Implicit 4D Gaussian Splatting for Fast Motion with Large Inter-Frame Displacements
Authors: Seung-gyeom Kim
Areum Kim
Yongjae Yoo
Sukmin Yun
Venue: ICLR 2026 Poster (2026)
Keywords: 4D Gaussian splatting
4D reconstruction
Dynamic rendering
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Recent 4D Gaussian Splatting (4DGS) methods often fail under fast motion with large inter-frame displacements, where Gaussian attributes are poorly learned during training, and fast-moving objects are often lost from the reconstruction. In this work, we introduce Spatiotemporal Position Implicit Network for 4DGS, coined SPIN-4DGS, which learns Gaussian attributes from explicitly collected spatiotemporal positions rather than modeling temporal displacements, thereby enabling more faithful splatting under fast motions with large inter-frame displacements. To avoid the heavy memory overhead of explicitly optimizing attributes across all spatiotemporal positions, we instead predict them with a lightweight feed-forward network trained under a rasterization-based reconstruction loss. Consequently, SPIN-4DGS learns shared representations across Gaussians, effectively capturing spatiotemporal consistency and enabling stable high-quality Gaussian splatting even under challenging motions. Across extensive experiments, SPIN-4DGS consistently achieves higher fidelity under large displacements, with clear improvements in PSNR and SSIM on challenging sports scenes from the CMU Panoptic dataset. For example, SPIN-4DGS notably outperforms the strongest baseline, D3DGS, by achieving +1.83 higher PSNR on the Basketball scene.

Published as a conference paper at ICLR 2026
IMPLICIT 4D GAUSSIAN SPLATTING FOR FAST Mo- TION WITH LARGE INTER-FRAME DISPLACEMENTS
Seung-gyeom Kim Areum Kim Yongjae Yoo Sukmin Yun" Department of Applied Artificial Intelligence, Hanyang University (akkim3533 dk fma0817, yongjaeyoo, sukmi hyunneaanaang
ABSTRACT
Recent 4D Gaussian Splatting (4DGS) methods often fail under fast motion with large inter-frame displacements, where Gaussian attributes are poorly learned dur- ing training, and fast-moving objects often lost from the reconstruction. In this work, we introduce Spatiotemporal Position Implicit Network for 4DGS, coined SPIN-4DGS, which learns Gaussian attributes from explicitly collected spatiotem- poral positions rather than modeling temporal displacements, thereby enabling faithful splatting under fast motions with large inter-frame displacements. To avoid the heavy memory overhead of explicitly optimizing attributes across all spatiotemporal positions, we instead predict them with lightweight feed-forward reconstruction loss. Consequently,
network trained under rasterization-bast SPIN-4DGS learns shared representations across Gaussians, effectively capturing spatiotemporal consistency and enabling stable high-quality Gaussian splatting even under challenging motions. Across extensive experiments, SPIN-4DGS con- sistently achieves higher fidelity under large displacements, with clear improve- ments in PSNR and SSIM on challenging sports scenes from the CMU Panoptic dataset. For example, SPIN-4DGS notably outperforms the strongest baseline, D3DGS, by achieving +1.83 higher PSNR on the Basketball scene.
4DGaussian
Realtime-4DDD 4DGG
D3DGS
Ours
Figure 1: Faithful reconstruction of fast motion with large inter-frame displacements. Existing 4DGS approaches often produce blurred or incomplete reconstructions of fast- Tast-moving objects. In contrast, ours successfully reconstructs clear and accurate details, such the basketball in the scene.
INTRODUCTION
Rendering fast motions with large inter-frame displacements remains challenging for dynamic scene reconstruction, despite its importance for a wide range of real-world applications. Recent advances in 4D Gaussian Splatting (4DGS) have shown remarkable efficiency and visual quality, making it promising framework for dynamic scene reconstruction. In particular, existing 4DGS methods (Yang al., 2024a; Duan et al., 2024; Wu al., 2024; Xu al., 2024) achieve strong results on dynamic scenes with small displacements (e.g., Neu3D (Li et al., 2022b)) across video frames.
However, as motions become faster and inter-frame shifts grow larger (e.g., Panoptic Sports (Joo et al., 2015)), existing 4DGS methods, including explicit 4D parametrization (Yang al., 2024a; Duan et al., 2024) and deformable approaches (Wu et al., 2024; Xu et al., 2024; Kwak et al., 2025), often fail to capture the rapid dynamics, producing blurred or even vanished objects. To be specific, in deformable approaches, Gaussians are defined in static canonical space and transformed over time through learned deformations. However, they often fail assign initial Gaussians for fast- moving objects in the canonical space, causing those objects to remain unseen during deformation
"Corresponding author. Also affiliated with Hanyang University FRICA.

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Published as a conference paper at ICLR 2026
(a) Left: 15K training iteration, Right: 30K training iteration.
(b) Canonical space
Failure modes on fast motions with large inter-frame displacements. We visualize failure modes of existing frameworks; (2a) explicit parameterization and (2b) deformable methods. Figure (2a) shows drastic degradation training iterations (i.e., 15K + 30K), and (2b) shows the canonical space of deformable initialization fails to assign Gaussians for fast motions.
Figure 2:
training. On the other hand, although explicit parameterization roughly tracks Gaussian positions that correspond to fast motions at the early stage of training, their attributes, including color, opacity, scale, and rotation, rapidly collapse in later training, leading drastic degradation. As result, both approaches show failure modes with blurred or even vanished motions, as shown in Figures 1 and 2.
To this end, we focus on addressing the failure in learning Gaussian attributes for fast-moving objects with large displacements. Although positions remain sufficiently accurate to capture motion, other attributes collapse more easily. This degradation arises because reconstruction loss is dominated by background Gaussians; fast-moving Gaussians at new positions incur higher reconstruction errors, while static backgrounds are easier to fit. As a result, both deformable and explicit 4DGS approaches tend to bias learning toward background fitting, eventually leading dynamic objects to disappear. In addition, such large displacements can cause cross-frame interference during frame-by- be--framee rasterization. Although Realtime-4DGS (Yang et al., 2024a) can be sliced differently each time, its parameters are shared, so optimizing for one frame makes other slices suboptimal unless we separate Gaussians by explicit spatiotemporal positions (x. y, z, l). This observation motivates us to leverage the explicit spatiotemporal positions of fast-moving Gaussians as inputs for generating their attributes, thereby achieving more faithful splatting under large displacements.
In this paper, we introduce SPIN-4DGS (Spatiotemporal Position Implicit Network for 4DGS), lightweight yet effective framework designed handle fast motions with large inter-frame dis- placements. To be specific, we first estimate high-quality spatiotemporal positions (z, y. 2, f) of Gaussians that can serve as the inputs for later attribute prediction, initially gathering them across the entire scene before refining them in frame-wise manner. Then, we leverage these positions to predict Gaussian attributes through lightweight ferd-forward network, avoiding the heavy memory overhead of explicitly optimizing attributes over all spatiotemporal positions. This design learns shared implicit representation across all Gaussians and decodes attributes directly from positions un- der rasterization loss. As result, learned attributes remain consistent across positions, and dynamic objects can stay stable even under large displacements. Meanwhile, attributes are stored implicitly in network parameters, rather than explicitly for each Gaussian, which significantly improves memory efficiency on large number of spatiotemporal positions.
To validate the effectiveness of the proposed SPIN-4DGS, we perform experiments various sports scenes from the CMU Panoptic Sports dataset, where human motions are rapid and small objects move across large inter-frame displacements. Across six sports scenes, SPIN-4DGS achieves the best performances, significantly outperforming all baselines. For example, SPIN-4DGS achieves +1.83 PSNR dB improvement compared to the strongest baseline, D3DGS (Luiten et al., 2024), with higher SSIM of 0.92 on the Basketball scene. Specifically, qualitative results in Figure 4 and Table demonstrate that prior methods often blur Gaussians fail capture fast-moving objects (e.g., Basketball), whereas SPIN-DDSS preserves them with sharp and stable reconstructions. In- terestingly, we further observe that SPIN-4DGS significantly improves performance when reusing pre-trained Gaussian positions from strong baselines, such D3DGS and Realtime-4DGS.
