TreeSplat: Mergeable Tree for Deformable Gaussian Splatting
Authors: Qiuhong Shen
Xingyi Yang
Xinchao Wang
Venue: NeurIPS 2025 poster ()
Keywords: Dynamic 3D Scenes
3D Gaussian Splatting
Primary area: applications
TL;DR: Deformable Gaussian Splatting, Adaptive Motion Tree structure

Abstract: Dynamic 3D scene reconstruction from multi-view videos demands representation to model complex deformations at scale. Current Gaussian Splatting based methods often either suffer from significant computation cost due to dense MLP-based modeling or explicit modeling deformation of each Gaussian independently. However, the dynamics of objects within a scene are typically hierarchical and exhibit structural correlations. To leverage these structural priors into the representation, we introduce **TreeSplat**, a **Tree** data structure for deformable Gaussian **Splat**ting. In TreeSplat, as the name suggests, motions of Gaussian are represented hierarchically within a tree. Each node learns coefficients for time-varying basis functions, defining a part of the motion. The full motion for any given Gaussian is then determined by accumulating these transformations along the tree path from its leaf node to the root node. This tree isn't predefined; instead, it is constructed adaptively alongside Gaussian densification, where cloning or splitting a Gaussian correspondingly creates new leaf nodes. One central property of TreeSplat is its mergeability; after optimization during training, the hierarchical motion parameters for each Gaussian can be efficiently consolidated. By performing this merging step before test time, we eliminate the need to traverse the tree explicitly for each Gaussian during rendering. This results in dramatically faster rendering over 200 FPS and compact storage, while maintaining state-of-the-art rendering quality. Experiments on diverse synthetic and real-world datasets validate these advantages.

TreeSplat: Mergeable Tree for Deformable Gaussian Splatting
Qiuhong Shen'
Xingyi Yang?.1 Xinchao Wang
National University of Singapore The Hong Kong Polytechnic University edu.hk, xinchaoθnus edu. sg
qiuhong... serhoog..shennee shen@u. wus.
Abstract
Dynamic 3D scene reconstruction from multi-view videos demands representation to model complex deformations at scale. Current Gaussian Splatting based methods often either suffer from significant computation cost due dense MLP-based mod- eling explicit modeling deformation of each Gaussian independently. However, the dynamics of objects within a scene are typically hierarchical and exhibit struc- tural correlations. To leverage these structural priors into the representation, we introduce TreeSplat, Tree data structure for deformable Gaussian Splatting. TreeSplat, as the name suggests, motions of Gaussian are represented hierarchically within tree. Each node learns coefficients for time-varying basis functions, defin- ing part of the motion. The full motion for any given Gaussian is then determined by accumulating these transformations along the tree path from its leaf node to the root node. This tree isn't predefined; instead, it is constructed adaptively alongside Gaussian densification, where cloning or splitting a Gaussian correspondingly creates new leaf nodes. One central property of TreeSplat is its mergeability; after optimization during training, the hierarchical motion parameters for each Gaussian can be efficiently consolidated. By performing this merging step before test time, we eliminate the need to traverse the tree explicitly for each Gaussian during rendering. This results in dramatically faster rendering compact storage, while maintaining state-of-the-ard rendering quality. Experiments diverse synthetic and real-world datasets validate these advantages. Code and results are available at hhtpp:: :// //gi thub. homm/fooorisshee/treeeeeee
200 FPS and
Introduction
Dynamic 3D scene reconstruction aims to recover deformable 3D representations from multi-view videos. This, in turn, makes it possible to synthesize novel views from different viewpoints and moments in time. Despite recent progress, achieving efficient dynamic 3D scene reconstruction remains challenging due to limitations fitting time, data storage, and rendering speed.
Neural Radiance Fields (NeRF) 1+6] have demonstrated remarkable performance in static 3D) reconstruction by optimizing multi layer perceptrons (MLPs) with volumetric ray marching. Several extensions 9 [8 incorporated temporal components into the MLP to capture scene deformations over time. However, these methods often suffer from high computational demands, significantly impacting their efficiency, particularly when scaling to complex dynamic scenes.
Recent developments in 3D Gaussian Splatting (3DGS) [9 have established it compelling alternative for efficient 3D scene reconstruction. Building upon this foundation, a growing body of work [16] 27 has incorporated temporal components into static Gaussians to model scene deformations over time. Among them, some approaches adopt isotropic 4D Gaussians 22] 23 or
"Corresponding Author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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polynomial functions [24 to explicitly represent motion. These representations circumvent dense MLP computation and thus enable efficient rendering.
Despite these success, a key limitation of these methods is the independent modeling of motion for each Gaussian. In reality, the dynamics not independent. They are inherently correlated across space and time, often exhibiting complex, hierarchical structures. Consequently, assuming independence prevents the capture of coherent and structured motion patterns, creating significant modeling gap. Thus, it is crucial to model deformations collaboratively, allowing Gaussians to share information with their neighbors and better reflect the structured nature of real-world motion.
To achieve this, we introduce TreeSplat, a novel representation that employs a tree data structure to explicitly model both individual Gaussian motions and their inter-correlations. The core idea is to organize motion hierarchically within this tree. Specifically, each node stores coefficients for set of shared, time-varying basis functions, with these coefficients defining component of the motion. The complete motion for any Gaussian is then determined by aggregating these component cunnsormations-ttyice
via weighted summation- along the path from its associated leaf node to the tree's ' root. Consequently, the tree explicitly defines the motions for all Gaussians, and crucially, Gaussians that share common ancestor nodes inherently share motion components, thus modeling their correlation.
One central problem is how construct the tree. Rather than manual rule- basee-baeddde creation, adaptively grow the tree in conjunction with Gaussian densification. As standard densification operations, cloning and splitting generate new Gaussians in adjacent regions, the tree structure grows alongside them.
Specifically, we define two forms tree growth modes, that operate alternately. Leaf Expansion broadens the tree. links motion of new Gaussians (resulting from densification) with new leaf nodes under the same parent as their source Gaussian. Depth Promotion increases the depth of the tree, It transforms an existing Gaussian's 's leaf node into a new parent, which then links to two new child leaf nodes associated with newly generated Gaussians. Furthermore, to control the influence of different tree levels, each Gaussian applics a learnable decay to the coefficients of motion nodes with increasing depth. This ensures that motion components defined by nodes deeper in the tree have smaller impact, while components closer to the root dictate more significant.
Our motion tree offers key advantage: its coefficients are mergeable after training. This mergeability means that although the tree structure is essential for training, it is not required at inference time. Once training is complete, we can merge the coefficient for each Gaussian by traversing its leaf-to-root path and accumulating the corresponding transformations. Crucially, this merging process occurs offline, before test time. Consequently, we eliminate the requirement for per- per-Gaussian tree traversal and significantly accelerating runtime performance.
To maintain computational efficiency during training, we periodically prune inactive motion nodes, preserving a sparse and lightweight tree structure. Once training converges, the tree structure is fixed, and the motion coefficients are merged offline as described. This final representation, with me-aggregated motion for each Gaussian, enables highly efficient rendering of complex dynamic scenes without runtime tree traversal overhead.
In summary, the contributions of this work are as follows:
We propose a hierarchical motion tree structure for dynamic Gaussian Splatting, where the tree is grown in conjunction with Gaussian densification to model collaborative and structured motion.
The motion tree is formulated as mergeable, in which the linear structure enables offline pre- aggregation of motion coefficients. This design eliminates the need for tree traversal during rendering, thereby substantially improving efficiency and reducing storage overhead.
Our TreeSplat framework achieves state-of-te the-art reconstruction quality on both synthetic and real-world datasets, while maintaining real-time rendering speed over 200 FPS.
2 Related works
Dynamic 3D Scene Reconstruction. 3D Gaussian Splatting (3DGS) 19
38
have become a
key approach for efficient 3D scene reconstruction. A stream of recent works [66 has extended 3DGS to dynamic scene reconstruction by introducing temporal components to model deformations over time. These methods can be broadly divided into two categories based on how they
20
36
41 4

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incorporate temporal components: implicit and explicit deformation modeling. In implicit approaches, several representative methods [20] [T] employ shared MLP to predict the deformation of each Gaussian over time. This design is similar to deformation components used in dynamic NeRFs. However, real-world dynamic scenes often require millions of Gaussians for accurate reconstruction. As result, querying an MLP for each Gaussian introduces significant computational overhead, which becomes a major bottleneck during rendering. To mitigate this issue, more recent work has focused on explicit deformation representations that avoid per- Car-aassiin MLP inference. Such methods either encode deformation using isotropic 4D Gaussians [22
2 or parameterize the deformation of each Gaussian using polynomial functions of time 26 While these techniques improve efficiency in both training and rendering, they learn motion parameters independently for each Gaussian and ignore the spatial dependencies between motions of Gaussians. This independence assumption neglects the hierarchical and coherent motion patterns often present in dynamic scenes, leaving a critical modeling gap. In contrast, our approach introduces hierarchical and mergeable motion tree that explicitly models collaborative motion across Gaussians, enabling improved dynamic scene reconstruction and rendering effiency.
