Frequency-aware Dynamic Gaussian Splatting
Authors: Qiaowei Miao
JinSheng Quan
Kehan Li
Yichao Xu
Yi Yang
Yawei Luo
Venue: ICLR 2026 Poster (2026)
Keywords: 4D reconstruction
Gasussian Slpatting
Deformation network
Primary area: learning on graphs and other geometries & topologies
TL;DR: Frequency-differentiated Gaussian Kernel and Fourier Deformation Network for 4D reconstruction

Abstract: We present \textbf{Frequency-Aware Dynamic Gaussian Splatting (FAGS)}, a novel approach to mitigating motion blur in 4D reconstruction, particularly under novel viewpoints. This blur stems from a fundamental spectral conflict in existing methods, which struggle to \textbf{balance  high-frequency rendering details with high-frequency motion.}
FAGS addresses this challenge with two key innovations. First, we introduce a frequency-differentiated Gaussian kernel that refines the alpha-blending process of 3D Gaussian Splatting. By adaptively classifying Gaussians into two types—a slowly varying kernel for smooth, low-frequency regions and a sharp-transitioning kernel for high-frequency boundaries—our method explicitly separates representation responsibilities, preserving fine details without sacrificing continuity.
Second, we propose a Fourier-Deformation Network that enhances motion expressiveness. This network employs high-frequency Fourier embeddings to capture diverse motion patterns by learning amplitudes across frequency components. To further improve accuracy, we integrate a frequency-aware gate in fusion module, which predicts and regulates the relative deformation of each Gaussian.
Extensive experiments on both synthetic and real-world 4D benchmarks demonstrate that FAGS significantly reduces motion blur and enhances structural details, achieving state-of-the-art performance.

Published as a conference paper at ICLR 2026
FREQUENCY-AWARE DYNAMIC GAUSSIAN SPLATTING
Qiaowei Miao, Jinsheng Quan; Kehan Li, Yichao Xu, Yi Yang, Yawei Luo Zhejiang University
ABSTRACT
We present Frequency-Aware Dynamic Gaussian Splatting (FAGS), a novel approach to mitigating motion blur in 4D reconstruction, particularly under novel viewpoints. This blur stems from a fundamental spectral conflict in existing methods, which struggle to balance high-frequency rendering details with high- frequency motion. FAGS addresses this challenge with two key innovations. First, we introduce blending process of 3D Gaussian Splatting. By adaptively classifying Gaussians into two types-a a slowly varying kernel for smooth, low-frequency regions and tharp-transitioning kernel for high-frequeng boundaries- our method explicitly separates representation responsibilities, preserving fine details without sacrificing continuity. Second, we propose a Fourier-Deformatioo Network that enhances motion expressiveness. This network employs high- high-frequency Fourier embed- dings to capture diverse motion patterns by learning amplitudes across frequency components. To further improve accuracy, we integrate a frequency-aware gate in fusion module, which predicts and regulates the relative deformation of each Gaussian. Extensive experiments on both synthetic and real-world 4D benchmarks demonstrate that FAGS significantly reduces motion blur and enhances structural details, achieving state-of-the-arr performance.
segguuccy--ifffrenttttee Gaussian kernel that refines the alpha-
INTRODUCTION
Recent advances in deformation--fell-driiee 3D Gaussian Splatting (3DGS) have achieved impres-
sive results in 4D reconstruction Yang et al. (202);; Wu et al. (2024a); Zhou et al.
(024): Huang
al.
2024); Lin al. (2024); et al. (2024); ; Xie al. (2024): Kratimenos al.
2023); You &
Hou 2024) Lu et al. (204)); Luiten et al. (023) Guo et al. (2024). Despite this progress, dynamic
reconstructions often suffer from pronounced motion blur especially under novel viewpoints. These
existing approaches attempt to alleviate this issue by refining deformation fields to better align
dynamic content across frames. However, a core limitation lies in balancing high- tigh-frequency rendering details and high-frequency motion.
