Thank you for the valuable feedback! We also appreciate your positive view of the improvements in our learning-based framework. We will do our best to address your concerns as detailed below.

1. Material property sensitivity:

We agree that traditional physics-based simulation models benefit from explicitly defined physical parameters (e.g., stiffness), which allow direct control across material types. In contrast, our approach formulates dynamic hair modeling as a data-driven task within the 3DGS representation. For example, here we would like to explain with some simple formulations:

• Physics-based formulation:

$$m \frac{d^2 \mathbf{x}}{dt^2} = -k (\mathbf{x} - \mathbf{x}_{0})- c \frac{d\mathbf{x}}{dt} + \mathbf{F}$$

This is a simplified spring-damper system formulation, left side indicates “how much the hair wants to move,” and the right side states “what is making it move.”, here $m$ is the mass of the hair segment, $\mathbf{x}$ its current position, $\mathbf{x}_{0}$ the rest position, $k$ the stiffness, $c$ the damping coefficient, and $\mathbf{F}$ represents external forces such as gravity. And the movement of each hair segment is controlled by these parameters.

• Data-driven formulation:

Here we show a simplified high-level formulation of data-driven model. We define a neural network $f_\theta$ that models hair dynamics, where $\theta$ denotes the learnable parameters. Given a hair current position $\mathbf{x}^i$, motion flow vector/velocity $\mathbf{v}^i$, and a style feature $\mathbf{s}$ (e.g., hair volume latent code), the network predicts a motion update:

$$\Delta \mathbf{x}^{i+1} = f_\theta(\mathbf{x}^i, \mathbf{v}^i, \mathbf{s})$$

The next position is obtained via residual addition: $\mathbf{x}^{i+1} = \mathbf{x}^i + \Delta \mathbf{x}^{i+1}$.

Therefore, rather than manually tuning physical parameters, our model learns motion priors from a large, diverse dataset (see Supple. A). While material properties (e.g., stiffness, damping) are not explicitly modeled, style features such as the hair latent code $\mathbf{s}$ serve as implicit priors that guide the learned dynamics in our data-driven framework. This enables robust generalization across unseen motion patterns without hair parameters tuning.

2. Realistic motion coverage and evaluation:

We agree that realistic and high-energy motion is essential for evaluating dynamic hair behavior. While the video highlights select cases (e.g., increased velocity), we are adding more diverse high-energy examples.

Hence, to further evaluate our model, we did evaluations on the public motion capture dataset Mixamo. We selected the “Nervously Look Around” sequence, which contains relatively high-energy head motions. For testing, we extracted the head rotation and upper body mesh, and used them as inputs.

We applied this motion to 3 hairstyles: Blowout, Ponytail, and Curly, to assess generalization to unseen, high-energy inputs.

Visually, our model generates smooth, and coherent dynamics by sharing volumetric priors across neighboring strands, resulting in unified, directional hair motion even under energetic inputs. Due to NeurIPS policy, we cannot include visual results via link at this stage. Instead, we report the L2 error metrics below, computed against physics-based XPBD ground truth over a 100-frame subsequence, and will include qualitative comparisons in the final revision.

3. The necessity of the proposed dynamic hair model:

The motivation for designing a learning-based dynamic hair model (Stage I) is the integration with the 3DGS representation, to enable dynamic Gaussian hair as a separate layer that integrates seamlessly with multi-layer Gaussian head avatars (Main L16–18). Unlike prior works [1,2] that focus on static hair or lack realistic dynamics [3], our volumetric formulation allows plausible hair deformation prediction from a dense point cloud or pre-trained 3DGS, without requiring explicit body meshes.

• DGH pipeline (Ours):

Pre-trained head GS avatar
→ Re-animation
→ DGH predicts dynamic Gaussian hair deformation (from half-body GS / point cloud)
→ Merge with head GS
→ Final avatar with dynamic hair

• Physics-cased pipeline:

Pre-trained head GS avatar
→ Re-animation
→ Convert to explicit mesh
→ Run physics-based hair simulation
→ Render with 3D engine and shaders to obtain hair appearance
→ Convert rendered hair to 3DGS representation
→ Merge
→ Final avatar

Unlike physics-based simulators, which rely on explicit meshes and require additional rendering and conversion steps, our DGH framework only needs head rotation and a dense point cloud/pre-trained GS avatar. By converting static hair and upper-body into volume, we enable mesh-free deformation prediction, making our model more compatible with Gaussian-based avatars and easier to integrate into learning-based re-animation pipelines without additional rigging or simulation overhead.