Hierarchy in Gaussian Splatting. Hierarchical representations are fundamental in 3D reconstruction. introduced strategies such as spatial partitioning and pyramid features into NeRF [1 to improve both rendering speed and visual quality across diverse 3D scenes. Thanks to its fully explicit formulation, Gaussian Splatting allows for more direct modeling over spatial structure, making it a natural candidate for hierarchical representation. Several recent works [46)50] have explored constructing hierarchical representations based Gaussian Splatting, HicrarchicalGS [6 proposed a tree- based hierarchy that enables the reconstruction of large-scale scenes by dividing them into independent spatial chunks. OctreeGS [48 employed octree data structure adaptively capture cevel-of-detall variations across different scene regions, while SVRaster [47] also adopted an
Early works 44 45]
octree structure and introduced sparse voxel rasterization method mitigate popping artifacts [5]
in Gaussian Splatting rendering.
More recently, HiCoM [49] explored hierarchical motion modeling using 4DGaussian 20 for streamable dynamic seene reconstruction. However, its hierarchy is constructed using fixed heuristics, which limits adaptability across varying scenes. Concurrent work HiMoR [50] introduced fixed- structure tree of depth 3 to represent motion for monocular dynamic scene reconstruction. Different from these approaches, our framework focuses on mining motion hierarchies between Gaussians in an adaptive manner. We couple tree construction with the densification process, enabling the tree to grow adaptively in both depth and width reflect motion complexity. Moreover, our linear tree structure supports pre-aggregation of motion coefficients after training, enabling highly efficient rendering without additional tree traversal overhead.
3 Preliminary: 3D Gaussian Splatting
Given a set of images captured from 3D scenes with known camera poses, 3D Gaussian Splatting (3DGS) [9 iteratively reconstructs the scene as a collection of isotropic Gaussians, denoted as { Each Gaussian is defined by its central position μa E R$, opacity a E [0, 1]. and view-dependent color h E IRd represented spherical harmonics coefficients. Its 3D covariance matrix Σ&D e 33x3 parameterized by scale vector 8 E R3 and a rotation quaternion q E IRd to ensure positive semi-definiteness Collectively, the i-th Gaussian is denoted as G: { Ts h;, St, q:).
To better represent the scene, adaptive density control, or densification, is employed by dynamically adjusting the number of Gaussians during optimization. It selectively densifies regions with large view- space positional gradients, which typically indicate either missing geometry (under-reconssrructinn) or excessive coverage dover-reconstruction Specifically, small Gaussians in under--econttrruced regions are cloned to cover new geometry, while large Gaussians in high-variance areas are split into smaller Gaussians to capture finer scene details.
For rendering a 2D image, all 3D Gaussians are first projected onto the image plane 2D Gaussians. The opacity of Gaussian i at a pixel x is given by:
1 - (ix-p,)" (-
(-
a = o; exp
where i., and EPD are the projected mean and covariance, respectively. After sorting Gaussians based on depth, a tile-based rasterizer is used to blend their contributions, producing the final image.
3

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Methodology
In this section, we first establish the base formulation of dynamic Gaussian Splatting Sec. 4.1 The detailed data structure of the motion tree is elaborated in Sec. 4.2 and the tree merging strategy for rendering is described in Sec. 4.3 Finally, the initialization and optimization scheme for dynamic Gaussian Splatting with the motion tree is presented in Sec. 4.4
4.1 Dynamic Gaussian Splatting
To adapt 3D Gaussian Splatting for dynamic scene reconstruction, adopt explicit temporal components to capture deformations over time. Specifically, per-Gaussian coefficients associated with shared basis function are applied encode temporal motion and rotation of each Gaussian as shown in Fig. Ta). Rather than relying on predefined motion bases such as Fourier series [2] or
polynomial [26] basis, we initially represent the motion field through per-Gaussian coefficients 25 with learnable bases:
B (tt) = pe ((()) = Me + Σ (t),,
q(t) q. g(t) = + Σ (t).
(2)
where ale and qe are the static Gaussian center and rotation quaternion, respectively, and B denotes the number of basis functions. Here, of E E and ef e R are learnable coefficients. The basis functions (t) E R3 and (t) E IR' are shared across all Gaussians and are generated by a lightweight multi-layer perceptron (MLP) fo with a sinusoidal time embedding:
So()(1) (1), (3))) 7(1) (sin(2 (t), cos(2" x()) k=
L-1
where 0 denotes the learnable parameters of the MIP, and (t) is sinusoidal positional encoding of order L to enhance the network's 's capacity to model high-frequency temporal variations.
Compared to MLP-based deformation modeling that requires querying the MLP millions of times 20
21. once for each Gaussian, our framework only performs single query fo per timestamp substantially reducing the computational overhead.
Leaf Expansion
(tt)
Node from Cloning
b
Mode from Spiiting
Depth Promation
Pruned Leaf Node
(t)
Query with time
Learnale deformale basis
(a) Dynamic Gaussian with Learnable Basis
(b) Leaf Expansion Depth Promotion
Figure I: Dynamic Gaussian Splatting with Hierarchical Motion Tree. Our framework encodes temporal motion and rotation using shared learnable basis functions combined with per-Gaussian coefficients. Each node the hierarchical motion tree stores a motion vector parameterized by learablee coefficients. The tree is constructed in conjunction with Gaussian densification, where Leaf Expansion and Depth Promotion are performed periodically to adaptively grow the hierarchy.
4.2 Hierarchical Motion Tree
Though the above dynamic Gaussian Splatting models per-Gaussian deformation using shared basis functions, the associated coefficients optimized independently for each Gaussian. However, mo- tions in real-world 3D scenes are inherently spatially entangled and exhibit hierarchical relationships across multiple scales, where the motion of one structure is often correlated with the motions of its neighbors. Motivated by this property, we introduce a hierarchical motion tree to collaboratively learn the temporal motion (i(() in Eq. among Gaussians.
In the motion tree structure, each node represents a motion vector encoded as a learnable coefficient vector in I and the entire motion field is denoted F MxB where M is the total number of

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nodes in the tree. Each leaf node is uniquely associated with one Gaussian, ensuring one-to-on correspondence between Gaussians and leaf nodes. Given N (N < M) dynamic Gaussians, the structure of the motion tree is maintained by the following data mappings:
Node entry & N maps each Gaussian to its leaf node index in the motion field F;;
Parent index P NM; records the parent motion node for each motion node;
Node level L E NN: specifies the number of nodes from Gaussian's 's leaf node to the root node;
Given a constructed motion tree, the motion (t) of Gaussian is computed by traversing its ancestral path with parent index P and aggregating motion vectors. Formally, we can formulate as:
B
anc (t),
(t)
(4)
k=
where E; denotes the level of Gaussian in the tree, and l indexes the nodes along its path from the leaf to the root. The function anc(i, k) returns the index in of the ancestor node steps above the leaf node of Gaussian i.
Tree Growth:
Leaf Expansion and Depth Promotion. As Gaussian densification progressively refines the scene from coarse to fine spatial levels by creating new Gaussians in neighboring regions, naturally aligns with the hierarchical motion modeling motivation. The growth of the motion tree is in conjunction with the densification during optimization. To adaptively balance the depth and width of the motion tree, we introduce two alternative modes to grow the tree at each densification step as shown in Fig. lb).
Leaf Expansion increases the number of leaf nodes horizontally without increasing tree depth. Newly densified Gaussians are linked to new leaf nodes under the same parent node as their source Gaussian. These new leaf nodes share the same parent index p N and node level E N the leaf node of their source Gaussian, preserving the flatness of the local tree structure.
Depth Promotion deepens the tree to refine the hierarchical organization of motions. It transforms an existing Gaussian's ' leaf node into new parent node. The densification operation, whether cloning or splitting, is treated and connect them to the newly promoted parent node. These new leaf nodes are assigned a node level of + 1 and their parent indices p point to the newly promoted parent node.
binary operation that creates two new Icaf nodes associated with Gaussians
For all newly created leaf nodes, the associated coefficients in the motion field FF are initialized to zero. This initialization ensures that the aggregated temporal motion (i() remains unchanged immediately before and after densification.
This two growth modes are scheduled periodically during optimization: multiple rounds of Leaf Expansion followed by Depth Promotion step. This design results in large, adaptively widening motion tree with limited depth, ensuring that the tree remains both scalable and capable of capturing multi-level motion structures throughout training. Besides, unused leaf nodes are periodically remove during optimization to maintain efficiency during training.
Decay- Weighted Aggregation. As the motion tree deepens, naive aggregation of ancestor nodes, as formulated in Eq.44 4 can result in unstable optimization. Specifically, given the upstream per-Gaussian gradient g: = a the gradient with respect to an ancestor node Fran((t.)] computed as
Oc
(g. (1), 9, (t))), .... g. (t) E R
(5)
In this naive aggregation, ancestor node accumulates the full strength of the upstream gradient from each of its descendants. Consequently, the total gradient magnitude node grows proportionally to the number of its descendant Gaussians, which can cause severe gradient explosion for some ancestor nodes and destabilize optimization.