Overall, our work introduces SPIN-4DGS, the first framework that learns Gaussian attributes di- rectly from jointly optimized frame-wise positions, enabling stable and high-quality 4DGS under large
displacements. This 4D reparameterization allows ours to mitigate temporal failure modes under such fast motion while still capturing rich temporal appearance dynamics. We believe SPIN-4DGS addresses a fundamental challenge of 4DGS by enabling stable learning in various real-world scenarios, thereby opening direction for advancing dynamic scene representation.
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2 RELATED WORK
Learning temporal dynamics for 3D Gaussian. Recent advances have shown significant progress in extending 3D Gaussian representations into the 4D domain by learning temporal dynamics. Early attempts (Luiten et al., 2024; Javed et al., 2024) incrementally propagated 3D Gaussians from the first frame, demonstrating the potential of 4D Gaussian splatting, but suffering from sequential in- efficiency and overfitting due to numerous per-frame iterations. However, their reliance on external supervision, such as segmentation masks, substantially increases training costs and computational overhead. Meanwhile, inspired by NeRF approaches (Cao & Johnson, 2023; Fridovich- Keil et al., 2023; Park et al., 2021), deformable frameworks (Wu et al., 2024; Yang et al., 2024b; Lu et al., 2024; Zhu et al., 2024; Lin et al., 2024; Xu et al., 2024) instead construct canonical space to ini- tialize Gaussians and then learn temporal displacements in rotation, scale, and position. Despite their robustness on motions with small inter-frame displacements, these methods still underperform on rapid motions with large displacements, as Gaussians that represent fast motion are often omitted during canonicalization and thus remain unseen in the subsequent deformation process. In contrast, we address these challenges without external supervision, showing that high-fidelit capture of fast motion can be achieved solely from raw video inputs.
Explicit 4D Gaussian Parameterizations. Another promising direction is to focus on directly parameterizing Gaussians in 4D from scratch (Yang et al., 2024a; Lee al., 2024; Duan et al., 2024), rather than optimizing each frame separately in the 3D domain. Such explicit 4D modeling unifies space and time into a continuous field and encodes dynamics 4D Gaussian splats, which can be temporally sliced for rendering. in contrast to deformable-based approaches. For instance, Realtime-4DGS (Yang et al., 2024a) performs temporal slicing of 4D Gaussians at each timestamp to obtain dynamic 3D Gaussians, which are then projected to the image plane. While explicit 4D parameterizations achieve higher frame rates (FPS) and improved rendering quality, they require longer training times and larger storage requirements. Moreover, under fast motion with large dis- placements, we observed that corresponding Gaussian attributes gradually blur due to cross-frame interference. A single 4D Gaussian must simultaneously explain all timestamps; however, rasteriza- tion is performed frame by frame, so optimization for one frame inevitably affects the others. This inherent conflict in the rasterization process makes it challenging to maintain temporal consistency in dynamic regions. In contrast, our method avoids such cross-frame degradation by directly decod- ing Gaussians explicit spatiotemporal positions in ford-forward manner. This design explicitly separates lage-diiplacemmet Gaussians at each timestamp, which prevents cross-frame degradation and leads to both stable training and consistent rendering quality.
METHOD
In this section, we present the Spatiotemporal Position Implicit Network for 4DGS (SPIN-4DGS), a framework for reconstructing dynamic scenes under motions with large inter-frame displacements. We first review 3D Gaussian Splatting as preliminaries in section 3.1. Then, section 3.2 describes how obtain explicit spatiotemporal Gaussian positions, and section 3.3 details how their attributes are predicted via feed-forward implicit network. The overall framework is illustrated in Figure 3.
3.1 PRELIMINARY: 3D GAUSSIAN SPLATTING
3D Gaussian Splatting (3DGS; Kerbl et al. (2023)) provides a differentiable volume rendering rep- resentation. It introduces anisotropic Gaussians where the parameters (i.e., position, scale, rotation, color, and opacity) of each Gaussian are defined and optimized for tile-based rendering. Structure- from-Motion (SfM; Schonberger & Frahm (2016)) techniques estimate the initial positions and col- ors of Gaussians from input images. For a given arbitrary point x E R33 in the 3D scene, Gaussian defined as follows:
GSP( eep (x- 11) T 11) 11).
(1)
where G3D (x) denotes the value of the Gaussian at arbitrary point x. The parameters of each Gaussian include the position μ E R opacity o E R, color с E Rd represented using spherical harmonics coefficients, and the covariance matrix Σ E TR3x3, which is defined in terms of diagonal
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Position
Bedinemes::
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Sliing
[+1(=01...))
Inpur: Multi-terg Dysamie Vidao
(A)
Spatiotemporal Position Estimation
Hiehh Encoder
Aftelbute-awarr Decoder
(9, 91 x]
Frne
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0-
Implicit Network for 4DGS
Figure 3: Illustration of the overall framework. SPIN-4DGS consists of two stages of (a) Spa- tiotemporal Position Estimation and (b) Implicit Network for 4DGS. Specifically, (a) slice Gaus- sians along the temporal axis to obtain spatiotemporal position sets and refine them with rasterization loss. Then, (b) the refined positions are normalized and passed through 4D hash encoder and multi- branch decoders to predict Gaussian attributes (scale, rotation, color, and opacity).
scale matrix S = diag(81, $2, $3) and rotation matrix R E SO(3), obtained from quaternions. To ensure that the covariance matrix remains Σ positive semi-definite, is computed as follows:
E&D = RSS R
(2)
To render via rasterization, the 3D Gaussians are first projected onto the 2D image plane. This is done by applying the viewing transformation W and the Jacobian matrix (Zwicker et al., 2001) J to compute the 2D covariance matrix Σnn as follows:
Enp = JW END W
(3)
During the rendering process, pixel values are computed via alpha blending. The alpha value (i.e. opacity) of each Gaussian is obtained by projecting the 3D Gaussian G, into 2D G?D. Specifi- cally, for each pixel, the alpha value af and the resulting color are computed as
N
df d o (x), C(x) = Σ C:
(
(4)
where o; is the intrinsic opacity of the i-th Gaussian, e; its color, and N the total number of Gaussians contributing to the pixel.
3.2 SPATIOTEMPORAL GAUSSIAN POSITIONS
In this section, our goal is to construct Gaussian point set that fully spans the trajectory of dynamic objects, ensuring sufficient coverage for faithful reconstruction. Prior methods perform reasonably well in regions where Gaussians are densely clustered, but under large inter-frame displacements, they often fail to maintain enough points around fast-moving objects. Even when positions sufficiently available, attributes remain challenging. To specific, when Gaussians spanning the entire trajectory optimized jointly, frame-specific supervision signals interfere with one another. Because rasterization is performed frame by frame, updates that make a Gaussian optimal for one timestamp can render it suboptimal for others. This cross-frame interference can potentially weaken the learning signal and degrade the quality of the reconstruction.
To overcome these issues, construct Gaussian sets independently at each time step, explicitly separating them by spatiotemporal positions. This formulation avoids interference across frames and enables more reliable attribute learning for fast-moving objects under large displacements.
fo y,
(x. y, 2, 255)),
t E (O...., T)-
(5)
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Published as a conference paper at ICLR 2026
Here, fo and I are explicit functions of the temporal axis predicting the position and color responding to each frame t. For example, the explicit approaches (Duan et al., 2024; Yang et al., 2024a) construct points by performing time slicing along the temporal axis, whereas a deformable approach (Wu et al., 2024; Xu et al., 2024; Bae et al., 2024) network can learn to construct them as vinevaayyigg structures. For SPIN-4DGS, method (Yang et al., 2024a) as a default. Lastly, we further refine the estimated position by utiliz- ing rasterization loss with corresponding colors every frame densify salient points and prune unnecessary ones.
estimate spatiotemporal positions by explicit
Refine (u., (ui,,cr:))) cri(),
1 0....., T.
(6)
After refinement, the Gaussian points at each timestamp are fixed as explicit spatiotemporal posi- tions and directly fed into our implicit network to learn the corresponding attributes.
