HAIF-GS: Hierarchical and Induced Flow-Guided Gaussian Splatting for Dynamic Scene

We thank the reviewer for the encouraging feedback. We are glad that the reviewer finds our method “achieving state-of-the-art performance across various scenes,” and considers the design of the induced flow-guided deformation and cycle loss to be “interesting and intuitive.”

Q1. Discussion on Method Paradigms and Our Positioning.

We thank the reviewer for raising this important question regarding our relation to MoSca[Lei et al., 2025] and Shape-of-Motion(SoM)[Wang et al., 2024]. As the reviewer pointed out, recent dynamic 3D reconstruction approaches tend to follow two distinct paradigms:

1. end-to-end learning from video data using high-level vision priors, as in MoSca and SoM;

2. explicit 3D modeling based on deformable Gaussian splatting, as in Deformable 3D-GS(D-3DGS)[44], 4DGS[38], as well as recent CVPR 2025 papers HiMoR [Liang et al., 2025] and MoDec-GS [Kwak et al., 2025].

Our work clearly belongs to the latter, where we build structured, interpretable deformation fields over explicit Gaussian representations. This difference in paradigm reflects fundamentally different design principles—our method favors geometric control and weak supervision, whereas MoSca/SoM rely on pretrained vision foundation models (VFM) and additional external signals.

Q2. Applicability to iPhone Dataset and Comparison with MoSca/SoM.

In response to the reviewer’s suggestion, we have conducted supplementary experiments on the DyCheck-iPhone dataset, also used by MoSca and SoM. Our method is fully compatible with this dataset and achieves higher PSNR (15.05) than 4DGS(13.68) and D-3DGS(13.72), though lower than MoSca(19.32) and SoM(17.32), as shown in the $\underline{Table\ 1}$ below.

We emphasize, however, that this performance gap is understandable due to the fundamentally different paradigms and resulting experimental settings.

• Challenging properties of the iPhone dataset. It involves strong non-rigid motion, large camera baselines, and noisy depth priors—all of which are known challenges in dynamic 3D reconstruction, especially when no auxiliary supervision is used.
• Heavy reliance on pretrained vision foundation models. MoSca leverages powerful pretrained components (e.g., BootsTAPIR) to obtain high-quality optical flow and depth, which significantly improve reconstruction but come with high computational cost and less interpretability.
• Access to ground-truth depth during training. MoSca further utilizes the iPhone dataset’s provided depth maps as ground-truth supervision, while our method operates entirely without depth supervision, making it applicable to real-world settings where such data is unavailable.

Despite these differences, our approach achieves strong performance on the iPhone dataset and outperforms prior explicit modeling methods (4DGS, D-3DGS), validating its effectiveness within its paradigm. Its lightweight and interpretable design makes it more suitable for general deployment compared to end-to-end alternatives.

We really appreciate the reviewer for pointing out this important connection. We have revised the final version of the Introduction to include a discussion on MoSca/SoM-style approaches and clarified the paradigm-level distinctions between methods.

Table1. Results(PSNR↑) on Dycheck-iphone dataset

Furthermore, this discussion inspires an exciting direction for future work. With the rapid advances of vision foundation models (VFMs), such as the recent VGGT [Wang et al., 2025], we recognize the growing potential of incorporating VFM-derived signals to address long-standing challenges in the 3DGS-based paradigm, including inaccurate camera poses and inefficient prior point cloud initialization. A promising research avenue lies in bridging the two paradigms, aiming to combine the controllability and efficiency of explicit Gaussian modeling with the powerful priors and robustness offered by VFMs.

Q3. Formalization of Temporal Feature Aggregation.

We appreciate the reviewer for the helpful suggestion. While the original text describes the core idea of temporal aggregation (Lines 184-192), we agree that presenting the information flow more formally would further enhance clarity and self-containment, especially without relying on Figure 2.

Below we provide a more structured and formalized version of this part, which we will include in the final camera-ready version.