To mitigate this issue, we introduce a learnable decay factor & E (0, 1] for each Gaussian. The motion aggregation is reformulated as:
(.((t)
B
ann(i.k) b9(())
(6)
K=
Ap=0
5

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where deeper ancestors are exponentially attenuated by powers of B, Correspondingly, gradients received by each ancestor node is scaled by the same decay factor, ensuring that gradients from distant descendants are substantially suppressed. The decay factors B; are differentiable and jointly optimized with other model parameters during training. closed-form derivation of their gradients provided in the Appendix.
This deigh-weighted aggregation strategy enables each Gaussian adaptively control its receptive field within the motion tree: a smaller 3; concentrates motion learning on nearby ancestors, while a larger 33 permits broader aggregation. By suppressing contributions from distant and irrelevant ancestors, it improves the robustness of both forward motion modeling and backward gradient flow, leading to more stable motion modeling.
4.3
Tree Merging for Rendering
During optimization, computing the motion (t) for each Gaussian requires traversing its ancestral path in the deformation tree. Once training complete and the tree structure is fixed, pre-aggregate the motion coefficients for each Gaussian by reordering the summation terms Eq. 6 Formally, can be expressed as:
B A( - Σ (1 1=1
B D0 1=1
II
Fancfi.k)
where c' E R2 is the merged motion coefficient vector for Gaussian i. This transformation enables highly efficient rendering, it eliminates the need to traverse the tree, the motion computation reduces to simple linear combination over the basis vectors per Gaussian.
It is important to note that this coefficient merging is only applied after training. During optimization, the internal motion nodes must be retained to receive gradient signals from multiple descendant Gaus- sians and propagate them back across the tree. Merging would prematurely remove the hierarchical structure necessary for effective gradient flow and motion disentanglement. Hence, mergeability property leveraged only in the inference stage accelerate rendering without compromising the training dynamics.
4.4 Training Framework
Following 3D Gaussian Splatting 19, we conduct interleaved iterative optimization and densification. Since the tree construction process is coupled with densification, the time overhead introduced by growing the deformation tree is negligible. Moreover, with our highly optimized CUDA imple- mentation, tree traversal for each Gaussian during optimization introduces only a marginal time increase.
Tree Initialization. We first point cloud initialize Nii Gaussians. The node levels I initialized to 0 for all Gaussians, corresponding to the root level of the tree. The initial motion field FF has the same length the number of Gaussians, with all entries initialized zero. For the node entry mapping E, each Gaussian is assigned to its corresponding motion node in order, initialized as [0, 1,..,, Ninit 1]. The parent indices P are initialized to -1 for all nodes, forming forest of independent singleton trees at initialization.
Optimization Scheme. During training, we simply adopt rendering loss composed of an MSE term and an SSIM term: L = (1 X) + XL where balances the two objectives. To stabilize training, initially reconstruct the static components of (tt) and q(t) over the first 10% of optimization iterations, effectively learning a canonical 3D space before introducing temporal dynamics. For interleaved densification, adopt the averaged screen-space 2D gradient of (u(t) as the density control indicator.
Experiments
5.1 Implementation details
To balance efficiency and performance, we model the time-varying shared basis So in Eq. using MLP with three hidden layers, each of width 512. The sinusoidal time embedding 7(t) is set

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as order L = 32 to capture high-frequee freeffrey temporal variations. The number of basis vectors B set 10 for the D-NeRF dataset and 16 for the Neural 3D Video dataset, to accommodate the complexity of real-world scenes. Motion tree construction begins at iteration 500 in conjunction with Gaussian densification. Depth Promotion performed at first step, after which Leaf Expansion is applied every 100 iterations and Depth Promotion every 500 iterations, alternating after every four rounds of Leaf Expansion. Densification is halted at iteration 15,000, after which the motion tree is fixed to capture stable collaborative motion patterns among Gaussians. To ensure fast per-frame motion computation, we implement Eq. 6 and Eq. as custom CUDA kernels separately. Through careful kernel design, including memory access optimization and parallel thread scheduling, ensure that tree traversal overhead is negligible even for real-world dynamic scenes. All other training hyperparameters, including densification thresholds and learning rates for Gaussian attributes, follow the original settings used in Gaussian Splatring. The learning rate for the decay factor / is set to 5 x 10-3, and the learning rate for the shared MLP so is set 5 10-1, All experiments conducted on an NVIDIA RTX4500 Ada GPU. For additional hyperparameter configurations, please refer the configuration table provided in the Appendix.
5.2 Comparison with State-of-the-art
D-NeRF Dataset 77]. The D-NeRF dataset comprises 8 synthetic dynamic scenes captured as monocular videos. At each time step, only a single training image from one viewpoint is available. Following standard protocols, we evaluate on test views from novel camera positions within the same temporal range as the training data. For initialization, we uniformly sample 100,000 points within the cubic volume [-1.2, 1.2]3. Quantitative results are reported in Tab. [ in terms of PSNR, SSIM, and LPIPS. Our TreeSplat achieves the highest reconstruction quality with an average PSNR of 37.11 dB, while maintaining compact model size of 28 MB and requiring only 4 minutes of training per scene. After tree merging, TreeSplat reaches a rendering speed of 230 FPS, outperforming all baselines. Moreover, it uses significantly fewer Gaussians, averaging only 85K per scene, demonstrating superior efficiency without compromising quality.
Table 1: Quantitative Evaluation on the D-NeRF 7 Dataset.
Method
PSNRT
SSIM
LPIPS
Train Time.
FPST
Storage
#Gauss
DNeRF
7
29.67
0.95
0.08
h
0.1
N/A
N/A
K-Planes [2
31.07
0.97
0.02
5h
1.2
N/A
N/A
HexPlanes
g
31.04
0.97
0.04
11 min
0.22
N/A
N/A
Vox [53
32.67
0.97
0.04
49 min
1.6
N/A
N/A
4DGaussian 20
34.05
0.98
0.02
19 min
85
19M
137K
CompactDGSS 24
32.19
0.97
0.04
4 min
202
32M
112K
DynMF 22
35.72
0.98
0.02
5 min
216
32M
101K
4DRotorGS [22
34.26
0.97
0.03
26 min
143
242M
392K
RealTime4DGGS 22
34.09
0.98
0.02
28 min
132
278M
445K
TreeSplat (ours)
37.11
0.98
0.02
4 min
230
28M
85K
Neural 3D Video Dataset. The Neural 3D Video (N3V) dataset consists of 6 indoor dynamic scenes captured with 18 to 21 cameras resolution of 2704 2028, each lasting seconds. Following standard protocols, we train and evaluate at the half resolution, using 300 frames per scene with the center camera held out for evaluation. For initialization, we sample 300,000 points from the COLMAP (54) point cloud using farthest point sampling (55). Tab. rab.2rrpports quantitative results in terms of PSNR, storage size, rendering speed, and training time. We compare our method against 7 NeRF-based approaches and representative Gaussian Splatting methods. Among them, 4DGaus- sian (20 and Grid4D (35) employ MLP-based modeling. while DynMF (25], RealTime4DGS (3] and Space Time 26 adopt explicit deformation representations. Our TreeSplat achieves the highest average reconstruction quality of 32.21 dB across scenes, while maintaining a compact model size of 170 MB and the fastest rendering speed of 206 FPS after tree merging, Remarkably, TreeSplat also trains significantly faster than most baselines, requiring only 0.57 hours on average per scene. Besides, we qualitatively compare novel view synthesis results on two representative scenes (Coffee Martini and Sear Steak) in Fig. 2 showing our method yields better reconstruction. These results highlight TreeSplat's superior trade-off between reconstruction quality and efficiency.
7

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Table 2: Quantitative Evaluation on the Neural 3D Video [2] Dataset.