3.3 IMPLICIT NETWORK FOR 4D GAUSSIAN SPLATTING
In this section, describe implicit network that is trained in an end-to-end manner directly predict 4D Gaussian parameters from learnable spatiotemporal Gaussian positions initialized from the collected ones. In contrast prior approaches that require pre-defined or pre-optimized Gaussian attributes (e.g., scale, rotation, opacity, color) to model temporal dynamics, our network is trained from scratch using only the collected spatiotemporal positions (H, E E imput. Given (μ. t), the network predicts all 4D Gaussian parameters, including opacity o E R.,, spherical harmonics R.d.
coefficients sh E 18 scale s E RR33 and rotation represented as a unit quaternion
Input position normalization. At each frame f. the spatiotemporal Gaussian positions serve as inputs to a feed-forward network for learning implicit representations other Gaussian parameters. Since the raw 3D Gaussian positions E IR on the scene are unbounded, we apply a normalization step to stabilize learning and preserve representational capacity. Specifically, following the scene contraction strategy of Mip-NeRF (Barron et al., 2021), first compress the coordinates into finite ball and then map them to the normalized range [0, 1]3, as defined in equation" 7.
||||| S 1,
contract((4) =
> 1, i == contract (/)) + E [0, 10. (7)
1
||||||
||
To keep spatial and temporal scales comparable, normalize time 10, 1] to match the scale of the spatial embedding. Concretely, we use the current timestamp divided by the total duration:
min
fnor
[0, 1] and
-[x
fnorm
[0, 1]
(8)
tmax
tmin
Our network adopts encoder-decoder architecture, where the encoder fene maps the normalized input & to a latent embedding (x)e(x) which the decoder takes as input. We note that the position is also parameterized and jointly optimized with the network, similar to existing frameworks (Wu et al., 2024; Xu et al., 2024).
Encoder architecture for shared latent representation. We directly extend the widely used 3D Ins (Müller et al., 2022) multi-hash grid to 4D by appending the temporal axis, producing a compact latent vector for each input. Given the normalized input =[n fuorm 1_, we map into a unified 4D embedding via single spatio temporal encoder. In contrast to low-rank decom- positions (e.g,, planar), which may reduce computation but degrade expressiveness as the number of Gaussians grows and incur extra cost from per-level hash management, we avoid such factorizations and employ the 4D hash encoder (Chen et al., 2025) directly as follows:
= ()) E LF
where L denotes the number of hash levels and F the number of channels per level. We concatenate features across all levels to form 2 E L... which we use as the latent representation.
Attribute-aware decoder for Gaussian attribute prediction. Given latent vector z. a multi-branch decoder to produce Gaussian parameters, scale, rotation, spherical harmonics coef- ficients, and opacity. Each attribute is predicted by a separate head (three-layer MI.P) taking the
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shared encoder output E R.P as imput. All decoder heads use GELU (Hendrycks & Gimpel, 2016) activations instead of ReLU (Agarap, 2018).
(5, sh, 6) (fscatezz), fro( fza(z), Fopucity fo)a)
(10)
We convert the raw outputs into valid parameter ranges using attribute-specifee activations and post- processing:
(s, r, sh, o) (exp(s), T sh, a())..
(11)
We also follow the Gaussian post-processing (Kerbl et al., 2023) pipeline, with a few additional steps for stable training.
To prevent gradient explosion from exponential growth, we clip the pre-scale in the backward pass: $ <- clip(š, max 20). We also initialize the final-layer bias to -5 to start from small scale, i.e., exp(-50 x 0.0067, and keep it trainable.
Scale decoder.
Rotation decoder. To bias the predicted quaternion toward the identity at the start of training, we set the final-layer bias to (1,0, 0,,), i.e., the first element to 1.0 and the remaining elements to O, so that the initial output satisfies r z (1, 0, 0, 0). This initialization lets the network learn rotations progressively while preserving stable initial structure.
Opacity decoder. To stabilize early training and encourage near-transparent start, we the final-layer bias to 1ogit(0.1) = 2.199 (trainable), initializing ô at = 0.1. The network then learns to increase opacity only where needed, focusing on informative points.
Color decoder. The decoder directly regresses color coefficients from encoder embeddings, with no special initialization, to capture the high-dimensional color required for SH-based rendering.
Loss objectives. Finally, frame images are rendered via rasterization, and we optimize the model using the standard 3DGS reconstruction loss as follows:
L (1 - X) C1 + X CD-SSIM.
(12)
where À is hyperparameter; we set À 0.2, following prior works (Kerbl et al., 2023).
EXPERIMENTS
In this section, we demonstrate the effectiveness the proposed method, SPIN-4DGS. Specifically, we choose to employ the recent explicit parameterization method for Realtime-4DGGS (Yang et al., 2024a), which is publicly available, only in the early training stage to estimate spatiotemporal Gaus- sian positions. These positions are then used in our framework to learn new Gaussian attributes. We then evaluate its ability to capture fast motion on various sports scene benchmarks from the CMU Panoptic Sports dataset (Joo et al., 2015), comparing it with existing 4DGS baselines.
Implementation details. The network uses a hidden dimension of 64, and the encoder is configured with T. 16 levels and F 4 features per level; the hash map size 221 Parameter groups in both the encoder and the decoder utilize separate learning rates, as Gaussian attributes (e.g., scale and rotation) are sensitive, and a uniform learning rate often leads unstable optimization. The encoder learning rate is initialized to 8 x 10-3, decoder learning rates are 1 x 10-3 3 for color, 3 x 10-4 4 for scale, 3 10-5 for rotation, and 10 4 for opacity. Position parameters use the same learning rate as 3DGS. We use Adam (Kingma & Ba, 2015) with a linear warm-up up and cosine decay schedule, under which every parameter's learning rate decays to 1 x 10-7 Experiments were conducted on RTX 4090 GPU (24 GB), and the implementation utilized PyTorch (Paszke et al., 2019) 2.1 with CUDA 11.8. By default, we train for 40K iterations with batch size of 3. We perform quantitative evaluations using PSNR (Peak Signal-to-Noise Ratio), SSIM (Wang et al. (2004); Structural Similarity Index), and LPIPS (Zhang et al. (2018); Learned Perceptual Image Patch Similarity), and additionally report frames per second (FPS) to assess rendering speed.
We employ the CMU Panoptic Sports dataset (Joo et al., 2015) to validate scenarios of fast motions with large -nter-rrame displacements in our experiments. Specifically, the Panoptic Sports dataset is a challenging benchmark containing six sports scenes: juggle, basketball, boxes, football, softball, and tennis. Each scene is recorded at 30 FPS for 5 seconds (150 frames per scene).
Datasets.

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Published as a conference paper at ICLR 2026
Table I: Comparisons on dynamic sports scenes in the CMU Panoptic Sports dataset. We evaluate ours with existing 4DGS baselines on benchmarks containing fast motions with large inter- frame displacements. We report PSNR and SSIM for six sports scene sequences across all baselines.
Velvv
CDEc Clangiry
Ractrdull
Pertul
Seepl
Svttill
Trael
H1S1
Strrng.
Crs4D mad.
Ixfermate
23/02
0.25
27.11
D51
25.03
20:91
22.33
22.05
0131
303
Metio GB (louk enal, 3329
Deficrr alda
27.13
0.40
34.17
040
17.09
060
33.33
0195
33.31
0.0
33 36
0192
23333
0.00
02
31
aUKeavee (We 2030
Iktermate mate
21:25
035
27:32
26.11
151
25.34
1091
27.34
101
27.85
109
22333
1831
40
62
(ivadd aral
Easrel speriiiie
27300
0.88
31.90
27.86
0889
Readii IDCGS (Vagg 20046
Eaplitt
832
25.35
035
35.5
2533
003
1233
8.0
24.9
600
31.11
31.31
1085
34.11
36:11
(031
1751
Ballebbal
Temnis
Softbel
Poohail
4DGausiies
Realtime 4DGS
DADGS
Ours
GT
Figure 4: Visualizations on dynamic sports scenes in the CMU Panoptic Sports dataset. Com- pared to prior 4D Gaussian baselines, where fast- fast-moving objects (e.g., ball, bat, and racket) often disappear or become corrupted, our method successfully preserves these objects throughout the se- quence, producing more faithful and consistent reconstructions.
total of cameras were used, and the native resolution of 640 x 360 was retained. Evaluation was referenced to four fixed test cameras (IDs of 0, 10, 15, and 30).
4DGS baselines. We compare our method with recent 4DGS baselines across various strategies, including (a) explicit parameterizations for 4DGS: Realtime-4DGS (Yang et al., 2024a), 4D-Rotor- Gaussians (Duan et al., 2024)', (b) deformable 4DGS: Grid4D (Xu et al., 2024), 4D Gaussian (Wu al., 2024), MoDec-GS (Kwak al., 2025), and (c) external supervision: D3DGS (Luiten al., 2024), TC3DGS (Javed et al., 2024). We note that D3DGS and TC3DGS are designed to handle large inter-frame displacements, such as the Panoptic Sports dataset. All baselines are evaluated following the dynamic scene setups specified in their papers.