To date, neural-based simulators are mostly quasi-static [4] and do not model dynamics (e.g., damping effect, acceleration) and upper-body (shoulder) intersections with realism [5]. We also view our learning-based model as a complementary alternative to traditional simulators. Rather than relying on explicit material parameters, it learns hair motion priors from data. We believe with more hairstyle data, this framework holds potential for a more generalizable and comprehensive solution to dynamic hair modeling. We also want to highlight that DGH also enables photorealistic rendering of dynamic hair (using 3DGS) at lower latency than traditional rendering with 3D engines running sophisticated hair shaders with physics-based simulation needs rendering on top. We have new results showing our dynamic hair integrated with real human Gaussian avatars, which we will include in the revision.

And we thank you again for the thoughtful suggestions, especially Q1, which provided valuable insights and inspired us to explore future extensions. As suggested, we are interested in exploring lightweight physics-inspired constraints to further enhance realism in future work.

[1] Luo, Haimin, et al. "Gaussianhair: Hair modeling and rendering with light-aware gaussians." arXiv preprint arXiv:2402.10483 (2024).

[2] Zakharov, Egor, et al. "Human hair reconstruction with strand-aligned 3d gaussians." ECCV 2024.

[3] Qian, Shenhan, et al. "Gaussianavatars: Photorealistic head avatars with rigged 3d gaussians." CVPR 2024.

[4] Stuyck, Tuur, et al. “Quaffure: Real-Time Quasi-Static Neural Hair Simulation”, CVPR 2025

[5] Wang, Ziyan, et al. “NeuWigs: ANeural Dynamic Model for Volumetric Hair Capture and Animation”, CVPR 2023

Thank you for the thoughtful feedback! We address your concerns in detail below and will make our best effort to incorporate the suggestions:

1. Stage naming ambiguity:

Thank you for pointing out the naming ambiguity. This will be clarified. As shown in Fig. 2, our framework consists of two main stages:

• Stage I: Coarse-to-fine dynamic hair modeling
• Stage II: Appearance optimization

Within Stage I, we adopt a coarse-to-fine design:

• The coarse stage learns hair deformation from static hair.
• The fine stage refines secondary dynamics (e.g., inertia, damping).

Therefore, the terms "fine stage" and "second stage" refer to different modules.

To improve clarity, we provide the following table:

As this caused confusion, we will rename Stage I and II as Hair Dynamics Model and Appearance Model, in the revision.

2. Curvature-based Gaussian blending:

Thank you for the insightful question. As stated in our hypothesis (L218–220), each hair strand is composed of discrete segments, which can lead to appearance discontinuities, particularly in high-curvature regions where the tangent direction changes abruptly.

While curvature does not directly impact visibility (which is related to camera viewpoint and depth ordering), it significantly affects the continuity of shading and appearance across segments.

Unlike continuous surfaces, Gaussian hair treats each segment as an independent shading unit, each with its own tangent vector $\mathbf{t_i}$. In high-curvature regions, if the angle between $\mathbf{t_i}$ and $\mathbf{t_{i+1}}$ becomes large, it will lead to discontinuities in shading intensity. Ideally, this can be mitigated by increasing segment density, but usually for hair tracking purpose, we use a fixed number of segments per hair strand, so an alternative approach is to apply curvature-aware blending to smooth visual transitions.

Here we give a simple hair diffuse shading formulation: $I_i \propto \max(0, \mathbf{t_i} \cdot \mathbf{l})$ where $I_i$ is the shading intensity of the $i$-th hair segment, $\mathbf{t_i}$ is its tangent direction, and $\mathbf{l}$ is the light direction. And the shading discontinuity between adjacent Gaussians is: $|I_i - I_{i+1}| \propto \left| \max(0, \mathbf{t_i} \cdot \mathbf{l}) - \max(0, \mathbf{t_{i+1}} \cdot \mathbf{l}) \right|.$ And this value increases with curvature. Our curvature-based blending design reduces this effect by weighting contributions from adjacent segments according to their angular deviation, ensuring smoother appearance without increasing segment density. Without blending, high-curvature areas may exhibit visual artifacts such as shading discontinuities, as shown in Fig. 7 (with zoom-in) and the video demo (02:57–03:09; quality may be reduced due to video compression).

We will include additional visual comparisons in the revision to further illustrate this contribution.