PSNR (dB)
MB
Framels
Hours
Mothod
Coffee Martini
Cook Spinach
Cut Roasted
Flame
Flame Steak
Average
Size
FPS
Training
NeRFPlayer
13
31.53
30.56
29.35
31.65
31.93
29.13
30.69
51.30
0.05
HyperReel
14
28.37
32.30
32.92
28.26
32.20
32.57
31.10
360
DyNeRF
12
NIA
NIA
29.58
N/A
N/A
29.58
28
0.015
1344
HexPlane
NiA
32.04
32.55
29.47
32.08
32.39
31.71
200
N/A
12
K-Planes
29.99
32.60
31.82
32.38
32.52
31.63
311
1.8
Mix Voxels-
15
29.63
32.25
32.40
29.81
31,83
32.10
31.34
500
37.7
1.3
Mix Voxels
15
30.39
32.31
30.60
32.10
32.33
31.73
4DGaussian
20
27.34
32.46
32.90
29.20
32.51
32:49
31.15
34
137
1.7
Grid4D
28.30
32.58
33.22
29.12
32.56
33.16
31.49
146
116
1.9
DynMF 25
28.87
33.09
32.66
29.03
32.70
32.02
31.40
176
197
0.52
Real DGG 23
28.33
32.93
33.85
29.38
34.03
33.51
32.01
2085
101
5.2
SpaceTimeGS
26
28.61
33.18
33.52
29.48
33,64
33.89
32,05
200
140
5.5
TreeSplat (ours)
28.91
33.17
33.69
29.50
33,89
34,10
32.21
170
206
0.57
4DGaussian
DynMF
4DGS
Ours
4DGaussian
DynMF
Figure 2: Qualitative comparisons on the Neural 3D Video Dataset. We qualitatively compare
our TreeSplat with 4DGaussian (20). DynMF (25). and RealTime4DGS 23 two representative
scenes coffee martini and sear steak from the Neural 3D Video dataset 12
5.3 Ablation and Discussion
Effects of Tree Depth. Our hierarchical motion tree grows in conjunction with Gaussian densification through periodically scheduled Leaf Expansion and Depth Promotion. The overall tree depth is controlled by adjusting the interval between Depth Promotion steps. In Tab. we conduct an ablation study across five configurations with maximum tree depths of 0, 4, 15, 29, and 73, corresponding to Depth Promotion intervals of co, 4000, 1000, 500, and 200, respectively. The results show that performance consistently improves as tree depth increases. Compared
the baseline without hierarchical structure (tree depth 0), our full model with depth 29 achieves notable PSNR gains, such as +2.63 on Hellwarrior and +1.40dB on Sear Steak. Even moderate depths (e.g., 4 or 15) already yield substantial improvements, demonstrating that our tree structure captures meaningful motion correlations with limited hierarchy.
Table 3: Ablation of tree depth. Evaluated representative scenes from D-NeRF (Hellwarrior, Mutant) and Neural 3D Video (Cut Roasted Beef, Sear Steak).
Hellwarrior
Mutant
Cut Roasted Beef'
Sear Steak PSNR
Tree Depth
PSNR1
SSIM
PSNRT
SSIM
PSNR*
SSIM
SSIM
73
38.26
0.97
43.28
1.00
33.31
0.96
34.05
0.97
29
38.34
0.97
43.81
1.00
33.69
0.96
34.10
0.97
15
38.11
0.97
42.57
1.00
32,79
0.96
33,81
0,97
4
37.49
0.97
42.79
1.00
33.63
0.96
33.39
0.96
0
35.71
0.95
41.47
0.99
32.15
0.96
32.65
0.96
However, excessively deep trees can reduce width the tree and may accumulate irrelevant motion noise. Moreover, they introduce greater computational overhead and may even cause minor performance degradation. Empirically, we find that a moderate depth of (interval 500) offers the best balance between performance, efficiency, and robustness.
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Effects of Tree Merging, The main difference between the training- time motion computation in Eq. aad the rendering-tima formulation in Eq. Ilies in the order aggregation. During training. we first compute time-dependent motion vectors for all nodes in the motion tree and then aggregate them for each Gaussian. In contrast, rendering pre-aggregates the motion coefficients per Gaussian before applying the basis functions, thereby eliminating the need to traverse the tree. While these two formulations are mathematically equivalent, numerical differences can arise due to floating-point accumulation order. To evaluate the impact of such differences, we conduct ablation experiments comparing models with and without coefficient merging. As shown in Tab. merging introduces negligible variation in reconstruction quality across PSNR, SSIM, and LPIPS, while significantly improving rendering speed and reducing storage size. These results validate the effectiveness of our mergeable design, which preserves visual fidelity while enabling high-performanee inference.
Table 4: Ablation on Tree Merging, We report the metric difference as "after merging" minus "before merging." Merging preserves reconstruction quality while improving efficiency and compactness.
Scene
APSNR
ASSIM
ALPIPS
AStorage (MB)
AFPS
Hellwarrior
3.81 x 10-7
+5.96 10-9
-4.77 10-8
0.62
+15
Mutant
+9.53 10-7
+2.98
10-9
-1.97
10-8
-1.55
+12
Cut Roasted Beef
+3.81
10
-7.94 x 10
-7.45
10-9
-8.57
+-2
Sear Steak
-1.27 10
+1.39 10
+7.45 x 10-9
-8.61
+74
Effects of Weight-Decayed Aggregation. To assess the impact of weight-decayed aggregation, we conduct ablation by disabling it during training on the D>-NRR dataset. As illustrated in Fig. 3 removing this strategy leads to blurred motion regions in the rendered results. This is caused by interference from irrelevant nodes in the motion tree. In contrast, enabling this strategy yields much better reconstruction quality, as the learnable decay factor in Eq. 6q.6oadde adaapiiv controls each Gaussian receptive field in the motion tree.
w/o Window
With Window
Scene
PSNR
#Gauss
PSNR
#Gauss
Hellwarrior
38.34
19K
37.87
22K
Mutant
43.81
70K
41.35
79K
with
Cut roasted beef
33.69
416K
33.36
460K
Sear steak 34.10
429K
33.89
519K
Table 5: Impact of Temporal Opacity window. We
Figure 3: Ablation of weight-decayed aggregation.
compare with and without opacity window.
Analysis of Tree Depths. To better understand the structure of motion hierarchies, we analyze the distribution of tree depths across four representative scenes: Hellwarrior and Mutant from the DNeRF dataset, and Cut Roasted Beef and Sear Steak from the Neural 3D Video dataset. As shown in Figure we divide tree depths into six intervals and visualize the results as histograms. For each interval, we also report the average number of Gaussians per tree. The resulting distributions exhibit a
pattern: over 97% of motion trees have depths less than or equal to 10, while only small fraction extend into deeper hierarchies, These findings demonstrate that most Gaussians are captured through relatively shallow hierarchical motion patterns, with deeper structures emerging only where necessary.
ELERcaGac Meal
Hellaande
15,003
242 000
7,500
7.500
150
5.00
100
320
303
2300
350
250
190
102
25
15 21
25
31 25 22
25
0227)
Aepth
08000
Figure 4: Visualization of hierarchical tree statistics. Here show statistics across four dynamic 3D scenes (Cut Roasted Beef, Sear Steak, Hellwarrior, and Mutant). For each scene, the histogram (blue bars) represents the number of trees at different depth intervals, while the dotted orange curve denotes the averaged number of Gaussians per tree within each depth range.

---

Temporal Opacity, Some prior works [23 26 model the opacity of each Gaussian as a time- varying unimodal function, often implemented as a temporal window. However, recent findings [56 57 suggest that Gaussians tend to learn overly short temporal windows, resulting in limited lifespans and degrading dynamic 3D reconstruction into near per-frame static modeling. To evaluate the necessity of temporal opacity in our framework, we follow the same design and assign each Gaussian a learnable ID Gaussian window. As reported Tab, []] introducing temporal windows degrades reconstruction quality despite noticeable increase in the number of Gaussians. This likely occurs because Gaussians with limited temporal visibility hinder the motion tree from learning coherent motion trajectories. These results confirm that temporal windowing is unnecessary in framework. The temporal modulation of opacity can be sufficiently expressed through Gaussian center motion, as reflected in the spatial formulation of opacity in Eq.
6 Conclusion
In this work, we present hierarchical and mergeable motion tree structure for dynamic Gaussian Splatting. By constructing motion tree in conjunction with Gaussian densification, our method enables collaborative motion learning across Gaussians in an adaptive, coarse-to-fie to-fie manner. A decay-weighted aggregation strategy further regulates the influence of ancestor nodes, improving both optimization stability and motion locality. To support efficient rendering, we introduced a pre- aggregation strategy that merges motion coefficients traversal overhead during rendering. Extensive experiments on both synthetic and real-world datasets demonstrate that method achieves state-of-the-arr reconstruction quality while maintaining high efficiency and compactness. Our approach offers a principled framework for hierarchical motion modeling and sets the stage for future extensions in scalable dynamic 3D representations.
the tree path of each Gaussian, eliminating
Acknowledgement
This project is supported by the National Research Foundation, Singapore, under its Medium Sized Center for Advanced Robotics Technology Innovation.