4.1 EXPERIMENTAL RESULTS ON PANOPTIC SPORTS
In this section, evaluate method with various 4DGS baselines six dynamic sports scenes (Basketball, Boxes, Football, Juggle, Softball, and Tennis) from the CMU Panoptic Sports dataset, which involve rapid human motions and small objects undergoing large inter-frame displacements.
As reported in Table 1, SPIN-4DGS achieves the best PSNR on all six scenes with an average of 30.11 dB, outperforming the strongest explicit baseline Realtime44DGS (28.38 dB) by +1.73 dB and the external supervision baseline D3DGS (28.70 70 dB) by +1.41 dB. SSIM also remains consistently high at 0.93, confirming stable reconstruction quality. In particular, our method even surpasses mod- els trained with external supervision such as segmentation maps (e.g., D3DGS, TC3DGS), showing that high fidelity can be achieved without costly priors. Beyond averages, the improvements are most significant challenging scenes with extreme motion. On Basketball, SPIN-4DGS improves We reimplemented the method using the official PyTorch code released by the authors.

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PSNR by over +1.83 dB against the best baseline, D3DGS (Luiten et al., 2024), while Tennis, where rackets move rapidly and cover large displacements, the margin also surpasses +1.64 dB against the best baseline, Realtime-4DGS (Yang et al., 2024a). Overall, those results highlight the robustness of our approach to challenging fast-motion scenarios where prior methods often fail.
Qualitative comparisons in Figure 4 further illustrate these differences. Deformable baseline (i.e., 4DGaussian, first column) results blur fine-grained structures, explicit Realtime-4DGS (second) results frequently lose moving objects, and even externally supervised (i.e., D3DGS, third) results suffer degradation on small, fast objects like tennis racket. In contrast, SPIN-4DGS preserves sharp and stable reconstructions across all frames, closely matching the ground truth.
As shown in Figure 4, only the externally supervised baselines (e.g., D3DGS) are able to repre- sent the fast-moving objects (e.g., basketball) in these sports scenes. Although D3DGS achieves high rendering speed, it requires external supervision during training and incurs substantial storage overhead (1994 MB) store a large set of Gaussian attributes for the entire sequence. Explicit Realtime-4DGS renders faster than SPIN-4DGS, yet still fails to reconstruct these fast-moving ob- jects and yields lower PSNR. In contrast, SPIN-4DGS attains higher fidelity with smaller footprint (1261 MB) by storing only Gaussian positions and the network. Such network-based approach also makes it possible to reconstruct only selected time intervals without storing all Gaussians of the entire sequence. Compared to other network- -asedd deformable baselines. SPIN-4DGS reaches 104 FPS, substantially higher than 4DGaussian (40 FPS) and MoDec-GS (62 FPS), while these methods still struggle represent fast-moving objects. These observations suggest that SPIN-4DGS offers practically usable trade-off among fidelity, storage, and speed for fast-motion sports scenes.
4.2 ABLATION STUDY AND ANALYSIS
We conduct a series of ablation experiments to demonstrate the proposed method further. First, we analyze the impacts of estimated spatiotemporal position quality and refinement in Table and 3. We also examine position-reuse setting in Table 4, where positions from existing 4DGS models are provided, validate the effectiveness of our attributes learning scheme. Finally, we validate the effect of each component of our implicit network in Table 5.
Table 2: Ablation study spatiotemporal positions. We perform ablation studies on (a) varying the early training duration used to estimate spatiotemporal Gaussian positions from the explicit baseline, ReaStime-4DGS (Yang et al., 2024a), evaluated without subsequent refinement, and (b) varying the number of frame-wiss wise refinement iterations applied after position estimation.
(a) Effect of carly training duration
(b) Effect of refinement iterations
Iteration
PSNR
SSIM
LPIPS
Time.
Iteration
PSNR1
SSIM
LPIPS
Timel
0.5K
29.86
0.92
0.14
33m
15K
29.57
0.92
0.15
10m
1K
29.89
0.92
0.14
55m
30K
29.39
0.91
0.15
30m
2K
30.05
0.92
0.14
1h 40m
Ablation on spatiotemporal positions. We investigate how the quality of estimated spatiotemporal positions and the amount of refinement affect the final reconstruction. Results are summarized in Table 2, evaluated on the Basketball sequence.
(a) Effect of early training duration. Using positions extracted after 15K iterations of Realtime- 4DGS (Yang et al., 2024a) already achieves strong performance (29.57 PSNR, 0.92 SSIM) with only 10 minutes of cost. Extending training to 30K iterations not only triples the runtime but also slightly degrades the quality, indicating that long optimization is unnecessary once positions are sufficiently stable.
(b) Effect of refinement iterations. We then vary the number of frame- refinement steps after position estimation. Increasing refinement from 0.5K to 2K iterations improves PSNR from 89.86 to 30.05, confirming that moderate refinement shows consistent benefits. In practice, also prune redundant Gaussians during refinement, which reduces background clutter and focuses updates on salient regions, further enhancing efficiency.
We further analyze the effect of spatiotemporal slicing in Table 3 and Figure 5. For fair comparison, fix the batch size and run all experiments on the
Effects of input position formulation.
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football sequence, varying only the position design. We compare two settings: (a) w/o spatiotempo- ral slicing. where all Gaussians are optimized jointly without slicing, and (b) spatiotemporal slicing (ours), where positions are sliced frame by frame and aligned along the time axis.
Without slicing, as shown in Table 3, Gaussians are optimized jointly in a unified 4D space. this formulation, single Gaussian must simultaneously explain multiple timestamps. However, raster- ization is performed frame by frame, so optimization that reduces the loss for one frame inevitably makes the Gaussian suboptimal for others. This cross-frame interference weakens the supervision signal, slows convergence, and increases both training time and memory usage. In contrast, spa- tiotemporal slicing explicitly separates Gaussians by (z, y, 2) and filters out irrelevant points at each frame. This avoids interference across frames and ensures that optimization is focused on the relevant Gaussians for each time step. As a result, slicing achieves both higher reconstruction fidelity and significantly lower training cost.
Qualitative comparisons in Figure 5 con- firm these findings. Under the unified 4D formulation, attributes collapse as Gaus- sians attempt to describe other timestamps, producing blurred faces and distorted fast- moving objects (e.g., football in the scene). Our sliced formulation decouples Gaus- sians over time, showing sharper details and temporally consistent reconstructions.
Table 3: Ablation on spatiotemporal slicing. We compare a unified 4D formulation (i.e., w/o slicing), where Gaussian positions are optimized jointly across space-time, against our spatiotemporal slicing strat- egy that assigns positions per frame.
Spatiotemporal Slicing
PSNRI
SSIM
Timel.
Train Cost.
27.48
0.89
1h 20m
18GB
28.96
0.92
25m
9GB
GT
w/o Slicing
Ours
Figure 5: Qualitative comparison of spatiotemporal slicing. Without slicing, Gaussians simul- taneously represent multiple time steps, causing their contributions to overlap and conflict during rasterization. This results blurred faces and distorted fast-moving objects. Our slicing explicitly separates Gaussians over time, enhancing qualities with temporally consistent reconstructions.
Impacts of implicit 4DGS scheme. We further validate the impacts of the proposed implicit 4DGS scheme by reusing positions from strong baselines and retraining only attributes with our framework. In this setting, we extract pre-trained spatiotemporal positions from D3DGS (Luiten et al., 2024) and Realtime4DGGS (Yang et al., 2024a). but discard all their learned attributes. SPIN- 4DGS then learns new attributes through its implicit network. while keeping the imported positions learnable to allow for refinement during training. This setup highlights not only the effectiveness of our attribute learning design but also its plug-and-play compatibility with existing 4DGS pipelines, where our scheme consistently enhances reconstruction quality regardless of the underlying position estimator.
As shown in Table 4, SPIN-4DGS consistently improves performance even when initialized with external positions. With D3DGS positions, our method improves PSNR by +2.49 dB and SSIM to 0.95 on the Softball scene. Notably, while D3DGS collapses Tennis (28.11/0.3 11/0.91), SPIN-4DGS still achieves 30.51/0.95 with sharp reconstructions. Even with 4DGS positions, our framework still achieves consistent gains overall, demonstrating the effectiveness of the proposed scheme. While SSIM occasionally drops slightly in some cases, we find that this minor loss is easily resolved by refinement step, showing that performance remains robust and stable.