We analyze the balancing problem between Gaussians and Deformation Network. As illustrated in Fig. I(a), vanilla 3DGS adopts a fixed opacity profile for each Gaussian-opaque at the center and gradually transparent toward the boundary. While this design works well for static scenes by relying overlapping Gaussians, it severely limits expressiveness in dynamic settings. The fixed profile forces the deformation network to handle two contradictory tasks simultaneously: on one hand, must orchestrate dense Gaussian stacking recover high-frequency appearance individual time steps; on the other hand, it must drive these Gaussians coherently across multiple frames to model high-frequency motion without causing scattering. This dual burden often biases the network toward uniform low- www-freuency motion as a compromise, which ultimately results in severe motion blur under novel views. As shown in Fig. 1(b), a more effective solution to enhance Gaussian expressiveness for high-free frequency details and to empower the deformation network with frequency- aware flexibility, thereby separating the responsibilities of representation and motion modeling.
In this work, we tackle this problem from frequency perspective, introducing Frequency-Aware Dynamic Gaussian Splatting (FAGS) model. Our approach explicitly decouples high-frequency detail representation from high-freynency motion modeling through two key components. First, the Gaussian Kernel employs learnable alpha modulation function that adaptively adjusts each Gaussian's 's projection. This allows Gaussians to specialize as either (a) sharp fiquenryy kernels for detail boundaries or (b) smooth low-frequency kernels for uniform regions,
'These authors contributed equally to this work.
1 Cooresponning author.

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Published as a conference paper at ICLR 2026
Baseline
Baseline
(a) Baseline
(b) Ours
Low nww-freqenccy
Original
Guussian Kernel
Gaussian
High-frsqueccy
Kernel
Low-frqquency
Low-frequency
Deformation
Defommation
High-frequeee frequency Deformation
Ours
Ours
High-fieqeency details and high-frequenne motion
Analysis of figu-nrry details and motion. (a) Baseline: Standard Gaussian kernels require dense overlapping to capture high-fite freh-freuuecyy details, which complicates deformation control and biases the network toward smooth, low-frequency trajectories, resulting in motion blur. (b) Our method: Gaussians in high- and low-frequency regions are differentiated, enabling the deformation network to capture high-frequency motion on top of global low-frequency deformations, allowing each Gaussian to follow its own fine-grained dynamics.
Figure I:
thereby reducing reliance on dense Gaussian stacking. Second, the models motion trajectories as a superposition of periodic movements multiple frequencies. By learning the amplitude distribution of high- and low-frequency components, it enables precise motion coomaaaion-caturrii rapid, high-freque fegefrreyyncc displacements over short intervals while maintaining stable, lowffreqyyncy trends globally. Our main contributions are follows:
Network
We identify motion blur in 4D reconstruction as arising from fundamental spectral conflict between balancing fighffreqeeccy rendering details and high-frequency motion.
We propose the Brruuecy--Diffrenntian Gaussian Kernel, which uses adaptive alpha modulation to allow Gaussians to specialize as high- or low-frequency kernels, separating the modeling of high-frequency details from smooth low- wwwfrreueeccy regions.
We design the Fourier-Deformation Network, incorporating high-frequency Fourier fea- tures and a frequency-avee aware gate to simultaneously capture high-frequency local deforma- tions while suppressing unnecessary motion in low-frequency points.
Extensive experiments on synthetic and real-world 4D benchmarks show that FAGS effec- tively reduces motion blur and sharpens structural details.
RELATED WORKS
Dynamic Neural Radiance Fields. Neural Radiance Fields (NeRF) have emerged as a powerful paradigm for representing scenes continuous volumetric functions. Early extensions to dynamic settings aimed to reconstruct 4D scenes. Neural 3D Video Li al. (0022) for example, introduces temporal latent variables combined with hierarchical training and importance sampling, achieving scalable performance and establishing DyNeRF as a benchmark for dynamic NeRF, Another promi- nent line of work leverages deformation fields to extend NeRF into the temporal domain, in Nerfies Park et al. aa) and D-NeRF Pumarola et al. (202T). Nerfies decomposes 4D space into a static NeRF template with time-dependent deformation fields, while D-NeRF directly predicts spatial displacements over time. [L al. (202T) further encode both geometry and motion by training a network to learn scene flow, thereby capturing spatial structure alongside temporal dynamics.