1. Given a motion anchor $x$ at timestamp $t$, the Induced Flow MLP predicts forward and backward flows:

$$F^{t-1},\ F^{t+1} = \\text{MLP}_{\\text{flow}}(x,\ t)$$

2. These flows define three temporally shifted queries:

$$q_{t-1} = (x + F^{t-1},\ t{-}1),\quad q_t = (x,\ t),\quad q_{t+1} = (x + F^{t+1},\ t{+}1)$$

3. Each query is passed through a shared Deformable MLP to extract a time-aware feature embedding: (Due to rendering issues on OpenReview, we temporarily replace $q_{t-1}$ and $q_{t+1}$ with $q1$和$q2$ below)

$$f_{t-1} = \\text{MLP}_{\\text{deform}}(q1)$$ $$f_t = \\text{MLP}_{\\text{deform}}(q_t)$$ $$f_{t+1} = \\text{MLP}_{\\text{deform}}(q2)$$

4. The final temporally aggregated feature is computed as: (Due to rendering issues on OpenReview, we temporarily replace $f_{t-1}$ and $f_{t+1}$ with $f1$和$f2$ below)

$$\\tilde{f}_t = \\lambda f_1 + (1 - 2\\lambda) f_t + \\lambda f_2$$

This formalization makes the process more transparent and easier to follow without relying on Figure 2. We appreciate the reviewer’s suggestion and will incorporate this revision into the main paper.

Q3. Visualization of scene flow and anchor densification.

We thank the reviewer for the valuable suggestion. Due to the rebuttal policy restricting figures and external links, we are unable to directly provide visualizations of the induced scene flow and anchor densification. Nevertheless, we have addressed these points indirectly in our response and will include both two in the final version and on the project page.

1. Scene flow without Cycle Consistency Loss.

We thank the reviewer for the suggestion and understand the motivation behind visualizing the induced scene flow with and without the cycle consistency loss ($L_{cycle}$) to better illustrate the ablation effects. Such visualizations can indeed be provided.

However, it is important to note that in our framework, the induced flow is not defined at the Gaussian level, but is instead computed at the anchor level and serves as an internal supervisory signal to guide motion learning. Since it is generated in a frame-specific and anchor-driven manner, the visualized flow field may not directly reflect global motion or deformation patterns. As a result, while the flow visualizations can highlight certain local differences (e.g., smoother or more consistent directions), their overall interpretability may be limited compared to direct quantitative comparisons.

That said, we have examined the induced scene flow qualitatively on D-NeRF. Without $L_{cycle}$, we observe:

• asymmetric forward and backward flows, failing to form closed temporal paths;
• increased noise in motion vectors, especially near thin or fast-moving regions (e.g., limbs, fingers);
• temporal jitter in dynamic parts of the flow field, disrupting inter-frame coherence.

These artifacts result in degraded deformation quality and ultimately lower rendering performance. We believe the most appropriate way to assess the effectiveness of $L_ {cycle}$ is through its quantitative impact on rendering quality and temporal consistency. As shown in the ablation study in Table 3 of the main paper, removing $L_{cycle}$ leads to a 0.12 PSNR drop, indicating its contribution to learning temporally coherent deformations.

2. Visual Comparison of Anchor Points Before and After Densification.

We thank the reviewer for the suggestion and understand the motivation to verify whether densification focuses on regions with complex and fine-grained motion. Such visualizations can be provided, and we will include them in the final version as well as on our project page.

We visualize anchor positions on D-NeRF scenes by rendering them together with the novel-view images. In JumpingJacks, densified anchors appear around limb-related parent anchors, with finer anchors added at the fingers. In Hook and HellWarrior, densification mainly occurs at joint regions with fine-grained deformations. These patterns match the areas where our method shows clearer motion reconstruction in Fig. 4 of the main paper, confirming that our hierarchical anchor densification (HAD) adaptively refines motion-complex regions rather than uniformly increasing anchor count. This is also supported by the ablation in Fig. 5 of the main paper.