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Answer: [Yes]
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Reviews:
[{"review_id": "wmY5da9b5b", "reviewer": "Reviewer_iFUQ", "summary": "This paper proposed a dynamic Gaussian splatting method which adopted a tree data structure to model the dependent motion. The deformation of each Gaussian primitive is computed through traversing the ancestral path, and make the motion of Gaussian primitives to be connected and not independent. Experiments on several popular datasets show the effectiveness.", "questions": "Please refer to the Weaknesses.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n1. It's reasonable that the motion or adjacent primitives is connected, and this paper designed a tree structure to model the independent motion of Gaussian primitives.\n2. Experiments on several datasets also show that this method has great trade-off between quality and efficiency.\n\n**Weaknesses**\n\n1. Some implementations or designs are not explained clearly. How to decide whether apply the \"Leaf Expansion\" and \"Depth Promotion\" operations? Is there any factor like the densification threshold?\n\n2. Missing some ablation studies like the threshold of \"Leaf Expansion\" and \"Depth Promotion\" operations.\n\n3. How to make the connected Gaussian primitives to be constructed in a motion tree if only dependent on the \"Leaf Expansion\" and \"Depth Promotion\" operations?\n\n4. In the initialization stage, each Gaussian primitive is bound to a single motion tree. And maybe it's not reasonable because there are some SFM points are connected.\n\n5. How to avoid the situation that the dependent Gaussian primitives are connected in a motion tree?", "was_revised": true, "final_justification": "After reading the response of authors and other reviewers' comments, I think the response solved some of my concerns and I decide to keep my original positive score. And I hope the author can add the necessary citation and comparison with [1].\n\n[1] 4d gaussian splatting with scale-aware residual field and adaptive optimization for real-time rendering of temporally complex dynamic scenes, ACMMM2024 Best Paper Candidate.", "rebuttal": "Thank you for your insightful comments! Below, we provide a point-by-point response to address your concerns. We welcome further discussion to improve the clarity and effectiveness of our work.\n\n> **W1-1: When to apply Leaf Expansion and Depth Promotion ?**\n\nIt is great that reviewer is asking! *Leaf Expansion* and *Depth Promotion* are applied in an alternating manner at each Gaussian densification step during training.  Following the original 3D Gaussian Splatting setup, Gaussian densification is performed every 100 iterations starting from the 500th iterations. At each densification step, we alternate the two operations according to a fixed schedule: for every 5 densification steps, we apply *Leaf Expansion* in the first 4 steps, followed by *Depth Promotion* in the 5th step. This simple strategy empirically balances the width and depth of the motion tree and leads to effective hierarchical motion modeling.  Details about when to apply these two operations are elaborated from line 261 to line 264 in the manuscript, we will make it clearer in revision.\n\n> **W1-2: Other factors in tree construction like densification threshold.**\n\nThanks! In our method, we do not introduce additional hyperparameters for tree growth. It is triggered automatically along the Gaussian densification procedure. To further clarify, we will revise the paper to explicitly mention this. \n\n> **W2: Threshold ablation of Leaf expansion and Depth promotion operations.**\n\nWe appreciate the reviewer’s interest in the details of tree growth! As stated earlier, there isn't a single threshold for growth that we can ablate. But indeed, we do control the growth process by tuning the schedule of different operations. In Section 5.3, we conduct an ablation (Effect of Tree Depth) by varying this interval of *Depth Promotion* relative to *Leaf Expansion*. The best performance is achieved when *Depth Promotion* is applied after every 4 steps of *Leaf Expansion*, which balances tree width and depth. We will clarify this coupling and highlight the ablation results more explicitly in the revision.\n\n> **W3: How to make the connected Gaussian primitives constructed in a motion tree if only dependent on the \"Leaf Expansion\" and \"Depth Promotion\" operations?**\n\nThank you for the question! The tree grows in conjunction with Gaussian densification, where new Gaussians are generated through either cloning or splitting from existing ones. These newly generated Gaussians are spatially adjacent to their source Gaussians, and our Leaf Expansion and Depth Promotion operations explicitly link them under in the tree as parent-child. This ensures that Gaussians with spatial and temporal proximity are hierarchically connected within the same motion tree. Over time, motion trees naturally group structurally related Gaussians, thereby enabling collaborative motion modeling across connected primitives.\n\n> **W4: In the initialization stage, each Gaussian primitive is bound to a single motion tree. And maybe it's not reasonable because there are some SFM points are connected.**\n\nThank you for the thoughtful observation. We agree that Gaussians reconstructed from SfM may exhibit spatial or structural connections. In our framework, each Gaussian is bound to a single motion tree throughout training. This design choice stems from the difficulty of reliably inferring motion dependencies from sparse SfM points, where inaccurate correlations could introduce significant noise and hinder reconstruction. To empirically validate this, we conducted an ablation on the DNeRF dataset: we partitioned the initialization volume ($[-1.2, 1.2]^3$) into a $16 \\times 16 \\times 16$ voxel grid, and assigned each Gaussian to a tree based on its voxel location. This voxel-based pre-grouping introduces hardcoded spatial correlations. As a result, the average PSNR dropped from 37.11 dB (default) to 35.89 dB. This demonstrates that enforcing spatial proximity as motion correlation can be detrimental. Our method instead learns motion tree structure progressively in conjunction with Gaussian densification, which proves to be more robust and effective in practice.\n\n> **W5: How to avoid the situation that the dependent Gaussian primitives are connected in a motion tree?**\n\nThank you for raising this concern. Actually, our design intentionally embraces spatial dependency among Gaussians, rather than avoiding it. The core motivation of our motion tree is to capture and exploit such correlations through hierarchical structure. During densification, new Gaussians are created in local neighborhoods, and their motion branches are extended from existing parent nodes, naturally preserving spatial continuity. Thus, Gaussians that are spatially related are encouraged to share motion components through shared ancestry in the tree. This promotes coherent motion modeling rather than viewing such dependency as a conflict."}, {"review_id": "ZXA9CTFZuJ", "reviewer": "Reviewer_QfP4", "summary": "This paper introduces TreeSplat, a novel method for dynamic 3D scene reconstruction based on Gaussian Splatting. The key contribution is a hierarchical motion tree structure designed to model the correlated and structured movements inherent in dynamic scenes, addressing the limitation of prior works that model each Gaussian's motion independently. In this framework, the motion of any given Gaussian is determined by accumulating transformations along a path from its associated leaf node to the tree's root. Critically, this tree structure is not predefined but grows adaptively in conjunction with the standard Gaussian densification process, forming a \"forest\" of trees that represent different moving parts of the scene. The paper's most significant technical innovation is the \"mergeability\" of this tree; after training, the hierarchical motion parameters can be pre-aggregated into a single coefficient vector for each Gaussian. This eliminates the need for tree traversal during inference, enabling state-of-the-art reconstruction quality at real-time rendering speeds (over 200 FPS).", "questions": "Potential for User Control: Your learned tree provides a powerful hierarchical motion representation. Have you considered its potential for user interaction, similar to the control offered by anchor-based methods like SC-GS? For instance, could manipulating a high-level node in your tree (e.g., a learned \"shoulder\" node) allow for intuitive control over all its descendants (the \"arm\" Gaussians)? While we understand this is not the paper's primary goal and do not expect experimental results, a brief discussion on this potential would be a valuable addition to contextualize your work.\nRobustness to Topological Changes & Role of Tree Growth: The paper does not seem to address how the model handles scenes with significant topological changes (e.g., an object breaking into two pieces). The learned tree establishes a fixed parent-child relationship for the duration of the training. Could you clarify how the model would represent the motion of two diverging pieces that were once connected? Am I correct in understanding that the \"Leaf Expansion\" and \"Depth Promotion\" mechanisms are designed solely to build and refine the motion hierarchy, rather than to adapt to such topological changes by, for instance, splitting a tree into two? A clarification on the precise role and limitations of these mechanisms would be very helpful.\nAnalysis of the Learned Forest Structure: As mentioned before, to better understand the model's behavior, could you provide some analysis of the learned forest structure? For example, a simple table with statistics on the number of trees and their average/max depth for different scenes would be very insightful. Furthermore, a qualitative visualization coloring the Gaussians by their tree ID would be highly compelling evidence that the method correctly segments objects based on their correlated motion.", "limitations": "The paper would benefit from a dedicated \"Limitations\" section. The authors have presented a strong conclusion, and adding a formal discussion of the method's boundaries would create a more complete and well-rounded manuscript. I suggest this section could acknowledge and reflect upon some of the points raised in the \"Weaknesses\" and \"Questions\" parts of this review.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n1.\tThe paper tackles a well-defined and significant problem in dynamic scene reconstruction: modeling coherent, structured motion efficiently. The core idea of an adaptively grown, mergeable motion tree is highly original. It shifts the paradigm from modeling independent primitives or relying on implicit MLPs to automatically discovering and representing the physical hierarchy of motion.