Dynamic Gaussian Splatting. Recent research extends static 3D Gaussian Splatting (3DGS) into the 4D domain Yang et al. (2024); Wu al. (2024a); Zhou al. (0044) ; Huang al. 2024):
Lin et al. (2024) Li et al. 2024); Miao et al. (2025b 2024 2025a): Quan et al. (225)), enabling efficient modeling of object motion and scene dynamics. By combining anisotropic Gaussians with
deformation fields, these methods achieve high- rendering with real-time efficiency Wu et al.
(2024b). Existing approaches fall into two categories: iterative and refoormation-basel Iterative methods update Gaussian parameters frame by frame, such as D-3DGS Luiten et al. (02.3) which propagates Gaussians across frames while enforcing temporal coherence. While conceptually simple, they often struggle with occlusions and unseen regions, and usually require multi-camera setups. In contrast, deformation boode methods adopt a shared canonical representation and use deformation fields to predict temporal offsets, avoiding per-frame optimization and improving scalability. For example, Yang et al. (2024) learn spatial and temporal adjustments via an MLP queried by 4D coordinates, while Wu et al. (0024a) integrate spatio-temporal decoder-decoder for efficient,
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Published as a conference paper at ICLR 2026
high-quality modeling. These approaches generally more scalable and robust, though they depend heavily on accurate deformation modeling.
Despite these advances, prior work mainly focuses refining deformation ficlds canonical representations while overlooking the spectral characteristics of motion. In particular, balancing high-frequency motion with high-frequency image detail remains unresolved, often leading motion blur in novel views. Our work addresses this gap by introducing a frequency-aware formulation that explicitly disentangles these spectral demands within the Gaussian representation.
METHODOL.OGY
3.1 PRELIMINARIES
3D Gaussian Splatting. 3D Gaussian Splatting Kerbl et al. (2023) (3DGS) represents a scene as of anisotropic 3D Gaussian primitives parameterized by position μ R rotation R. scaling S, spherical harmonic coefficients Cşи for view-dependent color, and opacity o. The covariance defined Σ RSS "ESTTRR R" ensure positive semi-defmiteness. Given a camera view, each Gaussian is projected to the image plane with center y220 and covariance y2D and the final pixel
color is rendered via alpha blending:
C(p) Σ C,a4 II
az);
a, o, exp
(I)
j=1
where N denotes the number of Gaussians overlapping pixel This formulation enables high-quality, differentiable rendering suitable for optimization.
Deformation Network. Deformation networks Wu et al. 2024a Xu et al. (2024) model temporal evolution of Gaussians in dynamic scenes. Specifically, given a Gaussian's 's position x and timestamp f, an MLP predicts residual updates (A,, AR.Ast to its position, rotation, and scaling. The deformed Gaussian (ar + A,, + AR. + As, CSH,O) o) is then rasterized using Eq. I This framework maintains shared canonical representation and improves temporal coherence compared to per- per-frame optimization. However, since deformation primarily modifies geometry while alpha blending handles color composition, it struggles to represent high-frequency motion and sharp appearance changes, often leading to motion blur, especially near object boundaries or during rapid deformations.
3.2
GAUSSIAN KERNEL
The limited expressiveness of individual Gaussians often forces the deformation network rely on overlapping kernels, biasing deformation fields toward real motion. To address this, we propose the Frequency-Diffen -iffferentiated Gaussian Kernel (FDGK), which endows each Gaussian with adaptive alpha modulation function. This enables specialization into high-frequency Gaussians for complex textures and oow-freuueccy Gaussians for smooth regions, reducing overlap and stabilizing defor- mation optimization. We realize this extension of Gaussian splatting through three straightforward modifications, detailed below.
