\lambda_{\text{rgb}}=10 italic_λ start_POSTSUBSCRIPT rgb end_POSTSUBSCRIPT = 10, λ mask=10 subscript 𝜆 mask 10\lambda_{\text{mask}}=10 italic_λ start_POSTSUBSCRIPT mask end_POSTSUBSCRIPT = 10, λ seg=1 subscript 𝜆 seg 1\lambda_{\text{seg}}=1 italic_λ start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT = 1, λ seg mesh=100 subscript superscript 𝜆 mesh seg 100\lambda^{\text{mesh}}_{\text{seg}}=100 italic_λ start_POSTSUPERSCRIPT mesh end_POSTSUPERSCRIPT start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT = 100, λ reg pos=0.1 subscript superscript 𝜆 pos reg 0.1\lambda^{\text{pos}}_{\text{reg}}=0.1 italic_λ start_POSTSUPERSCRIPT pos end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT = 0.1, λ reg scale=1 subscript superscript 𝜆 scale reg 1\lambda^{\text{scale}}_{\text{reg}}=1 italic_λ start_POSTSUPERSCRIPT scale end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT = 1, and λ reg uv=1 subscript superscript 𝜆 uv reg 1\lambda^{\text{uv}}_{\text{reg}}=1 italic_λ start_POSTSUPERSCRIPT uv end_POSTSUPERSCRIPT start_POSTSUBSCRIPT reg end_POSTSUBSCRIPT = 1 to balance the influence of different terms.

4. Experiments
--------------

We use multi-view capture data[Wuu et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib52); Saito et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib41)] to solve the linear blend shapes for our deformable hair geometry, and we use PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)] as the portrait image generator to train our generative model. For details about these datasets, please refer to Sec. A in supplemental.

### 4.1. Comparisons

We compare against several competitive baseline methods from the 3D GAN literature. Unless otherwise indicated, all baselines are their official checkpoints to maintain their original quality. We evaluate the quality of the generated multi-view images, both quantitatively and qualitatively.

#### 4.1.1. Qualitative Comparisons

[Fig.5](https://arxiv.org/html/2506.20875v1#S4.F5 "In 4.1.1. Qualitative Comparisons ‣ 4.1. Comparisons ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face") visually compares the image quality against baselines including EG3D[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8)], PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)], SphereHead[Li et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib25)], and GGHead [Kirschstein et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib24)], where EG3D is the pioneering work that synthesizes high-quality portrait images with the tri-plane representation and a 2D super-resolution network, PanoHead and SphereHead are two subsequent works that achieve full-head synthesis by improving the tri-plane representation, and GGHead utilizes a similar hybrid representation with 3DGS and a template mesh as ours. All synthesized images contain 5 5 5 5 different views, with yaw angles ranging from 0∘superscript 0 0^{\circ}0 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT to 180∘superscript 180 180^{\circ}180 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT. While all methods successfully synthesize realistic frontal-view images, the rendering quality of EG3D and GGHead deteriorates significantly when rendering from large camera poses or back-view areas, as these methods are not specifically designed for full-head image synthesis. Compared to SphereHead and PanoHead, our method achieves comparable visual quality while providing the additional advantage of compositionality.

![Image 5: Refer to caption](https://arxiv.org/html/2506.20875v1/x4.png)

Figure 5. Qualitative comparison with various 3D GANs. (a) EG3D[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8)] and (b) GGHead[Kirschstein et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib24)] are not specifically designed for full-head image synthesis, resulting in significant quality degradation when rendering large-pose or back-view images. (c) SphereHead[Li et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib25)] and (d) PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)] are two 3D GANs tailored for full-head image synthesis. Compared with these methods, our results (e-h) demonstrate comparable quality while offering the additional advantage of compositionality.

To prove the compositionality of our method, we first present samples generated by our model alongside the rendered hair-face segmentation maps and mesh normal maps in[Fig.6](https://arxiv.org/html/2506.20875v1#S4.F6 "In 4.1.1. Qualitative Comparisons ‣ 4.1. Comparisons ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face"). Leveraging our deformable hair geometry, we achieve smooth deformations of the hair mesh, effectively capturing the overall structure of various hairstyles. Additionally, the 3D Gaussians associated with the hair mesh exhibit a clear separation from the face Gaussians and are capable of representing some strand-level details, thus yielding hair-face segmentation maps with finer-grained details that are difficult to obtain from common image segmentation models. More uncurated samples can be found in Sec. D of our supplemental.

![Image 6: Refer to caption](https://arxiv.org/html/2506.20875v1/x5.png)

Figure 6. Generated samples with corresponding hair-face segmentation and deformed hair geometry. Our method enables smooth deformation of the hair mesh to represent various hairstyles, while assigning 3D Gaussians to capture strand-level details and appearance.