We find that high-quality positions alone are insufficient for stable reconstructions, as attributes play critical role in maintaining fidelity under large inter-frame displacements. We also observe that

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Table 4: Compatibility with existing 4DGS baselines. We reuse pre-trained positions from D3DGS (Luiten et al., 2024) and Realtime-DDGS (Yang et al., 2024a), replacing their attribute optimization with our proposed implicit network training. SPIN-4DGS consistently improves PSNR/SSIM across all scenes, highlighting the compatibility and effectiveness of the proposed im- plicit 4DGS scheme.
Basketball
Botes
Football
Juggle
Sefbblll
Tennis
Method
PSNR1
SSIM
PSNR1
SSIM1
PSNR1
SSIMI
PSNR1
SSIM
PSNK7
SSIM1
PSNR1
SSIM
Realtime 4DGS (Yang al,, 2024a)
27.89
0.92
28.17
0.93
28.35
0.93
23.68
0.93
28.67
0.93
28.50
0.93
Realtime-41X3 Ours
29.57
0.92
29.63
29,42
29,98
0.92
29.94
0,93
29.83
0,93
DJDGS (Luston al,, 2024)
28.22
0.91
29.46
0.91
28.89
0.91
29.48
0.92
28.43
0.91
26.11
0.91
DEDGS Ours
30.92
30.51
our implicit 4DGS formulation generalizes seamlessly across different baselines, showing strong compatibility and consistent improvements regardless of the source of positions. Taken together, these results highlight SPIN-4DGS as an effective and extensible 4DGS scheme that can enhance wide range of dynamic scene reconstruction tasks.
Table 5: Ablation on our implicit network design components. Starting from the original 4D hash encoder (Chen et al., 2025), we analyze the effects of making positions trainable, applying input position normalization, and changing activation functions. Each modification progressively enhances reconstruction quality. All experiments are performed on the Basketball scene.
Network Components
Results
Trainahle position
Normalization
Activation
Hash Map Size
PSNR1
SSIM
LPIPS
ReLU
221
18.64
0.78
0.45
ReLU
221
19.17
0.78
0.46
ReLU
221
29.89
0.92
0.16
/
GELU
221
30.05
0.92
0.14
GELU
225
30.25
0.93
0.13
Component analysis. We conduct ablation study the design components of our implicit network, summarized in Table 5. Starting from the original 4D hash encoder (Chen et al., 2025) encoder with fixed positions and ReLU activations, reconstruction quality is notably poor (18.6 64 PSNR, 0.78 SSIM, 0,45 LPIPS). Making positions trainable alone achieves only marginal improve- ment, indicating that position refinement is insufficient without additional modifications. Applying input position normalization shows a significant gain, boosting PSNR by over +10 dB and reduc- ing LPIPS from 0.45 to 16, highlighting its importance for stabilized training. Replacing ReLU with GELU further improves fidelity. enlarging the hash map size further achieves the best overall performances (30.25 PSNR, 0.93 SSIM, 0.13 L.PIS). These results confirm that each component contributes to stability and accuracy, with their combination being crucial for achieving high-qualit reconstructions.
5 CONCLUSION
In this work, we addressed the challenge of dynamic scene reconstruction under fast motions with large inter-frame displacements. Existing 4DGS methods, including deformable and explicit ap- proaches, often fail to maintain Gaussian attributes in such regimes, resulting in blurred or vanished objects. We introduced SPIN-4DGS, new framework that learns Gaussian attributes directly from explicit spatiotemporal positions via feed-forward network, rather than relying on temporal dis- placement modeling. By decoupling Gaussian position estimation from Gaussian attribute learning, SPIN-4DGS offers simple yet effective design principle for representing dynamic scenes under fast motions. SPIN-4DGS achieved high-quality reconstructions fast-moving objects under large inter-frame displacements, scenes in the CMU Panoptic Sports dataset. Overall, we believe SPIN-4DGS advances 4D Gaussian Splatting toward practical deployment in challenging real-world scenarios.
demonstrated through extensive experiments across dynamic sports
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ACKNOWLEDGMENT
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2025-24533937) and by the MSIT (Ministry Science and ICT), Korea, under the Convergence Security Core Talent Training Business Support Program (IITP-2024- RS-2024-00423071) 1), supervised by the IITP (Institute of Information & Communications Technol- ogy Planning & Evaluation).
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A MORE ABLATION STUDIES
Perceptual quality comparison. In terms of perceptual quality (LPIPS), SPIN-4DGS also de- livers competitive performance across all six scenes the CMU dataset. As shown in Table 6, our method achieves a mean LPIPS of 0.14, substantially improving over the strongest baseline D3DGS (0.18) while remaining close the explicit Realtime-4DGS (0.13). These results indi- cate that SPIN-4DGS effectively suppresses blur and collapse artifacts around fast-moving objects without sacrificing perceptual fidelity, and together with the PSNR/SSIM gains further confirm the robustness of our method under challenging fast-motion scenarios.
Table 6: Perceptual quality comparison. We report LPIPS across six sports scenes on the CMU
Panoptic Sports dataset. Lower scores indicate better perceptual quality.
Model
4DGS Category
Basketball
Boxes
Football
Juggle
Softball
Tennis
Avg.
D3DGS (Luiten al., 2024)
External supervision
0.18
0.17
0.19
0.15
0.19
0.17
0.18
Realtime 4DGS (Yang al., 2024s)
Explicit
0.14
0.12
0.14
0.13
0.13
Training budget. Compared to the strongest baseline D3DGS, SPIN-4DGS offers a better trade- off between reconstruction quality and training time, as summarized in Table 7. With a lightweight 15K-iteration configuration without refinement, SPIN-4DGS already attains 28.82 dB on Basketball, outperforming D3DGS (28.22 28.22 dB) while reducing training time from 100 45 minutes. Adding a short refinement stage (15K position iterations and 0.5K refinement itcrations) further improves PSNR to 29.13 dB in 73 minutes, still faster than D3DGS. With more compute, longer refinement yields additional gains: 15K + 2K reaches 29.51 dB in 142 minutes, and the full 40K + 2K set- ting achieves 30.05 dB in 195 minutes, i... +1.83 dB over D3DGS. Overall, our two-stage design can match or surpass D3DGS with a substantially smaller training budget (even without external supervision), while providing a smooth path higher fidelity when more budget is available.
Table 7: Training time breakdown and PSNR the Basketball scene. We compare PSNR, position- position-estimmtioo estimation time, refinement cost, network training time, and total training time across dif- ferent SPIN-4DGS configurations and the D3DGS baseline. All time measurements are reported in minutes.
Method
Setting
PSNR
Position
Refine
Network
Total time
D3DGS
Default
28.22
100
Ours
15K, No refine
28.82
10
0
35
45
15K, Refine (0.5K)
29.13
10
33
30
73
15K, Refine (2K)
29.51
10
100
32
142
40K, Refine (2K)
30.05
10
100
85
195
Neu3DV benchmark. We additionally evaluate SPIN-4DGS on the NLu3DV(Li et al., 2022h) benchmark, which features complex backgrounds and smaller motions. In this experiment, we keep the default SPIN-4DGS training setup without the refinement stage, training only on pre-refinement spatiotemporal positions, with the hash map size hyperparameter set to 223 throughout training. As summarized in Table 8, SPIN-4DGS attains the highest average PSNR of 32.19 dB, slightly outperforming the strongest explicit Realtime-4DGS (32.01 dB) by +0.18 dB and clearly improving over deformable methods such as Grid4D (31 11.49 dB) by +0.70 dB and 4DGaussian (31.01 dB) by +1.18 dB. Moreover, SPIN-DDGS improves over the externally supervised D3DGS baseline (31.04 dB) by 1.15 dB in mean PSNR, and SSIM also remains consistently high at 0.95, matching or surpassing the best competing methods. Qualitative comparisons in Figure show that moving objects (e.g., the tongs and knife) appear blurred or smeared with explicit Realtime-4DGS whereas SPIN-4DGS reconstructs them with much sharper details, confirming stable reconstruction quality on complex, dlower-motion scenes.