\n2.\tThe method is technically sound and its effectiveness is demonstrated through outstanding results. It achieves state-of-the-art performance on both synthetic (D-NeRF) and Neural 3D Video datasets. The ability to combine top-tier reconstruction quality with extremely fast rendering speeds (>200 FPS).\n3.\tThe technical design is elegant. Coupling the motion tree's growth with the Gaussian densification process is a clever and natural way to build the motion hierarchy. Furthermore, the \"mergeable\" design, which separates the complex training structure from a simple and fast inference model, is a crucial insight for practical application. The paper's quality is further reinforced by a comprehensive set of ablation studies that convincingly validate key design choices\nWeakness\n1.\tThe paper's core contribution is the motion forest, yet the experiments lack a perspective of this emergent structure itself. The paper does not provide quantitative data (e.g., the number and size distribution of trees per scene) or direct qualitative visualizations (e.g., coloring Gaussians by their tree ID) to explicitly show how the learned trees map to distinct, correlated objects. Such analysis would provide invaluable insight into the method's inner workings and offer stronger, more direct evidence for its claims.\n2.\tExploration of Failure Cases: The learned, fixed parent-child relationships in the tree might be a limitation for scenes with very complex, non-rigid deformations involving topological changes (e.g., cloth tearing, liquids splashing). The paper would be more complete if it discussed these potential failure cases where the assumed motion hierarchy might break down.", "was_revised": true, "final_justification": "After I check all discuss during rebuttal, I respect author's efforts and based on all information I got, I give my final score as before.", "rebuttal": "Thank you for your insightful and positive comments! Below, we provide a point-by-point response to address your concerns. We welcome further discussion to improve the clarity and effectiveness of our work.\n\n> **W1 & Q3: Analysis of constructed motion trees.**\n\nWe appreciate the reviewer’s suggestion to provide more insight into the learned motion forest structure. To address this, we have conducted a quantitative analysis of the distribution of tree depths across representative scenes from the DNeRF and Neural 3D Video datasets. In the following table, tree depths are divided into six bins. For each interval, the number of trees (**#Tree**) and the average number of Gaussians per tree (**#Gauss**) are reported across four scenes. This analysis reveals a long-tailed distribution: over 97% of motion trees have depths within 10, while only a few reach deeper hierarchies. This supports the claim that most Gaussians are captured through relatively shallow hierarchical motion patterns, with deeper structures emerging only where necessary. \n\n|      Scene       |  Depth   | #Tree | #Gauss |   Scene    |  Depth   | #Tree | #Gauss |\n| :--------------: | :------: | :---: | :----: | :--------: | :------: | :---: | :----: |\n| Cut Roasted Beef |  [1, 5]  | 10191 |  7.4   | Sear Steak |  [1, 5]  | 10572 |  7.9   |\n|                  | [6, 10]  | 1530  |  48.0  |            | [6, 10]  | 1482  |  40.9  |\n|                  | [11, 15] |  252  | 131.8  |            | [11, 15] |  208  | 196.7  |\n|                  | [16, 20] |  44   | 269.7  |            | [16, 20] |  37   | 190.1  |\n|                  | [21, 25] |   7   |  40.9  |            | [21, 25] |   4   |  61.0  |\n|                  | [26, 29] |   1   |  34.0  |            | [26, 29] |   0   |  0.0   |\n|   Hellwarrior    |  [1, 5]  |  529  |  4.9   |   Mutant   |  [1, 5]  |  639  |  9.7   |\n|                  | [6, 10]  |  159  |  36.3  |            | [6, 10]  |  279  |  83.6  |\n|                  | [11, 15] |  32   | 222.5  |            | [11, 15] |  89   | 367.7  |\n|                  | [16, 20] |   7   | 160.0  |            | [16, 20] |  16   | 321.0  |\n|                  | [21, 25] |   2   | 928.5  |            | [21, 25] |   2   | 328.0  |\n|                  | [26, 29] |   1   | 597.0  |            | [26, 29] |   0   |  0.0   |\n\nAdditionally, we visualized Gaussian trajectories on the Neural 3D Video dataset by coloring all Gaussians bound to the same motion tree with same color. The results reveal that coherent motion trees consistently emerge around moving objects. For instance, in the flame_salmon scene, a motion tree clearly corresponds to the motion of a hand, with its associated Gaussians localized around the hand. In contrast, the static background is typically composed of a large number of isolated Gaussians without parent node (i.e., node level = 0). This behavior arises naturally from our tree growth mechanism, which is coupled with Gaussian densification and driven purely by gradients from reconstruction loss. Since moving regions introduce higher pixel inconsistencies across time, their corresponding gradients tend to be larger, promoting more active tree growth and hierarchical modeling in dynamic regions. \n\nWhile figures are not able to be included figures in the rebuttal, we will incorporate both the quantitative statistics and qualitative visualizations in the revision to better illustrate the structure and interpretability of the learnt motion trees.\n\n> **W2: Exploration of Failure Cases.**\n\nWe thank the reviewer for pointing out this limitation. Indeed, our current formulation may struggle to fully capture topological changes or complex deformations such as cloth tearing or liquid splashing. These cases involve discontinuous motion patterns that challenge the assumption of temporally coherent, hierarchical motion. While our framework is effective for a wide range of objects and scenes with structured dynamics (as demonstrated in the benchmark datasets), we acknowledge that future extensions could explore more complex  tree topologies, or integrate additional cues such as segmentation or optical flow to better handle such extreme non-rigid phenomena. We will clarify this limitation in the revision.\n\n> **Q1: Discussion on potential for user interaction.**\n\nWe appreciate the reviewer’s insightful suggestion. We believe the contribution of TreeSplat is complementary to methods like SC-GS. SC-GS models the motion of static Gaussians via external control points and an implicit MLP, where the trajectory of each Gaussian is interpolated from nearby control points using a linear blend skinning [1]. It also incorporates an adaptive densification strategy for these control points. Points with high gradients is cloned to better capture complex motion.\n\nGiven this setup, TreeSplat can be naturally integrated into SC-GS by modeling hierarchical motion relationships among these control points. In such a framework, manipulating a high-level node (e.g., a learned \"shoulder\" node) could  propagate intuitive transformations to its descendants (e.g., \"arm\" Gaussians), enabling hierarchical editing or animation. Although not the primary focus of this work, we believe this integration offers a promising direction for future research in interactive 3D scene control. This discussion of the potential for user control will be included in the revision to better contextualize our contribution.\n\n[1] \"Embedded deformation for shape manipulation.\" ACM SIGGRAPH 2007 \n\n> **Q2: Robustness to Topological Changes & Role of Tree Growth.**\n\nWe appreciate the reviewer’s thoughtful question. Our current framework indeed models each Gaussian’s motion via a motion tree with a one-to-one binding between Gaussian primitives and leaf motion nodes. The tree growth, including Leaf Expansion and Depth Promotion mechanisms, are primarily designed to progressively refine and structure the motion hierarchy, capturing multi-scale, correlated motions across the scene. However, these mechanisms do not explicitly detect or adapt to topological changes such as objects breaking apart. In scenarios involving significant discontinuities or topological shifts, the fixed hierarchical relationship may not perfectly capture the underlying motion patterns. While such failure modes are rare in our benchmark datasets, we acknowledge this as a limitation and will clarify it in the revision."}, {"review_id": "GG2VFo8TLl", "reviewer": "Reviewer_gmM8", "summary": "The paper introduces TreeSplat, a Gaussian Splatting-based framework for dynamic 3D scene reconstruction. The core idea is to structure Gaussians hierarchically into trees, enabling deformation to be defined at the tree level with learnable coefficients. The tree hierarchy is constructed using the splitting and cloning strategies from 3D Gaussian Splatting (3DGS), resulting in a forest structure. This design allows MLP computations to be applied at the tree level rather than per Gaussian, reducing computational overhead, while maintaining reconstruction quality.", "questions": "1. As I understand it, the number of root nodes is dependent on the number of points in the initial point cloud. Since the root node count likely has the largest impact on computational overhead, is there any analysis between the size of the initial point cloud and performance?\n\n2. How much time does the tree merging process take in practice?\n\n3. Could you clarify the method used to identify the \"unused leaf nodes\" mentioned in weakness 3?\n\n4. I'm curious about how Gaussians are distributed within each tree. For example, do Gaussians within the same tree tend to represent the same object, or is there no such correlation?\n\n5. What are the SSIM and LPIPS results on the Neural 3D Video dataset?\n\n6. Overall, what is the typical decay factor between the root and leaf nodes in the tree?", "limitations": "As noted in the weaknesses, the paper lacks sufficient analysis of the proposed model and does not present results that clearly align with the authors' claims, making it difficult to assess the actual effectiveness of the approach.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "### Strengths\n1. This paper proposes a method for constructing a hierarchy of Gaussians without relying on heuristics, enabling motion hierarchy modeling that differs from prior approaches.\n \n2. The tree structure is built using the splitting and pruning from 3DGS, which is both intuitive and effective.\n\n3. The method demonstrates improved performance over existing approaches in quantitative evaluations.\n\n### Weaknesses\n1. In qualitative video results, moving objects (e.g., head of a dog or the hand) appear noticeably blurred, making it difficult to assess where rendering quality has actually improved.\n\n2. The paper lacks side-by-side video comparisons with other methods, which makes it hard to verify the claimed improvements visually.\n\n3. Some implementation details are missing. For instance, the term \"unused leaf nodes\" mentioned in line 202 is not clearly defined.