We then evaluate our compositionality through 3D hairstyle editing, where the 3D hairstyle in the reference sample is transferred to another one. The qualitative results are provided in[Fig.7](https://arxiv.org/html/2506.20875v1#S4.F7 "In 4.1.1. Qualitative Comparisons ‣ 4.1. Comparisons ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), demonstrating that our approach preserves the reference hairstyle with high fidelity while producing a natural blending around the hairline. Both the hair geometry and appearance are transferred through a simple latent code swap. Note that in 2D hairstyle editing methods, such as HairFastGAN[Nikolaev et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib33)], such hairstyle editing typically requires multiple processing steps and network modules. Furthermore, our editing results inherently maintain multi-view consistency, attributed to the 3D nature of our representations.

Original Hairstyle
![Image 7: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/edit-baseline/seed0052.png)
Edited Hairstyle Reference
![Image 8: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/edit-baseline/seed0052-0048-1.png)![Image 9: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/edit-baseline/seed0048.png)
![Image 10: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/edit-baseline/seed0052-0029.png)![Image 11: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/edit-baseline/seed0029.png)
![Image 12: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/edit-baseline/seed0052-0003.png)![Image 13: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/edit-baseline/seed0003.png)

Figure 7. Our method supports 3D hairstyle editing by swapping the hair latent code 𝐰 hair subscript 𝐰 hair\mathbf{w}_{\text{hair}}bold_w start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT from the reference samples. This editing process transfers both the hair geometry and appearance, while ensuring multi-view consistency thanks to the inherently 3D nature of our representations.

We finally investigate the impact of our hair-face correlation modeling technique by generating hair-face compositions with varying levels of the CFG scale factor ω 𝜔\omega italic_ω. As illustrated in[Fig.8](https://arxiv.org/html/2506.20875v1#S4.F8 "In 4.1.1. Qualitative Comparisons ‣ 4.1. Comparisons ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), when the reference face is male, it favors short-length hairstyles to align with plausible hairstyle distributions observed for this face condition in real life. Consequently, as ω 𝜔\omega italic_ω increases, the transferred hairstyle gradually becomes shorter while preserving the overall style of the reference. This experiment provides strong evidence for the effectiveness of our hair-face correlation module, which introduces an extra dimension for editing transferred hairstyles while maintaining plausibility – a critical point often overlooked by previous hairstyle editing methods.

![Image 14: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/cfg-scale/long-to-short/seed0002.png)![Image 15: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/cfg-scale/long-to-short/seed0004.png)![Image 16: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/cfg-scale/long-to-short/cfg-0.png)![Image 17: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/cfg-scale/long-to-short/cfg-0.50.png)![Image 18: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/cfg-scale/long-to-short/cfg-1.png)
Reference Face Reference Hair ω=0 𝜔 0\omega=0 italic_ω = 0 ω=0.5 𝜔 0.5\omega=0.5 italic_ω = 0.5 ω=1 𝜔 1\omega=1 italic_ω = 1

Figure 8. Analysis of the CFG scale factor ω 𝜔\omega italic_ω, where we present hair-face compositions generated using varying levels of ω 𝜔\omega italic_ω. When ω 𝜔\omega italic_ω is small, the hair-face correlation has weak influence on the final output, resulting in hairstyles more similar to the reference. As ω 𝜔\omega italic_ω increases, the composition process becomes more biased toward the face distribution, producing hairstyles that are more contextually appropriate for the given face.

#### 4.1.2. Quantitative Comparisons

Table 1. Quantitative comparison on different FID metrics.

We first quantitatively evaluate our generation quality by measuring the Fréchet Inception Distance (FID)[Heusel et al., [2017](https://arxiv.org/html/2506.20875v1#bib.bib16)] computed over 50⁢k 50 𝑘 50k 50 italic_k real and fake image samples. Since PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)] serves as our training data generator, its renderings are treated as real image samples for the FID evaluation. In addition to the overall FID (FID-all) computed on randomly sampled poses, we evaluate generation quality at a finer granularity by sampling camera poses from different regions. Specifically, FID-front evaluates facial details using images synthesized from frontal views (|y⁢a⁢w|<90∘𝑦 𝑎 𝑤 superscript 90|yaw|<90^{\circ}| italic_y italic_a italic_w | < 90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT), while FID-back assesses hair details using images synthesized from back views (|y⁢a⁢w|≥90∘𝑦 𝑎 𝑤 superscript 90|yaw|\geq 90^{\circ}| italic_y italic_a italic_w | ≥ 90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT). As shown in[Table 1](https://arxiv.org/html/2506.20875v1#S4.T1 "In 4.1.2. Quantitative Comparisons ‣ 4.1. Comparisons ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), all three metrics yield values less than 10 10 10 10, indicating that the quality of our generated results is still comparable to that of PanoHead.