MeetRoom benchmark. We further evaluate SPIN-4DGS on the three scenes (Discussion, Trim- ming, VR Headset) from the MeetRoom benchmark (Li al., 2022a), which contain cluttered in-
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Table 8: Comparisons on the Neu3DV scenes. We report PSNR (and SSIM when available) for
SPIN-4DGS and baselines across six sequences.
Method
aDGS Ciregery
Cerioo Mariin
Coit Sproch
Cat Resordl Heef
Plame Satrann
Flume Strat
Stock
Apg
PSNRT
S51M1
S53M1
S51M4
PSNR1
SSIM
S50M4
PSNRR
SSIM4
PSNRT
GIILD OKo dt
Defocmable
0:55
attoesoioon (W0 2000g
Deformoble
27
0.90
0.94
0.81
0.90
33.0
31.01
DJDGS (Lutton et ol.. 2004)
Extonaal supenianu
27.32
32.97
31.75
27.26
33.24
33.08
31.00
Doalmm--DD8 (Ying at al, 201443
Eoplian
20.33
52.95
55.8
29.36
54,03
53.51
$2.01
DD0iime---DGSeeeeeeee impta Clee 2015)
Explict
22,92
0.92
13.58
0.96
33.96
0.66
26.72
0.92
53.96
0.96
35.61
0.96
31.56
0.95
Oure
28.42
8.92
X1.1
0.96
1996
76.87
0.92
3790
0.96
3414
0.96
32.19
0.95
door backgrounds and relatively small motions. Using the same configuration in our main exper- iments, we train SPIN-4DGS only on the pre-refinement spatiotemporal positions, with the hash- map size fixed to 2 throughout training. Table 9 shows that SPIN-4DGS consistently achieves higher PSNR than all baselines, including StreamRF (26.72 dB), 3DGStream (30.79 dB), and ex- plicit ReaStime-4DGS (30.47 dB). Overall, it provides average improvement of +1.6 dB over the explicit Realtime-4DGS. In particular, on the Trimming scene, SPIN-4DGS attains 32.41 dB, im- proving over the explicit Realtime-DDGS (30.16 dB) by more than 2 dB, while also maintaining high SSIM of 0.96. Qualitative comparisons in Figure 10 illustrate these effects: while Realtime- 4DGS often fails to faithfully reconstruct objects due to noise and artifacts in both the foreground and background, SPIN-4DGS yields sharper object reconstructions and substantially cleaner back- grounds. These results suggest that our model remains robust even indoor scenes with cluttered backgrounds and relatively small motions.
Table 9: Comparisons on the MeetRoom scenes. We report PSNR and SSIM for SPIN-4DGS and baselines across three sequences and their average. Note that only average PSNR scores are available for StreamRF and 3DGStream.
Discussion
Trimming
VR Headset
AVG
Method
Category
PSNRf SSIM
PSNRf
SSIM
PSNR
SSIM
PSNR1
SSIMI
StreamRF (Li al., 2022a)
Implicit Explicit
26.72
3DGStream (San et al., 2024)
30.79
Realtime-4DG3s (Yang et al., 2024a)
Explicit
31.51
0.96
30.16
0.94
29.74
0.95
30.47
0.95
Ours
32.30
0.96
32.41
0.96
31.42
0.95
32.04
0.96
Comparison to frame-wise 3DGS. To verify the benefits of our temporally shared implicit repre- sentation over frame-wise 3DGS (i.e., collection of 3DGS on each frame), we directly compared SPIN-4DGS with frame- wise 3DGS (Kerbl et al., 2023) and D3DGS (Luiten et al., 2024) on the CMU Panoptic Sports benchmark, where we referred to the results reported in the D3DGS. Table 10 shows that SPIN-4DGS achieves the best performance on all six CMU Panoptic Sports scenes, sur- passing both frame-win wise 3DGS and D3DGS. Quantitatively, SPIN-4DGS improves PSNR by 1.9dB on average frame-wiis wise 3DGS and with gains of up to +3.03dB on Basketball. These substantial gains suggest that our temporally shared implicit field can better exploit temporal regularities and cross-frame correlations, yielding a more coherent 4D representation than a set of independently optimized frame-wise 3DGS models.
B MORE QUALITATIVE RESULTS
Qualitative results on spatiotemporal position refinement. Figure 6 visualizes the ablation study on the position refinement in Table 2. With only 0.5K refinement iterations, SPIN-4DGS already captures stable object structures without collapse, while increasing iterations to 1K and 2K further improves fine details such as ball edges and racket nets. Specifically, our refinement stage employs Gaussian densification, which both allocates new Gaussians regions that lack detail and prunes redundant ones, incrementally filling in missing structures while reducing the number of unnecessary Gaussians. This process can alleviate the dependence on initially collected positions, allowing SPIN-4DGS train reliable input point set. These results indicate that SPIN-4DGS is effective even with minimal refinement budgets and that additional iterations mainly serve to sharpen fine details rather than prevent collapse.
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Table 10: Comparison with frame-wise 3DGS on the CMU Panoptic Sports benchmark. We report PSNR across six sports, showing that SPIN-4DGS consistently outperforms both 3DGS and D3DGS across all sequences.
Model
Basketball
Boxes
Football
Juggle
Softball
Tennis
Avg.
3DGS (Kerbl al., 2023)
27.02
28.74
28.49
28.19
28.77
28.03
28.21
D3DGS (Luiten et al., 2024)
28.22
29.46
28.49
29.48
28.43
28.11
28.70
Ours
30.05
29.91
29.99
30.31
30.24
30.14
30.11
Tennis
Softball
Football
0.5K
1K
2K
Figure 6: Visualizations on spatiotemporal position refinement. We visualize the effect of vary- ing refinement iterations (0.5K, IK, 2K) corresponding to Table 2b. Even with only 0.5K iterations, SPIN-4DGS retains consistent object structures without collapse, while progressively increasing the number iterations recovers fine details such as ball edges and racket nets.
Qualitative results with various baselines. Figure shows qualitative comparisons on the CMU Panoptic Sports dataset for two baseline methods in Table 1: MoDec-GS and 4D-Rotor- 1D--Roor-Gauusians For MoDec-GS, while the background remains relatively stable, the player becomes heavily blurred and fast-moving objects (e.g., basketball, tennis racket) are often not reconstructed correctly, similar to prior deformable 4DGS approaches. ED-Rotor-Gaussianl retains these objects more reliably, but still exhibits noticeable blur and geometry instability of the player under fast motion. In contrast, SPIN-4DGS reconstructs both the moving objects and the player with sharp and temporally stable geometry, yielding visually cleaner and more consistent results than both baselines.
Qualitative results on compatibility with existing 4DGS baselines. Figure 8 presents qualita- tive results for the compatibility study in Table 4. Across scenes, method reconstructs stable backgrounds and more temporally consistent details, while the original baselines often blur or lose fast-moving objects. These results confirm that the proposed scheme integrates effectively with existing 4DGS approaches and potentially improves their reconstruction fidelity under large inter- frame displacements.
C DISCUSSIONS
Recent trends in 4DGS. Recent concurrent 4DGS methods (Dai al., 2025; Oh al., 2025; Lyu et al., 2025) have been introduced, often sharing similar architectural components but pursuing dif- ferent goals and design constraints than ours. 4DGV (Dai et al., 2025) focuses reducing model
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Dacieebal
Tennss
Inggle
Softball
Foothall
MoDec-GS
ED-Booor-Ganssaans
Figure 7: Visualization on dynamic sports scenes in the CMU Panoptic Sports dataset. We visualize the methods evaluated in Table including MoDec-GS and 1o0-Rotor-Gaussian These 4DGS baselines often exhibit geometry instability and fast-motion artifacts, whereas SPIN-4DGS preserves the object and player geometry sharply throughout the sequence.
Bloes
Iiggllo
Flwibelll
Resk-imo-4DUS
DEDGS
DaDGS
Figure 8: Visualizations on compatibility with existing 4DGS baselines. We visualize the results of compatibility ablation study in Table 4, where pre-trained positions from 4DGS and D3DGS are reused while attributes are retrained with SPIN-4DGS. Our method consistently produces clear and more stable reconstructions than the original baselines.
size for complex dynamic scenes by leveraging external 2D segmentation, thereby relying on exter- nal supervision. Hybrid 3D-4DGS (Oh et al., 2025) builds upon 4DGS and mitigates redundancy in static regions by converting Gaussians that barely change over time into 3D ones; however, dynamic Gaussians are still shared across multiple frames, leaving cross-frame interference unresolved for fast motions. SCas4D (Lyu et al., 2025), built on Dynamic3DGS, accelerates online 4D reconstruc- tion via cluster-wis wise shared transformations, but this design couples all Gaussians within cluster to a single motion model and makes the method sensitive to the initial K-means clustering. By contrast, SPIN-4DGS directly predicts frame-wise attributes from explicit spatiotemporal positions
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Qualitative comparison on the Neu3DV benchmark. We visualize representative results from two Neu3DV scenes (e.g., Cook Spinach and Cut Roasted Beef) reported in Table 8. 4DGS blurs the boundaries of moving objects (e.g., tongs and knife), whereas SPIN-4DGS achieves significantly cleaner and higher-fidelity reconstructions.