Reference

[1] Yiming Liang, Tianhan Xu, and Yuta Kikuchi. Himor: Monocular deformable gaussian reconstruction with hierarchical motion representation. In Proceedings of the Computer Vision and Pattern Recognition Conference, pages 886–895, 2025. 17

[2] Sangwoon Kwak, Joonsoo Kim, Jun Young Jeong, Won-Sik Cheong, Jihyong Oh, and Munchurl Kim. Modec-gs: Global-to-local motion decomposition and temporal interval adjustment for compact dynamic 3d gaussian splatting. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2025. 17

We thank the reviewer for the positive comments. We are glad that the reviewer finds our proposed modules “interesting and make sense,” including the motion anchors, induced flow-guided deformation module, and the coarse-to-fine hierarchical anchor densification strategy.

Q1. Clarification on Monocular Baselines.

We appreciate the reviewer’s comments and the suggested works Shape of Motion(SoM)[Wang et al., 2024] and MoSca[Lei et al., 2025].

First, we would like to clarify that all baselines used in Figure 1(b) and our experiments are strong and widely adopted monocular methods, and thus all our experimental comparisons and analyses are fair and appropriate. We will also explicitly clarify the monocular setting of these baselines in the final version to avoid potential misunderstandings.

In Figure 1(b), 4DGS[38] and D-3DGS[44] are both widely recognized and frequently used in the monocular dynamic reconstruction literature. Notably, SoM and MoSca suggested by the reviewer also adopt these baselines under monocular settings: SoM compares against D-3DGS, and MoSca includes 4DGS in its main evaluation. This further supports the relevance of using 4DGS and D-3DGS in Figure 1(b) to highlight the limitations of prior approaches in modeling fine-grained, non-rigid motion.

Beyond Figure 1, all baselines used in our experiments (e.g., SC-GS[12], HyperNeRF[29]) are either designed for or widely used in monocular dynamic reconstruction, and all evaluations are conducted under monocular training settings. Additionally, we have added SoM and MoSca as additional baselines in our main experiments, and we will detail the corresponding results in the response to $\underline{Q2}$.

We have also revised the manuscript to reference Figure 1(a) in the introduction.

Q2. Quantitative Comparison with MoSca/SoM.

We thank the reviewer for emphasizing the importance of including additional comparisons with SoM and MoSca, two recently released monocular methods. Both SoM and MoSca follow the paradigm of end-to-end learning from video data using high-level vision priors, in contrast to our method and prior works such as 4DGS, D-3DGS, and recent CVPR 2025 papers like HiMoR [Liang et al., 2025], which adopt explicit 3D modeling based on deformable Gaussian splatting.

In response, we conduct additional experiments on the NeRF-DS dataset, comparing our method with SoM and MoSca, as shown in $\underline{Table\ 1}$ below. These results show that our method outperforms (24.63) both SoM (24.11) and MoSca (24.51) in most scenes, achieving consistently higher reconstruction quality. It is worth noting that SoM and MoSca rely on pretrained vision foundation models (VFMs) and depth priors, which offer clear advantages on datasets with available depth. However, NeRF-DS provides no depth prior, making it a more challenging benchmark for evaluating monocular methods. In this setting, our method demonstrates better performance while remaining lightweight and free of external dependencies, such as pretrained models or auxiliary signals.

This improvement stems from our 3DGS-specific design, including sparse motion anchors, induced flow-guided deformation, and hierarchical anchor densification, which together enable accurate dynamic modeling under purely monocular supervision.

We have also included MoSca and SoM as comparison baselines in the final version of the paper, further strengthening the completeness of our evaluation.

Table1. Comparison(PSNR↑) with SP-GS on NeRF-DS

Q3. Additional ablation combinations and baseline without key modules.

We thank the reviewer for the suggestion. In response, we report additional combinations in $\underline{Table\ 2}$ below, including the complete baseline without all key modules (w/o Induced Flow (IF), Cycle Consistency Loss ($L_{cycle}$), Anchor Filtering (AF), and Hierarchical Anchor Densification (HAD)). Our original submission ($\underline{Appendix A.4}$) also includes an ablation study of loss weights settings.