We then conduct quantitative comparisons with EG3D[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8)], SphereHead[Li et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib25)], and GGHead[Kirschstein et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib24)] to evaluate multi-view consistency, in which we measure the identity similarity score (ID) by calculating the average Adaface[Kim et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib23)] cosine similarity between paired images rendered from different camera poses. As reported in [Table 2](https://arxiv.org/html/2506.20875v1#S4.T2 "In 4.1.2. Quantitative Comparisons ‣ 4.1. Comparisons ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), our method achieves the best multi-view consistency, since EG3D and GGHead struggle for large-pose images and SphereHead involves a 2D super-resolution network that may introduce artifacts.

Table 2. Quantitative comparison between our method and other 3D GANs on multi-view consistency.

EG3D GGHead SphereHead Ours
[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8)][Kirschstein et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib24)][Li et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib25)]
ID ↑↑\uparrow↑0.678 0.678 0.678 0.678 0.683 0.683 0.683 0.683 0.581 0.581 0.581 0.581 0.690 0.690\mathbf{0.690}bold_0.690

### 4.2. Ablation Study

In [Table 3](https://arxiv.org/html/2506.20875v1#S4.T3 "In 4.2. Ablation Study ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), we analyze key design decisions in our method, including the choice of supervision on segmentation maps, the use of deformable hair geometry, and variations in hair-face correlation modules. To assess the compositionality of our approach, we generate 50⁢k 50 𝑘 50k 50 italic_k samples by randomly swapping the intermediate latent codes 𝐰 hair subscript 𝐰 hair\mathbf{w}_{\text{hair}}bold_w start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT and 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT, thereby creating novel samples with mismatched hair and face combinations. We then compute FID for these swapped samples against the real samples, denoted as FID-swap, to evaluate the realism of the randomly combined hair and face outputs produced by our model.

In [Table 3](https://arxiv.org/html/2506.20875v1#S4.T3 "In 4.2. Ablation Study ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face"), the first 3 3 3 3 rows evaluate the impact of our choice of segmentation supervision. Specifically, _Seg. in 𝒟 𝒟\mathcal{D}caligraphic\_D_ refers to concatenate the rendered segmentation maps to the input of discriminator and let it determine whether the segmentation is realistic or not in an adversarial manner. Meanwhile, _w/o Seg. loss_ denotes setting λ seg subscript 𝜆 seg\lambda_{\text{seg}}italic_λ start_POSTSUBSCRIPT seg end_POSTSUBSCRIPT to 0 0. In these experiments, we observed that passing segmentation maps to the discriminator often caused mode collapse during the early stages of GAN training, resulting in meaningless outputs and high FID scores. We hypothesize that it is mainly due to the mismatch in value representations: the rendered segmentation maps contain continuous floating-point values, whereas the ground-truth segmentations parsed from RGB images are discrete labels. This is a fundamental difference between segmentation maps and RGB/mask images, since both ground truth RGB and mask images can contain continuous values between 0 and 1. Therefore, the discriminator can easily distinguish real and generated samples based on this quantization discrepancy, breaking the training process at an early stage. Surprisingly, removing the segmentation loss still produced reasonable generation results with acceptable segmentation quality. Adding the segmentation loss encouraged a cleaner separation between hair and face Gaussians, though it slightly increased the FID score due to the additional constraints imposed on Gaussians. We provide qualitative comparisons to discuss these observations in Fig. 1 of our supplemental. The 3 3 3 3 rd row further illustrates the importance of our deformable hair geometry. In this experiment, we replaced the deformable hair geometry with the average hair mesh fitted from studio capture data and trained our model using this fixed geometry. Quantitative results demonstrate that incorporating a deformable hair geometry improves overall generation quality. Visually, we observed that when the hair geometry is fixed, hair Gaussians need larger deviations to represent varying hairstyles, resulting in floating Gaussians appearing in random positions. Fig. 2 in supplemental includes a qualitative comparison of this artifact. The last 3 3 3 3 rows examine different hair-face correlation modules. In the 4 4 4 4 th row, we remove this module entirely, while the 5 5 5 5 th row replaces it with a mechanism that concatenates 𝐰 hair subscript 𝐰 hair\mathbf{w}_{\text{hair}}bold_w start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT and 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT with a lightweight MLP to fuse them and model their correlation. The results indicate that our cross-attention mechanism achieves the lowest FID, signifying better generation quality. Although the concatenation mechanism achieves a lower FID-swap, qualitative analysis reveals that it introduces a strong dependency on 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT, which reduces the diversity when 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT is fixed and 𝐰 hair subscript 𝐰 hair\mathbf{w}_{\text{hair}}bold_w start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT is swapped. Fig. 3 in supplemental shows this artifact. Overall, these experiments demonstrate that our final architecture design (as shown in the last row) achieves the best balance of generation quality and diversity, enabling 3D hairstyle editing in the generated results with a certain guarantee of realism.