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Figure 10: Qualitative comparison on the MeetRoom benchmark. We visualize representative results from two MeetRoom scenes (e.g., Trimming and VR Headset) reported in Table The 4DGS exhibit noticeable background noise and often fail to reconstruct the foreground objects faithfully, whereas SPIN-4DGS achieves sharper object reconstruction with substantially cleaner backgrounds.
with an implicit decoder, avoiding cross-frame interference and enabling stable reconstruction of fast motions without requiring external supervision or cluster-based initialization.
Key differences from prior 4DGS. The key conceptual difference between SPIN-4DGS and prior 4DGS methods is how temporal appearance is parameterized. SPIN-4DGS rasterizes each frame from explicit spatiotemporal positions and predicts Gaussian attributes function of the spa- tiotemporal coordinates via fo t). This design keeps positions explicit, allows only light per- sample adjustments during training, and decouples attribute optimization across timesteps, so dif- ferent samples can receive different attributes without directly sharing a single attribute vector over time.
In contrast, standard explicit 4DGS (e.g., Realtime-4DGS (Yang et al., 2024a), 4D-Rotor- Gaussians (Duan al., 2024)) generate each frame by time-slicing 4D primitive, and deformable 4DGS (e.g., 4DGaussian (Wu et al., 2024), Grid4D (Xu et al., 2024)) transform canonical Gaus- sians over time; in both cases, multiple timesteps share the same underlying Gaussian attributes. As a result, single set of Gaussian attributes (or transforms) simultaneously influences multiple frames, and updates driven by one frame can easily degrade others under large inter-frame displace- ments, leading to temporal collapse of fast-moving objects. Our temporal parameterization breaks this coupling at the attribute level and instead places the temporal representation in fo rather than in pointwise deformation field. As shown in Table 1, this leads to more stable training under large inter- frame displacements and yields higher reconstruction quality (PSNR/SSIM) on fast-motion scenes.
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Moreover, several deformable 4DGS methods deliberately avoid time-varying color and opacity, as allowing these attributes to change over time often produces unstable or implausible surfaces in novel views and makes tracking difficult. By predicting color and opacity from spatiotempo- ral coordinates through fo while keeping the underlying Gaussian support stable, SPIN-4DGS can model genuinely time-varying appearance without sacrificing temporal stability, which is crucial for fast-moving objects with large inter-frame displacements.
Limitations. We empirically observe that method is most effective when a sufficiently dense set of spatiotemporal positions available. In large-scale outdoor or highly cluttered scenes with sparse initial positions, achieving high reconstruction quality may require longer refinement (den- sify/prune) schedules to allocate more Gaussians, thereby increasing the overall training cost. In addition, for small objects or regions with very few initial points, we empirically observe that even multiple refinement iterations struggle to generate or recover sufficient missing points.
LLM policy. LLMs were used only for editing (grammar and typographical errors) and did contribute idea generation, analysis, experimental design, or interpretation.
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Reviews:
[{"review_id": "YXaKriLqVS", "reviewer": "Reviewer_9M6m", "summary": "This paper addresses the failure of 4D Gaussian Splatting (4DGS) to reconstruct scenes with fast motion and large inter-frame displacements, where objects often blur or disappear. The authors propose SPIN-4DGS, a novel framework that decouples spatiotemporal position estimation from Gaussian attribute learning. The core contribution is a hybrid approach where explicit 4D spatiotemporal positions (x, y, z, t) are used as inputs to a lightweight implicit network (a 4D hash encoder and MLP decoders) that predicts all other Gaussian attributes (e.g., scale, rotation, color, opacity). This design avoids the attribute collapse seen in prior work and demonstrates state-of-the-art reconstruction fidelity on challenging dynamic sports datasets.", "questions": "* Q1:Inference Cost Analysis: Could the authors confirm that the ~2x reduction in FPS (vs. 4DGS) is due to the inference cost of the 4D Hash Encoder and MLP decoders required for every Gaussian at render time? If so, this is a critical aspect of the method's efficiency profile and warrants clarification.\n* Q2: Storage Claims: Given the data in Table 1, the storage benefit appears negligible. Would the authors consider reframing this contribution? The novelty appears to be in the hybrid representation enabling high-fidelity reconstruction, not in achieving superior compression.\n* Q3: Total Training Budget: Please provide a comparative analysis of the total wall-clock training time for SPIN-4DGS (including all stages) versus the primary baselines (e.g., 4DGS, D3DGS) for a single scene.\n* Q4: Robustness of Stage 1: The method's success seems dependent on the Stage 1 position estimator. How does SPIN-4DGS handle cases where the explicit estimator (4DGS) completely fails to initialize any points for a fast-moving object? Does the refinement step (Sec 2.2)  only densify/prune, or can it also create new Gaussians in unobserved regions?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "* problem definition and diagnosis: The paper correctly identifies a significant and open challenge for the 4DGS paradigm: robustly modeling high-frequency dynamics. The analysis of failure modes in prior art—distinguishing between deformable methods (canonical space initialization failure ) and explicit 4D parameterizations (attribute collapse due to cross-frame interference )—is insightful and provides a methodologically sound basis for the proposed solution.\n*  novelty of the implicit attribute network: The core idea of decoupling explicit positions from implicitly-learned attributes is novel. This hybrid representation allows the model to leverage the efficiency of explicit splatting while using the generalization power of an implicit network to maintain spatio-temporal consistency for attributes. This directly addresses the attribute collapse observed in prior explicit 4DGS methods .\n* State-of-the-Art reconstruction fidelity: The method achieves significant quantitative and qualitative improvements on the CMU Panoptic Sports dataset, a highly appropriate and challenging benchmark for this task. The gains over strong baselines, including those using external supervision (e.g., +1.83 dB PSNR over D3DGS on 'Basketball'), are substantial and clearly demonstrate the method's effectiveness in capturing fast-moving objects.", "weaknesses": "* Efficiency-Quality Trade-off: The claims regarding rendering efficiency  are not fully substantiated and appear to be a key limitation. Table 1 indicates a significant drop in rendering speed (104 FPS) compared to the explicit 4DGS baseline (197 FPS) and especially deformable methods. This is likely due to the computational overhead of querying the implicit network for all Gaussian attributes per-frame during rasterization, which is a non-trivial trade-off for the gains in fidelity. This trade-off should be discussed more explicitly.\n* Storage Footprint: The paper's claim of \"reducing storage overhead\"  appears overstated. The reported storage (1261MB) is only marginally better than the 4DGS baseline (1293MB). This suggests the bulk of the memory is consumed by the explicit spatiotemporal positions, and the implicit network for attributes does not offer a significant storage advantage in practice. The contribution lies in enabling reconstruction, not in compressing the representation.\n* Training Scalability and Cost: The method introduces a two-stage training process. The total training cost (Stage 1 position estimation  + Stage 2 refinement  + Stage 2 implicit network training) relative to end-to-end baselines is not clearly reported. This makes it difficult to assess the practical scalability and computational budget required to deploy this method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BVb4QHN7ny", "reviewer": "Reviewer_APBY", "summary": "This paper presents SPIN-4DGS,  a practical and well-engineered solution to 4D dynamic spatial reconstruction. This paper observes the defects of previous 4DGS related methods and establishes a method with hybrid explicit and implicit modeling. The proposed method collects the spatial-temporal positions from other 4DGS methods and predicts the other Gaussian attributes based on the positional information in a feed-forward paradigm. This formulation avoids the shared properties across timesteps and achieves higher performance on sports related datasets.", "questions": "The main concerns are elaborated in the weakness, with confusions on the method formulation, performance claim and the training protocols. \n\nIf the authors' rebuttal solves misunderstandings in the review, I am willing to further adjust my score.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 1, "presentation": 2, "contribution": 2, "strengths": "1. This paper is well-motived. Presenting highly dynamic areas with large motions has been a long-standing problem in 4D reconstruction. This paper analyzes the origin of this phenomenon and concludes this as the temporally shared features.