The results show that each component contributes to performance, and their combination leads to significant improvements. In particular, removing induced flow and HAD results in clear drops in both reconstruction quality and consistency, confirming their central roles. These ablations validate the design motivation of HAIF-GS.

We have added the baseline configuration to the main ablation section in the revised paper and included all additional ablation combinations in the supplementary material.

Table2. Additional ablations on the key components on NeRF-DS.

Q4. Training and Rendering Efficiency.

We thank the reviewer for the helpful suggestion regarding efficiency. We have conducted extensive evaluations on the D-NeRF dataset (see $\underline{Table\ 3\ and\ 4}$ below). Our method achieves real-time rendering speed (215.4 FPS) while maintaining superior reconstruction quality (PSNR 42.00), outperforming both 4DGS and D-3DGS. These results demonstrate that our approach preserves the efficiency advantage of the 3DGS paradigm, while achieving significant gains in reconstruction quality. $\underline{Table\ 4}$ presents detailed statistics of our method on each D-NeRF scene. All methods are evaluated on an RTX 3090 GPU at a resolution of 800×800.

We have included this efficiency evaluation in the final version of the paper to better support the practical value of our method.

Table3. Comparison of efficiency on D-NeRF dataset

Table4. Evaluation of efficiency on D-NeRF dataset

Typos: Thank you for pointing this out. We have corrected the typo accordingly.

Thanks for the effort on the rebuttal. I have carefully read my responses, as well as the questions and responses of other reviewers.

Reply to authors' Responses: Thanks for the effort in supplementing the clarifications and experiments during the rebuttal.

• Q1: I am convinced by the added clarification. I agree that 4DGS and D-3DGS can be the baselines of the monocular dynamic reconstruction. However, I still advise adding more recent methods to the motivation part of this work for enhancing the effectiveness of the proposed method.
• Q2: I appreciate the authors' effort on the supplemental experiments. However, I find it difficult to accept the effectiveness of the method presented in the experimental results of Table 1. Indeed, the proposed method lacks many pre-trained priors compared to MoSca and SoM, but I think that for the task of monocular dynamic reconstruction, which lacks a lot of visual information, adding priors to improve performance is reasonable and necessary. Furthermore, a promising way for future work is supplementing video generation models, and some works have already been done for it.
• Q2-Addition: Meanwhile, I have also read the responses to other reviewers (related to the experiments of MoSca and SoM). I notice the experimental results of comparisons with MoSca and SoM on the DyCheck dataset in response to reviewer CwJy. Experiments on the DyCheck dataset show that the proposed method has a large performance gap compared with MoSca and SoM. The authors also mainly use pre-training priors as an explanation. However, in my opinion, the current situation of monocular dynamic reconstruction is that we cannot yet implement a method that can synthesize high-quality novel views (for example, we can observe the visual results of MoSca on the DyCheck dataset and some causual videos). Therefore, I think the main challenge at present is how to achieve high-quality reconstruction, no matter what existing technology we use.
• Q3: Therefore, I can only look for the innovations and effectiveness at the 4D representation level. However, it still cannot convince me of the presented ablation results in Table 2. We can only notice that the proposed Induced Flow MLP (IF) is the most important module, while the ablations of other proposed modules seem cannot show their effectiveness. So, I advise that more detailed ablations inside IF are supposed to be added in the future.
• Q4: I am convinced that the added experiments of time-consuming. The results of the tested training and rendering time show the efficiency of the proposed method compared with the 4DGS and D-3DGS baselines.

Overall, I decide to maintain my rating (borderline of reject), because although I recognize the innovation of the method proposed in this work, its ablation experiments and performance comparison with the SOTA methods make it difficult for me to recognize its effectiveness.

We thank the reviewer for the positive feedback. We are glad that the reviewer recognizes our method as “consistently higher performance over other baselines” and finds that “Anchor Filter, Inductive-Flow-Guided Deformation Module and Hierarchical Anchor Propagation mechanism are all novel and effective.”

Q1. Additional evaluation on more challenging real-world datasets.