Table 3. Ablation studies on segmentation supervision, deformable hair geometry, and hair-face correlation module. The last row refers to our final architecture design.

### 4.3. Latent Space Interpolation

Figure 9. Linear interpolation in the latent space of 3DGH. Top: Interpolation of 𝐰 hair subscript 𝐰 hair\mathbf{w}_{\text{hair}}bold_w start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT with the facial identity fixed, demonstrating smooth transitions between hairstyles. Bottom: Interpolation of 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT while keeping the hairstyle constant, illustrating gradual changes in facial features.

[Fig.9](https://arxiv.org/html/2506.20875v1#S4.F9 "In 4.3. Latent Space Interpolation ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face") illustrates how variations in the generated 3D head correspond to interpolations in the latent space of 3DGH. We begin by randomly sampling two pairs of latent codes, which are linearly interpolated to produce intermediate representations. The resulting renderings, arranged from left to right, show a smooth semantic transition between two identities. Leveraging our composable design, we independently interpolate between 𝐰 hair subscript 𝐰 hair\mathbf{w}_{\text{hair}}bold_w start_POSTSUBSCRIPT hair end_POSTSUBSCRIPT and 𝐰 face subscript 𝐰 face\mathbf{w}_{\text{face}}bold_w start_POSTSUBSCRIPT face end_POSTSUBSCRIPT, enabling disentangled control over hair and facial features. The seamless transitions and consistent semantic structure across interpolations highlight the continuity and expressiveness of the latent space learned by our model.

5. Discussion
-------------

##### Limitations and Future Work

While our method demonstrates strong performance, it still faces several limitations. First, the expressiveness of our model is constrained by the quality and diversity of the training data, which in our case are the images generated by PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)]. A clear domain gap exists between these synthetic images and in-the-wild images, making certain hairstyles, such as buns and braids, difficult to generate. Addressing this issue necessitates a large-scale dataset of in-the-wild images with comprehensive coverage of frontal and back views, accurate camera calibration, and reliable image alignment. Although works like PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)] and SphereHead[Li et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib25)] have made progress in this direction, their in-house training data are not publicly available at this time, and specific processing steps are still needed to calibrate and align back views in the absence of facial landmarks. Therefore, combining real-world multi-view datasets such as RenderMe-360[Pan et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib35)] with synthetic data would be an interesting future work to explore that may alleviate these training data issues. Second, our model occasionally produces back-view artifacts for long hairstyles that occupy a large portion of the frontal view, as illustrated in[Fig.10](https://arxiv.org/html/2506.20875v1#S5.F10 "In Limitations and Future Work ‣ 5. Discussion ‣ 3DGH: 3D Head Generation with Composable Hair and Face"). We attribute this to our generator’s conditioning on both the latent code and camera pose, following the design choice of EG3D[Chan et al., [2022](https://arxiv.org/html/2506.20875v1#bib.bib8)] and PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)]. Despite using an 80%percent 80 80\%80 % pose-swapping probability during training, rendering quality degrades when rendering poses differ significantly from the conditioning poses. This limitation is also observed in PanoHead[An et al., [2023](https://arxiv.org/html/2506.20875v1#bib.bib4)] and SphereHead[Li et al., [2024](https://arxiv.org/html/2506.20875v1#bib.bib25)] because full-head image synthesis requires 360-degree rendering. Better conditioning on camera pose may require an advanced architecture as a future work. Third, our method can produce hollow artifacts, particularly in hair regions, due to the stretching and scaling of Gaussian primitives to represent thin strand structures. While increasing the number of Gaussians may alleviate this problem by providing denser coverage, it would also lead to higher computational cost in terms of model size and training time. Fourth, while our design choice of the cross-attention layer in[Eq.3](https://arxiv.org/html/2506.20875v1#S3.E3 "In 3.2.2. Hair-Face Correlation ‣ 3.2. Network Architecture ‣ 3. Methodology ‣ 3DGH: 3D Head Generation with Composable Hair and Face") is motivated by the real-world observation that there exist correlations between ethnic facial features and culturally associated hairstyles, our analysis in[Fig.8](https://arxiv.org/html/2506.20875v1#S4.F8 "In 4.1.1. Qualitative Comparisons ‣ 4.1. Comparisons ‣ 4. Experiments ‣ 3DGH: 3D Head Generation with Composable Hair and Face") does not fully cover various correlations other than gender. This is mainly because gender is the dominant factor in hair-face correlations in the dataset we used. Lastly, extending our framework toward animatable 3D avatars is an exciting future direction. By incorporating parametric models such as FLAME[Li et al., [2017](https://arxiv.org/html/2506.20875v1#bib.bib26)], our method could be adapted to support disentangled control over head pose, facial expression, and hairstyle, paving the way for more versatile and customizable 3D avatar generation.