\n\n4. The paper lacks an in-depth analysis of the tree structure's formation and behavior. Since computational overhead likely scales with the number of root nodes, it would be helpful to analyze the size and structure of the tree/forest in different scenes.\n\n5. It appears that the purpose of modeling a motion hierarchy is to automatically capture dependencies among the motions of Gaussians. Therefore, a detailed comparison with heuristic motion hierarchy generation methods, and a clearer analysis of how the proposed tree structure differs and performs better, would be valuable. This is not sufficiently addressed.\n\n6. If deeper trees lead to better results, it implies that Gaussians are more independent. However, this seems misaligned with the paper's claim that capturing coherent motion is better.\n\n7. I wonder why comparisons with D-3DGS[21] and SC-GS[32] on the D-NeRF dataset are missing.\n\n8. The term tree merging is confusing. It is used to describe precomputing motion coefficients within a single tree, rather than merging multiple trees. A clearer terminology would help avoid misunderstanding.", "was_revised": true, "final_justification": "After carefully reading the authors' reply and other reviewers' comments, I have decided my final rating as borderline accept. My main concern is related to the visual results presented by the authors. Specifically, the current results shown in the main paper and supplementary materials are insufficient to clearly demonstrate how the proposed method (representing Gaussians using a tree structure) contributes to the improvements. I believe this issue has been partially addressed through the authors' clarification and the additional materials being prepared. Aside from this issue, I agree with the novelty of the proposed tree construction mechanism. I recommend that the authors further include results demonstrating the proposed tree mechanism and its improvements.", "rebuttal": "Thank you for your insightful comments! Below, we provide a point-by-point response to address your concerns. We welcome further discussion to improve the clarity and effectiveness of our work.\n\n> **W1: Motion blur in video results.**\n\nWe acknowledge this is one of our limitations. Such blurred artifacts are commonly observed in dynamic Gaussian Splatting without incoporating the temporal opacity (as described in Sec 5.3). Through ablation experiments, we found that enabling temporal opacity helps reduce such motion blur artifacts, particularly on fast-moving parts like the head of the dog. However, it introduces a notable increase in the number of Gaussians and slightly compromise overall rendering quality. We believe this reflects a trade-off between spatial sharpness and temporal consistency.\n\n> **W2: Side-by-side video comparison.**\n\nWe appreciate the reviewer’s interest in comparison with video results. While videos are not able to be included in the rebuttal, we kindly invite the reviewer to refer to Fig.2, which presents a side-by-side visual comparison with three representative baselines: 4DGaussian, DynMF (our direct baseline), and 4DGS. Visual improvements are zoomed in and cropped for clarity. Our method consistently produces sharper details and fewer artifacts, supporting the improvements we claim.\n\n> **W3 & Q3: Clarification on unused leaf nodes.**\n\nThank you for pointing this out. The term unused leaf node refers to those leaf motion nodes whose associated Gaussians have been pruned during training. We will clarify this term in the revision. \n\n> **W4: Tree structure and computation overhead analysis.**\n\nThank you for the insightful comment. In practice, our implementation is parallelized at the Gaussian level. Specifically, our custom CUDA kernel launches a thread for each Gaussian, which independently traverses its associated motion tree path to compute the aggregated motion. Therefore, the actual computational overhead scales with the number of Gaussians, and the computation time (latency) is influenced by the maximum depth of the tree path each Gaussian must traverse. For the tree structure, we analyze the distribution of tree depths across scenes. As shown in the table presented in response to reviewer QfP4, the tree structures follow a long-tailed distribution, with over 97% of motion trees exhibiting depths within 10. This indicates that the majority of Gaussians are connected to shallow trees, ensuring efficient computation while still capturing hierarchical motion.\n\n> **W5: Compare to heuristic motion hierarchy.**\n\nThank you for the reviewer’s suggestion to include comparisons with heuristic motion hierarchy construction.  We implemented a baseline on the Neural 3D Video dataset by generating heuristic hierarchies using semantic segmentation. Specifically, the SfM points from initialization are projected onto the first frame of Camera 0. We apply the Segment Anything Model (SAM) to segment this frame and assign each projected point a semantic label based on its 2D location. Points projected outside the image are labeled as invalid (−1). For each valid semantic label, we manually construct a two-layer motion tree, assigning a shared parent motion node and a leaf node to each Gaussian within the same segment. Experimental results on two representative scenes (Cut Roasted Beef and Sear Steak) show that this heuristic tree structure leads to a drop in reconstruction quality. \n| Method           | PSNR (Cut Roasted Beef) | SSIM | PSNR (Sear Steak ) | SSIM |\n| :---------------: | :---------------------: | :--: | :----------------: | :--: |\n| Heuristic        |          32.73          | 0.96 |       32.69       | 0.96 |\n| Treesplat (ours) |          33.69          | 0.96 |       34.10        | 0.97 |\n\nSuch heuristic motion hierarchy faces difficulty in reliably inferring motion dependencies from sparse SfM points in dynamic scenes, where inaccurate correlations could introduce significant noise and hinder reconstruction. In contrast, our tree is adaptively constructed in conjunction with Gaussian densification, guided solely by reconstruction loss.\n\n> **W6: Clarification on tree depth vs. motion coherence.**\n\nWe appreciate the reviewer’s insightful concern. As shown in the table presented in response to reviewer QfP4, most Gaussians are connected to shallow trees, indicating local motion coherence rather than independence. Moreover, our ablation experiments of tree depth (from line 315 to 325) in Sec. 5.3 demonstrate that moderate tree depth leads to the best reconstruction performance, deeper trees do not necessarily yield better results. This suggests that the benefits of TreeSplat come from modeling local hierarchies, rather than from increasing depth arbitrarily. \n\n> **W7: Comparison with D-3DGS [21] and SC-GS[32].**\n\nWe apologize for this omission. This was due to differences in the experimental protocols: all dynamic Gaussian Splatting baselines in Table 1 were trained with 30k iterations for comparison, whereas D-3DGS and SC-GS were trained with 40k and 80k iterations respectively. Including them directly may introduce inconsistency.  Given the reviewer’s helpful suggestion, we will include both methods in revision, with a clear table footnote clarifying this discrepancy to ensure informative comparison.\n\n> **W8: Potential confusion of the term Merging.**\n\nWe appreciate the reviewer’s comment regarding this potential confusion.  *Tree merging* refers to merge coefficients rather than merging the tree structure. It is the process of consolidating the hierarchical motion coefficients along a Gaussian's ancestral path into a single coefficient vector prior to rendering. We agree that the current term may be confusing and will adopt clearer terminology such as motion coefficient consolidation in the revision to better reflect the actual process.\n\n> **Q1: Impact of Initial Point Cloud Size on Performance.**\n\nWe thank the reviewer for this insightful question. We have empirically validated the impact of initial point cloud size on performance. On the DNeRF dataset, the initialization points are randomly sampled from a cubic volume. Most of these points are pruned before tree construction (typically by the 500th iteration), resulting in minimal influence on the final motion tree structure and negligible effect on runtime.\n\nOn the Neural 3D Video dataset, initialization is based on SfM point clouds, sampled using farthest point sampling. We varied the number of initialization points from the baseline 300k to 600k and 30k. Increasing from 300k to 600k leads to no observable training time increase, and the resulting number of Gaussians remains in the same order of magnitude. However, reducing the initialization to 30k increases the average training time from 34 minutes to 41 minutes. This is because a sparser initialization requires the model to densify more Gaussians during training, which in turn leads to a larger number of deep motion trees.\n\nAs discussed in our response to W4, the computation time (latency) is influenced by the maximum depth of the tree path each Gaussian must traverse. With a larger number of deep trees, each CUDA block during kernel launch is more likely to encounter threads with deep tree paths, leading to an observable increase in training time.\n\n> **Q2: Time cost of tree merging.**\n\nThank you for the question. The tree merging process is highly efficient with our customized CUDA kernel. It takes 0.84 ms per scene on DNeRF and 1.22 ms per scene on Neural 3D Video dataset when evaluated on NVIDIA RTX4500 Ada GPU. This is negligible compared to the training time and has no impact on rendering quality. We will clarify this point in the revised version.\n\n> **Q4: Internal structure of motion trees.**\n\nWe appreciate the reviewer’s interest in the internal structure of the motion trees. To investigate this, we visualized Gaussian trajectories on the Neural 3D Video dataset by coloring all Gaussians bound to the same motion tree with same color. The results reveal that coherent motion trees consistently emerge around moving objects. For instance, in the flame_salmon scene, a motion tree clearly corresponds to the motion of a hand, with its associated Gaussians localized around the hand. In contrast, the static background is typically composed of a large number of isolated Gaussians without parent node (i.e., node level = 0). This behavior arises naturally from our tree growth mechanism, which is coupled with Gaussian densification and driven by gradients from reconstruction loss. Since moving regions introduce higher pixel inconsistencies across time, their corresponding gradients tend to be larger, promoting more active tree growth and hierarchical modeling in dynamic regions.\n\n> **Q5: SSIM and LPIPS on N3V Dataset.**\n\nWe sincerely apologize for omitting them in the manuscript. In the following table, we provide the per-scene SSIM and LPIPS results. These results will be included in the revised version.