We thank the reviewer for the suggestion. We agree that further evaluation on more challenging scenes is important. Our original submission already includes real-world results on the NeRF-DS dataset. In response to the concern regarding potential failure in real-world dynamic scenes with limited multi-view clues, we conduct additional evaluations on two challenging datasets:

• HyperNeRF (misc) [29] with topology change and limited multi-view cues;
• DyCheck-iPhone [Gao et al., 2022], featuring large motion and difficult test viewpoints.

As shown in $\underline{Table\ 1\ and\ 2}$ below (PSNR↑), our method consistently outperforms D-3DGS and 4DGS on most scenes, especially under severe motion or topology changes. These results conform that the key modules in HAIF-GS (anchor filtering, hierarchical motion propagation, and the induced flow-guided deformation) remain stable and effective even under limited multi-view supervision or large non-rigid motion. Despite the potential sensitivity to the optimization process, our experiments show that these components do not collapse or diverge, and can still yield accurate reconstructions across diverse challenging scenes. We have included these additional results and corresponding discussions in the final version of the paper.

Table1. Results(PSNR↑) on HyperNeRF (misc)

Table2. Results(PSNR↑) on Dycheck-iphone

Q2. Experimental evidence for efficiency.

We thank the reviewer for pointing this out. We now provide experimental results in $\underline{Table\ 3\ and\ 4}$ to support the efficiency claim. And we have added these results and analyses to the main paper.

As shown in $\underline{Table\ 3}$, our method achieves significantly faster rendering (215.4 FPS) than 4DGS (134.8) and D-3DGS (53.7), with a much lighter query structure. Despite the reduced cost, we achieve higher PSNR (42.00) than both baselines, owing to the Induced Flow module, which enables accurate deformation via sparse anchors. $\underline{Table\ 4}$ reports scene-wise statistics. All methods are tested on an RTX 3090 at 800×800 resolution.

As noted in Section A.5, We acknowledge the relatively larger memory usage due to additional anchor parameters and hierarchy management. However, our model (2.9GB) is still lighter than D-3DGS (4.8GB), striking a good balance between performance and storage. We plan to further optimize memory usage in future work by compressing anchor features or dynamically pruning less-contributing anchors during training.

Table3. Comparison of efficiency on D-NeRF dataset

Table4. Evaluation of efficiency on D-NeRF dataset

Q3. Quantitative comparison with SP-GS.

We thank the reviewer for the comment. As shown in $\underline{Table\ 5}$, our method outperforms SP-GS[5] on NeRF-DS (24.63 vs. 23.15) and D-NeRF (42.00 vs. 37.97; see $\underline{Appendix\ A.4}$). Due to space limits, we included only one sparse-anchor baseline in the main paper, choosing the more recent and competitive SC-GS[12] (24.05 / 41.65) over SP-GS. We have added full comparisons in the final version.

Table5. Comparison(PSNR) with SP-GS on NeRF-DS

Q4. Storyline consistency.

We thank the reviewer for the feedback on storyline clarity. To clarify, let us briefly explain the reasoning behind this organization. The three limitations mentioned in the abstract are addressed sequentially: (1) redundant Gaussian updates motivates our sparse anchor design, while (2) and (3) are further analyzed as two underlying challenges —limited expressiveness and insufficient supervision— caused by previous anchor-based methods. Our three modules (Motion Anchors, IFGD, and Hierarchical Anchors) correspond directly to these limitations. We have revised the abstract and introduction to clarify this mapping and ensure better consistency in presentation.

Q5. Clarification on Qualitative comparison in Figure 4.

We thank the reviewer for the suggestion. The qualitative results in Figure 4 highlight our method’s superiority in modeling fine-grained details (red-circled regions) over 4DGS. For instance, in HellWarrior, we reconstruct armor rivets and straps missed by 4DGS; in Hook, joint textures are sharp, while 4DGS remains vague. These qualitative differences, along with significant PSNR gains (+13.7dB on HellWarrior, +6.4dB on Hook), demonstrate our strength in capturing local deformations. As D-NeRF scenes are object-centric with simple global structure, performance differences mainly manifest in such fine details—where our method excels. We will consider including more diverse viewpoints in the final version.