![Image 19: Refer to caption](https://arxiv.org/html/2506.20875v1/extracted/6571704/fig/img/seed0064.png)

Figure 10. Failure case illustrating artifacts in the back-view rendering of a long hairstyle.

##### Ethical considerations

As with other generative models for digital avatars, our method carries potential risks related to misuse (e.g., identity manipulation) and biases. These concerns are partly due to the use of synthetic training data, which may lack sufficient diversity in demographics and hairstyles, limiting the representation of hair-face correlations across different ethnicities (see Fig. 4 in supplemental). To mitigate such issues, we strongly advocate for the responsible use of 3DGH, transparency in its deployment, and the continued development of diverse, representative datasets. We explicitly oppose any use of our work for malicious purposes, including the spread of misinformation or the violation of individual rights.

6. Conclusion
-------------

We introduce 3DGH, a Gaussian-based 3D GAN framework that supports composable hair and face generation. Leveraging multi-view studio capture data, we propose a novel data representation with template-based 3DGS, in which hair Gaussians are rigged to a deformable hair geometry constructed using PCA-based linear blend shapes. This data representation drives the design of our network architecture, which incorporates dual branches to independently generate hair and face Gaussians. A cross-attention mechanism is introduced to model the inherent correlation between hair and face, ensuring coherent and realistic outputs. Our model is then trained using a comprehensive objective that includes adversarial loss, reconstruction terms, and regularization terms designed to stabilize training and facilitate hair-face separation. We evaluate the trained model both qualitatively and quantitatively, demonstrating its superior performance in unconditional full-head image synthesis and composable 3D hairstyle editing.