\n\n|      Scene       | PSNR  | SSIM | LPIPS |    Scene     | PSNR  | SSIM | LPIPS |\n| :--------------: | :---: | :--: | :---: | :----------: | :---: | :--: | :---: |\n|  Coffee Martini  | 28.91 | 0.92 | 0.061 | Cook Spinach | 33.17 | 0.96 | 0.042 |\n| Cut Roasted Beef | 33.69 | 0.96 | 0.044 | Flame Salmon | 29.50 | 0.93 | 0.056 |\n|   Flame Steak    | 33.89 | 0.97 | 0.032 |  Sear Steak  | 34.10 | 0.97 | 0.035 |\n\n> **Q6:  Typical decay factor.**\n\nWe thank the reviewer for this question. For the learned decay factor $\\beta$, we computed statistics across all Gaussians associated with leaf motion nodes on Neural 3D Video dataset. Initialized at 0.5, the learned $\\beta$ values after training range from a minimum of $3.64 \\times 10^{-9}$ to a maximum of 1.0, with a mean value of 0.15. This indicates that while some Gaussians retain strong influence from ancestors, many exhibit rapid decay, enabling flexible control of motion inheritance depth."}, {"review_id": "GD1k00bVHB", "reviewer": "Reviewer_wnrg", "summary": "Overall, this submission focuses on the Dynamic 3D scene reconstruction task. Instead of regarding each Gaussian kernel to hold independent motion patterns, this submission aggregate the motion patterns of correlated Gaussian kernels to better simulate the real-world scenario and thus achieve better performance in general.", "questions": "Overall, the reviewer currently holds around a borderline view for this submission. Below are his current concerns.\n\n1.  Firstly, the authors seem to deeply couple the construction of the tree with the densification process of the original Gaussian Splatting pipeline. The reviewer holds the following concerns w.r.t. this design choice.\n\n1.1. On the one hand, this choice seems to assume that any Gaussians densified from the same parent Gaussian must be correlated (i.e., share the same motion pattern group). The reviewer is curious w.r.t. this assumption. For example, while two Gaussians cloned from the same one can be close to each other once they are just cloned, it is possible that they are learnt to become generally distant from each other during the optimization process. In this case, is it reasonable or limiting to assume that potentially distant Gaussians to necessarily be under the same motion pattern?\n\n1.2. Moreover, the proposed method seems to lack mechanisms that can be used to split the tree into two or more different trees as well. The reviewer, especially with the above concern 1.1, is hesitating on whether this counts a limitation and thus appreciates further clarification and explanation.\n\n2. The authors are appreciated to better elaborate their difference from existing works, e.g., [48]. For example, when the authors say that [48] only use a fixed-structure tree to represent motion. Does this mean [48]'s mechanism choose to do so or [48]'s mechanism only supports pre-fixed mechanism. The reviewer believes that such difference from existing works, especially the most similar few, needs to be better elaborated. Meanwhile, the emprical comparison with such very similar methods, such as [47, 48] is also felt to be necessary by the reviewer.\n\n3. W.r.t. the experiments part, the reviewer is confused w.r.t. the reported training time. Specifically, if the reviewer is not wrong, the authors even use the whole section 4.3 to show how they accelerate rendering during the inference stage. This leaves the reviewer an expectation that the training may be not very fast for this method. Yet, referring to the experiments section, the reviewer surprisingly find that the training time is very fast. The authors are appreciated to explain this part. E.g., do they train the pipeline for the same number of iterations as existing methods?\n\n4. Meanwhile, it is good to see that the authors admit that their method \"brings moderate\noverhead during training\". Yet, as discussed in the above concern 3, this overhead seems to be not from the time perspective but rather from the memory perspective? If this is the case, the authors are appreciated to report such overhead beyond just the Storage memory (Model size) in Table 1 and Table 2, in order for the readers to better get the characteristics of this method.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strength:\n\n1. Overall, this submission is easy-to-understand.\n\n2. The emphrical results of this submission in general demonstrate its effectiveness.\n\nWeakness:\n\n(See questions section for more details)", "was_revised": true, "final_justification": "After reading the author's rebuttal, I think my concerns are largely solved. Thus, despite the admitted increase in GPU memory overhead, I keep my positive rating of this submission.", "rebuttal": "Thank you for your insightful comments! Below, we provide a point-by-point response to address your concerns. We welcome further discussion to improve the clarity and effectiveness of our work.\n\n> **Q1-1: Correlation between Gaussians from same parent.**\n\nWe thank the reviewer for this insightful observation. It is indeed possible for two Gaussians cloned from the same parent to gradually diverge in motion trajectory during optimization. Our model addresses this through the decay-weighted motion aggregation defined in Eq. (6), where each Gaussian inherits motion from its ancestors scaled by a learnable decay factor $\\beta$. Empirically, we observe that the learned $\\beta$ values after training span a wide range: from as low as $3.64 \\times 10^{-9} $ to 1.0, with a mean of 0.15. When $\\beta_i$ approaches zero, the influence from parent motion nodes becomes negligible, allowing the Gaussian $G_i$ to rely primarily on its own leaf motion. This mechanism provides flexibility for Gaussians that were initially correlated (due to cloning) to learn independently when required, effectively address this limitation.\n\n> **Q1-2:  Lack mechanisms to split the tree into two or more different trees as well.**\n\nWe appreciate the reviewer’s thoughtful question. While our method does not include an explicit tree-splitting mechanism, the decay-weighted motion aggregation introduced in Eq. (6) implicitly enables flexible motion decoupling. Specifically, since the influence of ancestor nodes is attenuated exponentially by powers of the learned decay factor $\\beta$, each Gaussian can adaptively learn to minimize its reliance on earlier parts of the tree. When the accumulated decay becomes negligible (i.e., $\\beta^k \\approx 0$ ), the Gaussian effectively becomes disconnected from its ancestor nodes. This in practice achieves the effect of tree splitting without requiring explicit structural modifications.\n\n> **Q2: Comparison with similar works of fixed tree structure.**\n\nWe thank the reviewer for highlighting the need for a more detailed comparison with prior hierarchical motion modeling works. HiMoR [48] adopts a fixed 3-layer tree structure that is manually defined and not adaptable during training. This reflects a design constraint rather than a design choice, HiMoR’s architecture only supports pre-defined hierarchies. In contrast, our method builds a dynamic motion tree structure in a data-driven manner.\n\nDirect empirical comparison with these two methods is challenging, as HiMoR [48] is tailored for monocular dynamic scene reconstruction and Hicom [47] is developed for streamable dynamic scenes. Both are evaluated on domain-specific benchmarks that differ from ours. To enable a fair comparison, we re-implemented their respective hierarchical motion strategies within our framework. As shown in the table below, our learned adaptive tree consistently outperforms these fixed or heuristic hierarchies across two representative scenes, demonstrating the effectiveness of our approach. \n\n|      Method      | PSNR (Cut Roasted Beef) | SSIM | PSNR (Sear Steak) | SSIM |\n| :--------------: | :---------------------: | :--: | :---------------: | :--: |\n| HiMoR-reproduced |          32.68          | 0.96 |       32.25       | 0.96 |\n| Hicom-reproduced |          31.93          | 0.95 |       32.11       | 0.96 |\n| Treesplat (ours) |          33.69          | 0.96 |       34.10       | 0.97 |\n\nWe will clarify these differences in the related work section and include the corresponding empirical results in the revised paper.\n\n> **Q3: Confusion about training efficiency.**\n\nWe apologize for the confusion. Our pipeline uses the same number of iterations (30k) as existing dynamic Gaussian Splatting works. Given that the method involves a large number of Gaussians with varying node levels, we devoted substantial engineering efforts to implement both the forward and backward passes of Eq.~(6) as optimized CUDA kernels (more details can be found in Appendix B.1). This ensures high computational efficiency during training. As a result, the additional overhead introduced by the hierarchical tree structure is minimal: compared to our direct baseline DynMF, the average training time on the Neural 3D Video dataset only increases from 31 minutes to 34 minutes. We will clarify this by explicitly mentioning these speedup details at the last paragraph of Section 4.2 in the revision.\n\n> **Q4: Overhead of motion tree compared to baselines.**\n\nWe appreciate the reviewer’s suggestion. As mentioned in the response of Q3, the extra training time overhead of our method is minimal. However, we acknowledge that the GPU memory overhead  is moderately increased due to additional data structures required to maintain the hierarchical motion trees during training. Specifically, our method incurs an average of 200MB additional memory on DNeRF scenes and 850MB on Neural 3D Video scenes. We will include GPU memory usage during training in Tables 1 and 2 in the revised version. This will provide a more complete view of the method’s resource characteristics."}]

Author rebuttal:

Meta-review: The paper introduces a dynamic gaussian splatting method that uses hierarchical motion tree for coarse-to-fine motion representation. For high performance, the method also proposes a pre-aggregation strategy that liminates traversal overhead. The method achieves better rendering reconstruction accuracy with competitive runtime performance (eg, training time, FPS, storage)

In the initial reviews, reviewers raised questions and concerns on:
- Carity (iFUQ), implementation details (iFUQ), ablation study (iFUQ)
- Analyses on learned motion tree sturucture (QfP4)
- Limitation (QfP4)
- Further explanation on visual results (gmM8)
- Detail mechanism in the tree structure (wnrg)
- Difference from existing method [48] (wnrg)

After the discussion phase, most of the concerns are resolved. All the reviewers give **positive ratings (3 Borderline accept, Accept)**. AC recommends **accepting the paper**. It is highly recommend to incorporate all these feedbacks and discussions with reviewers in the final version.
Decision: Accept (poster)