Q6. Visualization and video results.

We thank the reviewer for the valuable suggestion. Due to the rebuttal policy restricting figures and external links, we are unable to directly provide visualizations of the induced scene flow, dynamic-static separation, and video results. Nevertheless, we have addressed these points indirectly in our response and will include all three in the final version and on the project page.

1. dynamic-static separation

Despite visualization constraints, we provide the following evidence to support the effectiveness of our motion segmentation:

• Anchor-level statistics. $\underline{Table\ 6}$ below reports per-scene motion decomposition on NeRF-DS, including total Gaussians, number of dynamic anchors, and the dynamic ratio (anchors with confidence > 0.5). The overall dynamic ratio is low, aligning with the mostly static content of the scenes.
• Spatial distribution. Visualizations (included in the final version) reveal that dynamic anchors cluster around moving objects, while static anchors are background-distributed, qualitatively confirming correct separation.
• Ablation results. Removing this module causes a 0.18dB PSNR drop on D-NeRF (Tab. 3), indicating that filtering static anchors improves both quality and efficiency.

Table6. Statistics of Motion Anchors on NeRF-DS

2. induced scene flow

Despite visualization constraints, we clarify that:

• Visualization is possible and prepared. The induced flow can be visualized as 3D vectors at anchor locations. We have produced such visualizations and will release them in the final version and on the project page.
• Nature of the induced flow. The induced scene flow is not a directly supervised or dense optical flow field. Instead, it is a sparse, anchor-level motion signal induced implicitly through multi-frame alignment and cycle consistency loss. Its purpose is not to produce explicit flow output, but to serve as internal guidance for temporally consistent deformation. While visualizations are possible and will be provided, we believe the most appropriate way to assess its effectiveness is through its quantitative impact on rendering quality and motion stability.
• Quantitative validation. As shown in Tab.3 in main paper, removing the induced flow module results in a significant drop in rendering quality (PSNR ↓0.72, LPIPS ↑0.028 on NeRF-DS), confirming its importance in motion modeling.

3. video results

We have created a demo video showcasing dynamic reconstruction from novel views on both NeRF-DS and D-NeRF datasets, which will be released on our project page.

We thank the reviewer for recognition of our contributions. We are glad that the reviewer considers “the induced flow-guided deformation module is a reasonable design” and acknowledges that our method “surpasses existing baselines in quantitative evaluation.”

Q1. Clarification on Relation to HiMoR.

We thank the reviewer for pointing out the relation to HiMoR [Liang et al., 2025], which also includes a hierarchical anchor design. While this module shares a structural resemblance, our method follows a fundamentally different formulation and design goal, addressing key challenges that HiMoR does not explicitly consider:

• Ensuring temporal consistency. HiMoR models motion at each frame independently, without enforcing consistency across time. This limits its ability to learn smooth and coherent trajectories. In contrast, we propose an Induced Flow-Guided Deformation module that predicts forward and backward flow in a self-supervised manner. Combined with a cycle consistency loss, this encourages temporally aligned anchor motion throughout the sequence. We also appreciate that the reviewer recognized this component as a reasonable and well-designed part of our framework.

• Reducing reliance on external priors. HiMoR depends on pretrained tracking, segmentation, and monocular depth models to initialize motion bases and guide training. Such reliance may limit its robustness in less controlled settings. Our framework is trained fully end-to-end using only photometric and temporal self-supervision, without any external annotations, making it more generalizable and deployment-friendly.

• Handling static regions efficiently. HiMoR applies motion modeling uniformly across the scene, including static backgrounds, leading to unnecessary optimization and redundancy. Our method introduces an Anchor Filter that learns motion confidence for each anchor and filters out static ones, allowing the model to focus computation on dynamic regions and improve efficiency without sacrificing expressiveness.

These differences reflect a distinct design goal: adaptive, efficient, and self-supervised motion learning, rather than structure-driven modeling under external priors.