References
----------

*   [1]
*   Abdal et al. [2024] Rameen Abdal, Wang Yifan, Zifan Shi, Yinghao Xu, Ryan Po, Zhengfei Kuang, Qifeng Chen, Dit-Yan Yeung, and Gordon Wetzstein. 2024. Gaussian Shell Maps for Efficient 3D Human Generation. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 9441–9451. 
*   Aigerman et al. [2022] Noam Aigerman, Kunal Gupta, Vladimir G. Kim, Siddhartha Chaudhuri, Jun Saito, and Thibault Groueix. 2022. Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes. _ACM Trans. Graph._ 41, 4, Article 109 (July 2022), 17 pages. 
*   An et al. [2023] Sizhe An, Hongyi Xu, Yichun Shi, Guoxian Song, Umit Y. Ogras, and Linjie Luo. 2023. PanoHead: Geometry-Aware 3D Full-Head Synthesis in 360∘. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_. 20950–20959. 
*   Bilecen et al. [2024] Bahri Batuhan Bilecen, Yigit Yalin, Ning Yu, and Aysegul Dundar. 2024. Reference-Based 3D-Aware Image Editing with Triplane. _arXiv preprint arXiv:2404.03632_ (2024). 
*   Blanz and Vetter [1999] Volker Blanz and Thomas Vetter. 1999. A Morphable Model for the Synthesis of 3D Faces. In _Proceedings of the 26th annual conference on Computer graphics and interactive techniques_. 187–194. 
*   Chai et al. [2016] Menglei Chai, Tianjia Shao, Hongzhi Wu, Yanlin Weng, and Kun Zhou. 2016. AutoHair: Fully Automatic Hair Modeling from a Single Image. _ACM Transactions on Graphics_ 35, 4, Article 116 (jul 2016), 12 pages. 
*   Chan et al. [2022] Eric R Chan, Connor Z Lin, Matthew A Chan, Koki Nagano, Boxiao Pan, Shalini De Mello, Orazio Gallo, Leonidas J Guibas, Jonathan Tremblay, Sameh Khamis, et al. 2022. Efficient Geometry-aware 3D Generative Adversarial Networks. In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_. 16123–16133. 
*   Chan et al. [2021] Eric R Chan, Marco Monteiro, Petr Kellnhofer, Jiajun Wu, and Gordon Wetzstein. 2021. pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis. In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_. 5799–5809. 
*   Chen et al. [2020] Shu-Yu Chen, Wanchao Su, Lin Gao, Shihong Xia, and Hongbo Fu. 2020. Deep Generation of Face Images from Sketches. _arXiv preprint arXiv:2006.01047_ (2020). 
*   Chen et al. [2023] Xingyu Chen, Yu Deng, and Baoyuan Wang. 2023. Mimic3D: Thriving 3D-Aware GANs Via 3D-to-2D Imitation. In _Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)_. 
*   Gao et al. [2023] Lin Gao, Feng-Lin Liu, Shu-Yu Chen, Kaiwen Jiang, Chun-Peng Li, Yu-Kun Lai, and Hongbo Fu. 2023. SketchFaceNeRF: Sketch-Based Facial Generation and Editing in Neural Radiance Fields. _ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2023)_ 42, 4 (2023), 159:1–159:17. 
*   Goodfellow et al. [2014] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. 2014. Generative Adversarial Nets. _Advances in neural information processing systems_ 27 (2014). 
*   Gu et al. [2021] Jiatao Gu, Lingjie Liu, Peng Wang, and Christian Theobalt. 2021. StyleNeRF: A Style-based 3D-Aware Generator for High-resolution Image Synthesis. _arXiv preprint arXiv:2110.08985_ (2021). 
*   He et al. [2025] Chengan He, Xin Sun, Zhixin Shu, Fujun Luan, Sören Pirk, Jorge Alejandro Amador Herrera, Dominik L. Michels, Tuanfeng Y. Wang, Meng Zhang, Holly Rushmeier, and Yi Zhou. 2025. Perm: A Parametric Representation for Multi-Style 3D Hair Modeling. In _International Conference on Learning Representations_. 
*   Heusel et al. [2017] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. 2017. GANs Trained by a Two Time-scale Update Rule Converge to a Local Nash Equilibrium. _Advances in neural information processing systems_ 30 (2017). 
*   Ho and Salimans [2022] Jonathan Ho and Tim Salimans. 2022. Classifier-Free Diffusion Guidance. _arXiv preprint arXiv:2207.12598_ (2022). 
*   Hu et al. [2015] Liwen Hu, Chongyang Ma, Linjie Luo, and Hao Li. 2015. Single-View Hair Modeling Using a Hairstyle Database. _ACM Transactions on Graphics (Proceedings SIGGRAPH 2015)_ 34, 4 (July 2015). 
*   Jakob et al. [2009] Wenzel Jakob, Jonathan T. Moon, and Steve Marschner. 2009. Capturing Hair Assemblies Fiber by Fiber. _ACM Trans. Graph._ 28, 5 (dec 2009), 1–9. 
*   Karras et al. [2019] Tero Karras, Samuli Laine, and Timo Aila. 2019. A Style-Based Generator Architecture for Generative Adversarial Networks. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_. 
*   Karras et al. [2020] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. 2020. Analyzing and Improving the Image Quality of StyleGAN. In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_. 8110–8119. 
*   Kerbl et al. [2023] Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis. 2023. 3D Gaussian Splatting for Real-Time Radiance Field Rendering. _ACM Transactions on Graphics_ 42, 4 (July 2023). 
*   Kim et al. [2022] Minchul Kim, Anil K Jain, and Xiaoming Liu. 2022. AdaFace: Quality Adaptive Margin for Face Recognition. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 