3. Robustness to unseen motion patterns (e.g., sudden downward movements):

Thanks to our coarse-to-fine dynamic hair modeling framework (Fig. 2 Framework Overview) and training on large-scale motion sequences (Supple. A), our model is robust to unseen head motions, including sudden downward movements. As shown in the demo video (02:34–02:48), under a sudden head drop and turn, the coarse stage captures the primary deformation, while the fine stage models secondary motion (e.g., damping effects) and preserves realistic hair dynamics. Due to NeurIPS policy, we cannot include additional PDFs for visual results at this stage. As suggested, we will add more qualitative results, including re-animation results with dynamic hair merged into real human avatars, in the final version to further illustrate this.

Thank you for the thoughtful feedback! We address your concerns in below and will do our best to incorporate the suggestions (equation clarity, section orders, etc ):

1. Equation clarity:

(a) From L161-163, and in Eq. (1), no clear formula for $\mathcal{L_\text{point}}$ and $\mathcal{L_\text{SDF}}$.

Thank you for noting the missing explicit definitions of $\mathcal{L_\text{point}}$ and $\mathcal{L_\text{SDF}}$ in Eq. (1). While briefly described in L162–163, we agree that providing formal formulas will improve clarity.

• Point MSE loss

$$\mathcal{L_\text{point}} = \frac{1}{N} \sum_{i=1}^{N} \left\| \hat{\mathbf{p}}_i - \mathbf{p}_i^{\mathrm{GT}} \right\|_2^2$$

where $\hat{\mathbf{p}}_i$ is the predicted 3D hair point and $\mathbf{p}_i^{\text{GT}}$ is the corresponding ground-truth hair point.

• SDF penalty loss

$$\mathcal{L_\text{SDF}} = \frac{1}{N} \sum_{i=1}^{N} \max\left( 0,\ -\mathrm{SDF}(\hat{\mathbf{p}}_i) \right)$$

where $\mathrm{SDF}(\hat{p}_i)$ is the signed distance to the body surface, and we penalize points inside the mesh by applying ReLU.

We will include these definitions in the final version.

(2) Tangent vector definition.

The hair tangent vector represents the local hair direction and the visual definition is in Fig. 3. And Yes, the formal definition is given in Eq (7). Thank you for the suggestion, we will clarify the explanation order in the revision.

(3) Section structure.

Thank you for the suggestion. We will reorder the sections as suggested to improve the logical flow.

2. Training strategy:

Our learning-based framework follows a two-stage training strategy, as described in Introduction (L57–75). The model is not trained end-to-end (to be explored in future work). We first train a hair deformation model that includes a secondary dynamics module, and then train a separate appearance model. Training times for each model are provided in the Supple. (L101–103). During inference, we first predict hair dynamics, then generate appearance from the deformed hair.

3. Real-world generalization and hair complexity:

We understand the concerns regarding real data testing. Our model is robust to real-world hair complexity, supported by a well-prepared synthetic dataset and a learning-based architecture. As the first data-driven framework for dynamic hair modeling with 3DGS representations, our method also offers a novel solution to the rigid hair problem in Gaussian head avatar re-animation.

Due to NeurIPS policy, we cannot include PDFs for visual results this year. However, we have conducted new tests combining additional motion with pre-trained real human Gaussian avatars, demonstrating that our model serves as a novel and effective supplement for multi-layer Gaussian avatar re-animation.

To capture lighting effects, our appearance model estimates spherical harmonics (SH) coefficients as a compact color representation. The training dataset includes artist-designed hair shaders under natural lighting conditions to simulate real-world scenarios.

While our current setup is based on synthetic data, we acknowledge its limitations and consider future directions such as dataset expansion and hair relighting to further improve realism and generalization.

As noted in the Introduction (L51–52) and Limitations (Supple. L155–157), capturing strand-level dynamic hair in-the-wild is challenging due to hardware limitations and the lack of robust hair tracking. To address this, we created a large-scale, lab-controlled synthetic dataset driven by various head movements (Main L243–249, Supple. A). This dataset includes diverse head poses and motions, and photorealistic rendering, which we believe generalize well to real scenarios, as demonstrated in video (03:11).

As mentioned in Main L87, we also plan to release our synthetic dataset to support and accelerate data-driven dynamic hair modeling.