In addition to the aforementioned contribution differences, we highlight several methodological distinctions from HiMoR regarding the sparse and hierarchical anchor design, as well as additional components in our system:

• Sparse anchors without external initialization. HiMoR relies on pretrained tracking and depth models to initialize motion bases and nodes, while we adopt a simple FPS-based initialization and fully end-to-end optimization, enhancing generality and ease of use.
• Flexible hierarchical modeling. While both methods use multi-level anchor structures, HiMoR applies a strict tree-structured SE(3) decomposition and recursively composes transformations. In contrast, we adopt layer-wise interpolation and confidence-based fusion, allowing each layer to contribute independently. This flexible design better handles complex motion and avoids the rigidity of explicit trees.
• Temporal flow-guided deformation. HiMoR does not model inter-frame motion explicitly and applies no temporal flow estimation. We introduce a self-supervised flow prediction module that infers forward and backward anchor motion using multi-frame temporal queries, facilitating temporally consistent anchor trajectories and improving motion alignment across frames.
• Adaptive hierarchical densification. HiMoR grows its tree by analyzing per-node neighborhoods, but its densification strategy is hand-designed and not adaptive to local motion complexity. In contrast, we quantify per-anchor motion variance and densify anchors hierarchically only in complex regions. This yields a more targeted and efficient refinement of motion representation.

To further validate this design, we compare our method with HiMoR on the Dycheck-iPhone[Gao et al., 2022] dataset using the same perceptual metric adopted in their paper. As shown in $\underline{Table\ 1}$ below, our method achieves a lower LPIPS score (ours: 0.405 vs. HiMoR: 0.463), indicating improved temporal consistency. This supports the effectiveness of our Induced Flow-Guided Deformation and other innovations in addressing the temporal challenges that HiMoR does not explicitly resolve. We have also incorporated a discussion of HiMoR as a recent anchor-based method into the main paper to provide clearer context and positioning.

Table1. Results(LPIPS↓) on Dycheck-iphone (HiMoR scores from [Liang et al., 2025])

Q2. Results for dynamic-static decomposition.

We appreciate the reviewer’s interest in the dynamic-static decomposition results. While we are unable to include images or external links due to rebuttal guidelines, we provide the following supporting evidence to demonstrate the effectiveness of our motion segmentation:

• Statistics of Motion Anchors. We provide $\underline{Table\ 2}$ below reporting per-scene anchor-level motion decomposition on the NeRF-DS dataset. Specifically, #Gaussians denotes the total number of 3D Gaussians, #Dynamic Anchors is the number of Motion Anchors, and Dynamic Ratio represents the percentage of anchors predicted as dynamic (i.e., confidence > 0.5). As shown in the table, the predicted dynamic ratio is generally low, which matches the scene composition with mostly static content and limited motion, confirming the effectiveness of our decomposition. In basin and plate, where dynamic objects are more dominant, the ratio is higher, further supporting the segmentation accuracy.
• Spatial distribution of dynamic and static anchors. We visualized the dynamic and static anchors on the NeRF-DS dataset. While we cannot include these figures here, the results show that dynamic anchors are predominantly concentrated around the central moving objects, whereas static anchors are distributed across the background. This spatial separation provides strong qualitative evidence of accurate dynamic-static decomposition. We have included anchor visualizations in the final version of the paper.
• Ablation impact. As shown in Tab.3 in main paper, removing the dynamic-static segmentation module results in 0.18dB average PSNR drop on the D-NeRF dataset. This suggests that filtering static anchors improves both rendering quality and motion modeling efficiency.

Table2. Statistics of Motion Anchors on NeRF-DS

We have included visualization of segmentation masks from novel views in the final version of the paper. These will highlight temporally coherent motion boundaries, consistent with our confidence maps.

Dear Reviewer,

I hope this message finds you well. As the discussion period is nearing its end with less than one days remaining, I want to ensure we have addressed all your concerns satisfactorily. If there are any additional points or feedback you'd like us to consider, please let us know. Your insights are invaluable to us, and we're eager to address any remaining issues to improve our work.

Thank you for your time and effort in reviewing our paper.