*   Kirschstein et al. [2024] Tobias Kirschstein, Simon Giebenhain, Jiapeng Tang, Markos Georgopoulos, and Matthias Nießner. 2024. GGHead: Fast and Generalizable 3D Gaussian Heads. In _SIGGRAPH Asia 2024 Conference Papers_ _(SA ’24)_. Article 126, 11 pages. 
*   Li et al. [2024] Heyuan Li, Ce Chen, Tianhao Shi, Yuda Qiu, Sizhe An, Guanying Chen, and Xiaoguang Han. 2024. SphereHead: Stable 3D Full-head Synthesis with Spherical Tri-plane Representation. _arXiv preprint arXiv:2404.05680_ (2024). 
*   Li et al. [2017] Tianye Li, Timo Bolkart, Michael.J. Black, Hao Li, and Javier Romero. 2017. Learning a Model of Facial Shape and Expression from 4D Scans. _ACM Transactions on Graphics, (Proc. SIGGRAPH Asia)_ 36, 6 (2017), 194:1–194:17. 
*   Lin et al. [2021] Shanchuan Lin, Andrey Ryabtsev, Soumyadip Sengupta, Brian L Curless, Steven M Seitz, and Ira Kemelmacher-Shlizerman. 2021. Real-Time High-Resolution Background Matting. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 8762–8771. 
*   Loper et al. [2015] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J. Black. 2015. SMPL: a Skinned Multi-Person Linear Model. _ACM Trans. Graphics (Proc. SIGGRAPH Asia)_ 34, 6 (Oct. 2015), 248:1–248:16. 
*   Luo et al. [2024] Haimin Luo, Min Ouyang, Zijun Zhao, Suyi Jiang, Longwen Zhang, Qixuan Zhang, Wei Yang, Lan Xu, and Jingyi Yu. 2024. GaussianHair: Hair Modeling and Rendering with Light-aware Gaussians. _arXiv preprint arXiv:2402.10483_ (2024). 
*   Mescheder et al. [2018] Lars Mescheder, Andreas Geiger, and Sebastian Nowozin. 2018. Which Training Methods for GANs Do Actually Converge?. In _International conference on machine learning_. PMLR, 3481–3490. 
*   Mildenhall et al. [2020] Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. 2020. NeRF: Representing Scenes As Neural Radiance Fields for View Synthesis. In _ECCV_. 
*   Niemeyer and Geiger [2021] Michael Niemeyer and Andreas Geiger. 2021. GIRAFFE: Representing Scenes As Compositional Generative Neural Feature Fields. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 11453–11464. 
*   Nikolaev et al. [2024] Maxim Nikolaev, Mikhail Kuznetsov, Dmitry Vetrov, and Aibek Alanov. 2024. HairFastGAN: Realistic and Robust Hair Transfer with a Fast Encoder-Based Approach. _arXiv preprint arXiv:2404.01094_ (2024). 
*   Or-El et al. [2022] Roy Or-El, Xuan Luo, Mengyi Shan, Eli Shechtman, Jeong Joon Park, and Ira Kemelmacher-Shlizerman. 2022. StyleSDF: High-resolution 3D-Consistent Image and Geometry Generation. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 13503–13513. 
*   Pan et al. [2023] Dongwei Pan, Long Zhuo, Jingtan Piao, Huiwen Luo, Wei Cheng, Yuxin Wang, Siming Fan, Shengqi Liu, Lei Yang, Bo Dai, et al. 2023. RenderMe-360: a Large Digital Asset Library and Benchmarks Towards High-fidelity Head Avatars. _Advances in Neural Information Processing Systems_ 36 (2023), 7993–8005. 
*   Paris et al. [2004] Sylvain Paris, Hector M. Briceño, and François X. Sillion. 2004. Capture of Hair Geometry from Multiple Images. _ACM Trans. Graph._ 23, 3 (aug 2004), 712–719. 
*   Park et al. [2019] Taesung Park, Ming-Yu Liu, Ting-Chun Wang, and Jun-Yan Zhu. 2019. Semantic Image Synthesis with Spatially-Adaptive Normalization. In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_. 2337–2346. 
*   Pidhorskyi et al. [2024] Stanislav Pidhorskyi, Tomas Simon, Gabriel Schwartz, He Wen, Yaser Sheikh, and Jason Saragih. 2024. Rasterized Edge Gradients: Handling Discontinuities Differentiably. arXiv preprint. arXiv:2405.02508. 
*   Richardson et al. [2021] Elad Richardson, Yuval Alaluf, Or Patashnik, Yotam Nitzan, Yaniv Azar, Stav Shapiro, and Daniel Cohen-Or. 2021. Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation. In _IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_. 
*   Saito et al. [2018] Shunsuke Saito, Liwen Hu, Chongyang Ma, Hikaru Ibayashi, Linjie Luo, and Hao Li. 2018. 3D Hair Synthesis Using Volumetric Variational Autoencoders. _ACM Trans. Graph._ 37, 6, Article 208 (dec 2018), 12 pages. 
*   Saito et al. [2024] Shunsuke Saito, Gabriel Schwartz, Tomas Simon, Junxuan Li, and Giljoo Nam. 2024. Relightable Gaussian Codec Avatars. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 130–141. 
*   Schwarz et al. [2020] Katja Schwarz, Yiyi Liao, Michael Niemeyer, and Andreas Geiger. 2020. GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis. _Advances in Neural Information Processing Systems_ 33 (2020), 20154–20166. 
*   Shen et al. [2023] Yuefan Shen, Shunsuke Saito, Ziyan Wang, Olivier Maury, Chenglei Wu, Jessica Hodgins, Youyi Zheng, and Giljoo Nam. 2023. CT2Hair: High-Fidelity 3D Hair Modeling Using Computed Tomography. _ACM Transactions on Graphics_ 42, 4 (2023), 1–13. 