\n2. Satisfying performance. The proposed method maintains high-fidelity reconstruction for large-motion 4D scenes, from both the quantitative results and visual effects.", "weaknesses": "1. Method formulation. The proposed pipeline tries to directly capture the spatio-temporal positions from previous 4DGS representations and build a feed-forward network to estimate the other properties. However, the position prior from other methods may introduce bias from individual methods, as different 4DGS methods show different specialties, making this design unstable and unrobust. Besides, this method trains a feed-forward network to estimate the Gaussian attributes to avoid temporally shared properties, which is a proxy of 'per-time 3DGS', i.e., the upper bound of this method is just naively maintaining a set of 3DGS for each timestep (which handles the large-motion areas best), and their method is merely trying to save these per-timestep 3DGS into a larger feed-forward network. In my opinion, this design is not of novelty or significance, and does not figures the core problem out. Besides, this method naively integrates the hash MLP and feed-forward attribute estimations, which is a similar pipeline with Instant Gaussian Stream (CVPR 25), and these techniques have been used in HAC (ECCV 24), 3DGStream (CVPR 24) and feed-forward reconstruction pipelines such as MVGaussian (ECCV 24), TranSplat (AAAI 25). \n2. Possible overclaim. This work claims in Line 104 to 106: 'our design preserves the rendering efficiency of prior 4DGS methods while improving storage and training stability, thereby enhancing the efficiency–quality balance required for practical deployment', which introduces confusions: Do we need to inference the feed-forward network multiple times before obtaining the final 4D result, or do we need to inference and store the estimated per-timestep Gaussian attributes in ahead? If the former applies, the method requires network inference before each rendering, thus the rendering speed is highly lagged. If the later applies, the method requires saving per-timestep Gaussian attributes, thus the storage overhead is huge. This leads to an overclaim of the method performance.\n2. Training dataset and generality. The proposed evaluation is implemented on the Panoptic dataset, while how the feed-forward network is trained is unclear. Is the training implemented on the same dataset? It is not clear whether this paradigm guarantees a correct evaluation. If the network is trained across all scenes in Panoptic dataset, will it obtain a better performance by per-scene per-training? Besides, it is wondered how this feed-forward network obtains generality as the training and evaluation datasets are of small size. It is also interesting to investigate its performance on other 4D reconstruction benchmark.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KiOATAQp3o", "reviewer": "Reviewer_B2ix", "summary": "The paper proposes a novel approach for dynamic scene reconstruction, with a particular focus on handling fast object motions. The proposed model, SPIN-4DGS, predicts Gaussian attributes directly from spatiotemporal positions using a lightweight network that learns shared representations across Gaussians. Unlike conventional methods that store attributes explicitly for each Gaussian, SPIN-4DGS encodes them implicitly within the network parameters, thereby significantly improving memory efficiency. Experimental results show that the proposed approach achieves substantially higher accuracy than existing methods, especially in scenes involving rapid motion.", "questions": "See weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- The paper is well written and easy to follow, clearly articulating its motivation and main contributions.\n- It introduces a lightweight yet effective framework for dynamic scene reconstruction that performs robustly in scenarios involving fast object motions.\n- The idea of predicting Gaussian attributes directly from spatiotemporal positions is novel and well-motivated, leading to more reliable attribute learning for fast-moving objects with large displacements.\n- The paper provides comprehensive ablation studies and analyses that effectively demonstrate the impact of the estimated spatiotemporal positions and the proposed attribute learning mechanism on overall performance.", "weaknesses": "- Experiments are conducted only on sequences from the Panoptic dataset, which limits the generalizability of the results. Additional evaluations on some other challenging benchmarks with complex motions such as D-NeRF, Neu3DV, MeetRoom, and DeskGames would strengthen the empirical validation.\n- The paper does not include comparisons with the recently proposed MoDec-GS model, which is a closely related approach and an important baseline for dynamic scene reconstruction.\n- The evaluation in Table 1 relies solely on distortion-based metrics (PSNR and SSIM) and does not report perceptual quality measures such as LPIPS, which are essential for a more comprehensive assessment.\n- Several recent related works including 4DGV [1], 3D-4DGS [2], and SCas4D [3] are missing from the related work discussion and could provide valuable context and comparison for positioning the proposed method.\n\n     [1] Dai et al., 4D Gaussian Videos with Motion Layering, ACM TOG 2025\n\n     [2] Oh et al., Hybrid 3D-4D Gaussian Splatting for Fast Dynamic Scene Representation, arXiv 2025\n\n     [3] Lyu et al., SCas4D: Structural Cascaded Optimization for Boosting Persistent 4D Novel View Synthesis, TMLR 2025\n\n- The authors did not discuss any limitation of the suggested approach? For instance, could the authors provide results or discussion on the model’s performance in static or near-static scenes, where inter-frame displacements are minimal?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "8bTQ5Q0I0z", "reviewer": "Reviewer_H2vU", "summary": "The paper presents SPIN-4DGS, a new 4D Gaussian Splatting (4DGS) method designed to handle scenes with fast-moving objects, which typically degrade reconstruction quality and cause motion blur or object disappearance. Instead of employing a time-varying, deformable formulation, SPIN-4DGS follows an explicit strategy and first constructs Gaussian sets independently per frame, then employs a lightweight neural network to refine latent features in a frame-wise manner, which are then fed into implicit decoder to predict Gaussian attributes. Experiments on the CMU Panoptic dataset, which includes sports sequences with fast motion (e.g., moving balls and players), demonstrate improved reconstruction quality over tested methods in terms of PSNR and SSIM.", "questions": "1. Could you elaborate on the key conceptual differences between SPIN-4DGS and other explicit 4DGS-based methods (e.g., 4DGS, 4D-Rotor-Gaussians)? Specifically, how does your per-frame refinement compare to time-slicing or deformable formulations in terms of accuracy and efficiency?\n2. Please include quantitative comparisons against 4D-Rotor-Gaussians (Duan et al., 2024) to provide a more complete empirical evaluation.\n3. To assess the generalizability of the proposed method, it would be valuable to add experiments on N3DV and D-NeRF datasets or discuss potential limitations when applied to more complex outdoor or cluttered environments.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The quantitative and qualitative results show clear improvements over existing dynamic Gaussian splatting methods, including 4DGS and others that rely on depth supervision or deformable modeling.\n- The paper offers thorough ablation studies, systematically analyzing the contributions of different components such as training iterations, refinement steps, and network design choices.\n- The proposed refinement module is modular and lightweight, making it a potential plug-and-play replacement for attribute optimization stages in existing 4DGS pipelines to enhance reconstruction performance in both PSNR and SSIM metrics.\n- The approach is conceptually simple yet effective, avoiding complex temporal modeling while still capturing inter-frame consistency through learned refinements.", "weaknesses": "- The paper briefly mentions other explicit 4DGS approaches, such as 4DGS (Yang et al., 2023) and 4D-Rotor-Gaussians (Duan et al., 2024), but lacks an in-depth comparison or discussion of their relative advantages and limitations. In particular, results for 4D-Rotor-Gaussians are missing from the comparison table, which limits the reader’s ability to judge empirical progress.\n- The method is evaluated solely on the CMU Panoptic dataset, which features controlled indoor scenes with limited background complexity. Evaluation on more diverse benchmarks (e.g., N3DV (Li et al., CVPR 2022) and D-NeRF (Pumarola et al., 2021)), commonly used in prior dynamic scene reconstruction works, would better establish the generalizability of the proposed approach.\n- The novelty claim could be articulated more clearly. The proposed frame-wise construction and refinement pipeline resembles modular post-processing strategies from prior 4DGS extensions. A more explicit positioning of the technical contribution relative to these prior methods would help.\n\nMinor Issues\n- Confirm whether cited preprints were published at major conferences (e.g., Yang et al., 2023 appeared at ICLR 2024).\n- Line #177: should read f<sub>θ</sub> instead of F<sub>θ</sub>.\n\n**References**\n- Li et al. Neural 3D Video Synthesis from Multi-View Video. CVPR 2022.\n- Pumarola et al. D-NeRF: Neural Radiance Fields for Dynamic Scenes. CVPR 2021.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)