Recalling Eq. decay is primarily governed by the subsequent power operation g. making it sensitive to numerical fluctuations. We generalize the computation as
ag = m))((o)(()))0009)) ( = rg+ where = exp (p- 2 (E))) 11
(2)
Here, the slope r modulates a's smoothness (r + 1) versus sharpness (r + oc), effectively generating high- and frequeeuy Gaussians, with a standard Gaussian corresponding I and b = 0. While DRK Huang et al. (2025) also adjusts r to enhance expressiveness, the mapping boundaries are implicitly determined by r, so Gaussians sharing the same slope inherit identical differentiated regions. This coupling constrains the separation between high- and low- frequency Gaussians. In contrast, FDGK introduces a learnable boundary parameter 3 for each Gaussian, dynamically controlling its differentiation region independently of thereby enabling each Gaussian to adapt its frequency characteristics and differentiation span and substantially improving representational flexibility. We provide more detailed results to illustrate the effects of (3 in Appn.
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Published as a conference paper at ICLR 2026
First, to simplify the analysis, partition the original mapping range into three intervals and constrain the central interval to pass through (0.5, 0.5). This construction enables us to focus on the middle region for Gaussian differentiation. Building on this foundation, introduce the adaptive alpha modulation function (g)):
0.5+A-0.53-A0 0.5+X-B
9,
g E [0, pi),
Pi max 0.5+A-8 00,
(()))
(0.5 + +1g (0.25 0.5X),
prlp E (Pr, 1].
1+2A
(3)
Pr min
0.5+2+8
1).
0.5+A-053-M6 A8
(g 1) +1,,
142X
0.5+2-B
Here, Pt and Pr denote the left and right endpoints of the central mapping in- terval, defining the mid- dle range, as illustrated in Fig. 2 We introduce controlling parameter À E [0, 1] to adjust the slope of the mapping within this interval. Specifically, the slope and offset are defined r 0.5 À and b 0.25 - 0.5A, with À 0.5 serving as the demar- cation to differentiate high- and now-frequency Gaus- sians. Fig. 2 visualizes
((g)
(G)
(())
0.5 A
1 0.5, or
< <
β =
1- B 0.5
01-B B 0.5
0 01-8 B 0.5
Iligh-frequency Gaussian
cegquuney-differeniiin based on
Low-frequency
optimizing and
Gaussian
how varying affects 3D Gaussians: when X 0.5, the Gaussians correspond to standard 3D Gaussians with a gradual transparency gra- dient from the projection center outward; for À < 0.5,
Figure 2: Adaptive alpha modulation function of the frequency- differentiated Gaussian kernel. The piecewise activation function (g) regulates the a values of Gaussian projections, with its slope modulated by the learnable parameters À and f3. By optimizing these parameters, the activation becomes differentiated, enabling Gaussians to specialize into low-frequency and high-frequency representations.
(g)) varies slowly with g. producing smooth, uniform transparency typical of low- cow-freuueccy Gaus- sians; for X > 0.5, (g)) changes rapidly, yielding sharp transitions and distinct boundaries character- istic of freeufryy Gaussians.
To further control the differentiated region, we introduce a boundary parameter 3. Let gu denote the point where (gu) 0. The distance dg. between Do and 0.5 defines the allowable span of the frequency-diiffrrenttaee region. We scale this distance by /3 to determine the left and right endpoints as pt = 0.5 Bdgo and p. = 0.5 + 3d as formulated in Eq. Optimizing À and 33 allows each Gaussian to adaptively regulate its frequency and span.
The values of and / for each Gaussian can be directly applied in the rasterization process and gradient backpropagation. As continuous and differentiable piecewise function spanning the full range of g E [0, 1), (g(g) preserves the opacity representation of Gaussians. The X and 3 can be optimized by backpropagation:
(0.5+ 9,
82 8
g [0, pt) E Prt,Pr]
0.25 X2 (0.5+ 115+ 9, 0,
g E (0,
(v(())
0.5,
E (pt.Pr)
0x
03
(0.6+A-J7) 2Jz 1);
8a
g (pr.