*   Sklyarova et al. [2024] Vanessa Sklyarova, Egor Zakharov, Otmar Hilliges, Michael J. Black, and Justus Thies. 2024. Text-Conditioned Generative Model of 3D Strand-based Human Hairstyles. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_. 4703–4712. 
*   Sun et al. [2022] Jingxiang Sun, Xuan Wang, Yichun Shi, Lizhen Wang, Jue Wang, and Yebin Liu. 2022. IDE-3D: Interactive Disentangled Editing for High-Resolution 3D-aware Portrait Synthesis. _ACM Transactions on Graphics (TOG)_ 41, 6, Article 270 (2022), 10 pages. 
*   Vaswani et al. [2017] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin. 2017. Attention Is All You Need. In _Advances in Neural Information Processing Systems_, Vol.30. 
*   Wang et al. [2022] Ziyan Wang, Giljoo Nam, Tuur Stuyck, Stephen Lombardi, Michael Zollhöfer, Jessica Hodgins, and Christoph Lassner. 2022. HVH: Learning a Hybrid Neural Volumetric Representation for Dynamic Hair Performance Capture. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 6143–6154. 
*   Ward et al. [2007] Kelly Ward, Florence Bertails, Tae-Yong Kim, Stephen R Marschner, Marie-Paule Cani, and Ming C Lin. 2007. A Survey on Hair Modeling: Styling, Simulation, and Rendering. _IEEE transactions on visualization and computer graphics_ 13, 2 (2007), 213–234. 
*   Wei et al. [2022] Tianyi Wei, Dongdong Chen, Wenbo Zhou, Jing Liao, Zhentao Tan, Lu Yuan, Weiming Zhang, and Nenghai Yu. 2022. HairCLIP: Design Your Hair by Text and Reference Image. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 18072–18081. 
*   Wei et al. [2023] Tianyi Wei, Dongdong Chen, Wenbo Zhou, Jing Liao, Weiming Zhang, Gang Hua, and Nenghai Yu. 2023. HairCLIPv2: Unifying Hair Editing Via Proxy Feature Blending. In _Proceedings of the IEEE/CVF International Conference on Computer Vision_. 23589–23599. 
*   Wu et al. [2022] Keyu Wu, Yifan Ye, Lingchen Yang, Hongbo Fu, Kun Zhou, and Youyi Zheng. 2022. NeuralHDHair: Automatic High-fidelity Hair Modeling from a Single Image Using Implicit Neural Representations. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 1526–1535. 
*   Wuu et al. [2022] Cheng-hsin Wuu, Ningyuan Zheng, Scott Ardisson, Rohan Bali, Danielle Belko, Eric Brockmeyer, Lucas Evans, Timothy Godisart, Hyowon Ha, Xuhua Huang, et al. 2022. Multiface: A Dataset for Neural Face Rendering. _arXiv preprint arXiv:2207.11243_ (2022). 
*   Xu et al. [2014] Zexiang Xu, Hsiang-Tao Wu, Lvdi Wang, Changxi Zheng, Xin Tong, and Yue Qi. 2014. Dynamic Hair Capture Using Spacetime Optimization. _ACM Transactions on Graphics (TOG)_ 33, 6, Article 224 (nov 2014), 11 pages. 
*   Xue et al. [2022] Yang Xue, Yuheng Li, Krishna Kumar Singh, and Yong Jae Lee. 2022. GIRAFFE HD: A High-Resolution 3D-aware Generative Model. In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_. 18440–18449. 
*   Zakharov et al. [2024] Egor Zakharov, Vanessa Sklyarova, Michael J Black, Giljoo Nam, Justus Thies, and Otmar Hilliges. 2024. Human Hair Reconstruction with Strand-Aligned 3D Gaussians. In _European Conference of Computer Vision (ECCV)_. 
*   Zhang et al. [2017] Meng Zhang, Menglei Chai, Hongzhi Wu, Hao Yang, and Kun Zhou. 2017. A Data-driven Approach to Four-view Image-based Hair Modeling. _ACM Trans. Graph._ 36, 4 (2017), 156–1. 
*   Zheng et al. [2023] Yujian Zheng, Zirong Jin, Moran Li, Haibin Huang, Chongyang Ma, Shuguang Cui, and Xiaoguang Han. 2023. HairStep: Transfer Synthetic to Real Using Strand and Depth Maps for Single-View 3D Hair Modeling. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 
*   Zheng et al. [2022] Yinglin Zheng, Hao Yang, Ting Zhang, Jianmin Bao, Dongdong Chen, Yangyu Huang, Lu Yuan, Dong Chen, Ming Zeng, and Fang Wen. 2022. General Facial Representation Learning in a Visual-linguistic Manner. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_. 18697–18709. 
*   Zhou et al. [2023] Yuxiao Zhou, Menglei Chai, Alessandro Pepe, Markus Gross, and Thabo Beeler. 2023. GroomGen: A High-Quality Generative Hair Model Using Hierarchical Latent Representations. _ACM Trans. Graph._ 42, 6, Article 270 (Dec. 2023), 16 pages. 
*   Zhou et al. [2018] Yi Zhou, Liwen Hu, Jun Xing, Weikai Chen, Han-Wei Kung, Xin Tong, and Hao Li. 2018. HairNet: Single-View Hair Reconstruction Using Convolutional Neural Networks. In _Proceedings of the European Conference on Computer Vision (ECCV)_. 235–251. 
*   Zhu et al. [2021] Peihao Zhu, Rameen Abdal, John Femiani, and Peter Wonka. 2021. Barbershop: GAN-based Image Compositing Using Segmentation Masks. _arXiv preprint arXiv:2106.01505_ (2021). 
*   Zhu et al. [2020] Peihao Zhu, Rameen Abdal, Yipeng Qin, and Peter Wonka. 2020. Sean: Image Synthesis with Semantic Region-Adaptive Normalization. In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_. 5104–5113. 
*   Zwicker et al. [2001] Matthias Zwicker, Hanspeter Pfister, Jeroen Van Baar, and Markus Gross. 2001. EWA Volume Splatting. In _Proceedings Visualization, 2001. VIS’01._ IEEE, 29–538.