Thank you for your valuable feedback! We carefully considered your comments and provide detailed responses below:

1. Generalization to real data:

Our method relies on synthetic data for ground-truth (dynamic hair) and supervised training, as discussed in the Introduction (L51–52) and Limitations (Supple. L155–157), as capturing strand-level dynamic hair in the wild remains challenging due to hardware limitations and the absence of robust hair tracking systems. Hence, we opted to create photorealistic dynamic hair data at scale, using state-of-the-art offline toolkits from the graphics community (i.e., physics-based simulation, head motion, and 3D engine with hair shaders for rendering), as detailed in the paper (Main L243–249, Supple. A).

This dataset includes a wide range of head poses and dynamics, enabling our model to generalize to realistic motions, as demonstrated in the video (03:11). While we initially explored unsupervised training using in-the-wild videos and coarse hair meshes, the results lacked strand-level precision and visual sharpness required for dynamic Gaussian rendering.

Beyond hair prediction, our other goal is to align with the 3DGS representation. Our learning-based Stage I model supports dynamic Gaussian hair as a separate layer, designed to integrate seamlessly with multi-layer Gaussian head avatars (Main L16–18). This (point-based) mesh-free design enables re-animation of arbitrary hairstyles (long hair, curls, ponytails) with plausible dynamics while avoiding the complexities of physics-based simulation pipelines.

Our DGH framework is compatible with 3DGS avatars and can be extended to improve head avatar realism. The pipeline is as follows:

Real multi-view images → Strand-based static hair reconstruction [1] → DGH → Merge with animation-ready 3DGS avatar

Due to NeurIPS policy, we cannot include visual results at this stage, but we will present additional results with dynamic hair merged into human avatars in the final version. As mentioned in Main L87, we also plan to release our synthetic dataset to support and accelerate data-driven dynamic hair modeling.

[1] Sklyarova, Vanessa, et al. "Neural haircut: Prior-guided strand-based hair reconstruction." ICCV 2023.

2. SDF regularization in fine stage:

Thank you for the thoughtful observation. While the coarse stage includes SDF constraints to discourage hair-body interpenetration, we do not apply the same constraints in the fine stage. This is because the fine stage operates in a residual manner, predicting subtle flow-based refinements on top of the coarse deformation. These updates are typically small and designed to model secondary dynamics (e.g., acceleration, damping), rather than introducing large displacements that could lead to new penetrations.

Based on our observations, we omitted SDF supervision in the fine stage, and also especially since real-time SDF evaluations are computationally expensive in training. That said, we agree that incorporating lightweight geometric constraints in the fine stage could further improve robustness under fast motion, and we are planning to explore this direction in future work.

3. The impact of temporal window size:

Let us clarify what we refer to as "temporal modeling". As described in L65–69 and Fig. 2 (Framework Overview), our Stage I consists of two modules:

• Coarse stage: Uses only the current frame’s pose to predict the hair deformation relative to the rigid hair. Since no temporal history is involved, this stage models first-order, pose-conditioned deformation.

• Fine stage: Refines the deformation by predicting per-frame flow vectors $\Delta x_{t}$ from previously deformed hair. By leveraging information from $t{-}2$ and $t{-}1$, this stage captures second-order dynamics (acceleration, damping), while also ensuring temporal coherence. (L166-173)

Specifically, the fine (temporal) stage learns the flow vector from the deformed hair at $t{-}1$ to $t$, conditioned on deformation and flow from earlier steps ($t{-}2$ to $t{-}1$). This enables the model to implicitly capture second-order dynamics, such as acceleration, by observing how motion evolves over time.

Acceleration is computed via finite differences of velocity, requiring 3 positions:

$$a_t = \frac{(x_{t} - x_{t-1}) - (x_{t-1} - x_{t-2})}{\Delta t^2}$$

Our fine model predicts $x_t$ based on:

• $x_{t-2}$ and $x_{t-1}$: previous deformed hair
• $\Delta x_{t-1} = x_{t-1} - x_{t-2}$: the previous flow vector

The current model already observes the change in flow via $x_{t-2} \rightarrow x_{t-1}$ and it implicitly captures second-order effects (acceleration) using two positions and one velocity vector. With enough training data, it can learn acceleration-like patterns from local motion trends. We agree that expanding the temporal window ($t{-}3$, $t{-}4$) could help capture longer-term trends, we find the two-frame design effective for modeling higher-order dynamics.

This capability is demonstrated in our video (02:35–02:48), where we can see the damping effects. We will clarify this temporal modeling strategy and include the window size discussion in the revised version.