0.25- (0.5+>
ーーー (g 1),
g E (pr, 1]
(4)
By jointly optimizing À and the boundary parameter 3. the activation function (b(g) is adaptively learned, differentiating Gaussians into high- and low-frequency types while stabilizing a values within controlled range, thereby ensuring robust and stable training of the deformation network.
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Published as a conference paper at ICLR 2026
Parameter
High-frequency Goussians
Feature
Dot product
Deformation
Canonical Gaussians
Low- wow-Irequency Gaussians
Rg. ,s π
High-frequency feature
Multi-head Decoder
sinteryze cos (1777
High lowy frequency
MLP+ ReLU
y,
festure
Hoshocoding
y,t
Frequeney- aware Giate
M-.--
X,
y,2,t
Amplitude
MLP:ReLU
x,
Low-frequency feature
Figure 3: Overview of Frequency-Aware Gaussian Splatting. Top: Gaussians are initialized in canonical state and progressively differentiate into low- and high-frequency types during optimization, fitting low-frequency smooth regions and high-frequency details, respectively. Bottom: Coordinates J, y: and time t are hash-encoded to generate low-frequency features, which are then fused with high-frequency Fourier embeddings form unified high-low frequency representation. This representation is processed by a multi-head decoder to predict deformations, with frequency-avee gate modulating motion strength. Finally, rendering Gaussians to produce the final outputs.
3.3
FOURIER-DEFORNMEE DEFORMATION NETWORK
Existing deformation network Xu et al. 2024): Yang al. (2024) Wu al. (202aa) Cao & Johnson (2023) typically apply hash encoding to 4D coordinates (z, y, 2, t) and use MLP to model the motion of Gaussian points. While hash encoding preserves strong spatiotemporal continuity and maintains geometric consistency in the reconstruction, these methods remain limited in modeling rapid temporal motion. This inherent trade-off between capturing high-frequency spatial details and high-frequency motion often leads to motion blur.
To address this, propose the frequency temporal variations for each Gaussian. Directly optimizing trajectories over all time steps is computationally prohibitive for scenes with over 100k Gaussians. Instead, encode high- frequency motion for each point, integrate it with low-frequency spatial features, and leverage the resulting high-low frequency feature to efficiently predict Gaussian deformations.
Network, which explicitly models high-
Specifically, we decompose the 4D coordinate (æ., y, 2, f) into four 3D hash encodings: (x. y. 2). (x. y. t), (y, 2, t), and (Ir, 2, t). capturing different spatial-tempont interactions. These embeddings produce spatial feature Sspa and temporal feature fue via MLP:
Sspa MLP MLP((Hazz y, =)), fuem MT. (coneat Hy (x, y, t), Haze 2, 1), Hyze(a, 2,
(5)
High-frequency Fourier Embedding. We formulate each Gaussian's 's motion as segment of an infinitely repeating cycle, allowing its trajectory be decomposed through Fourier analysis into paplitude-frequence components. To better capture high-frequency temporal variations, we design dedicated high-frequency Fourier embedding for each Gaussian:
Froe [wi sin (), Wi cos(T)yt).
Wm sin tm) Wm t)
(6)
where 7/ m = g. D denotes the dimension of fapa. This temporal encoding adopts denser sampling designed to effectively span multiple temporal scales. The amplitude vector [wi,... Wm] specific to each Gaussian and time-invariant, predicted from its spatial feature Sapa via an MLP:
34
[w....., Wm MLPP(spaa.
The resulting Fourier feature fite captures periodic high- figh-freeuency motion, which can be aligned or scaled to complement wow-frequeccy temporal embeddings ftem- By fusing fite with low-frequency features, the deformation network achieves precise control over both slow and rapid motions, enabling accurate and stable reconstruction of dynamic scenes.
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Published as a conference paper at ICLR 2026
Hell Warrior
Hook
Jumping Jacks
4D-GS
DeformGS
SC-GS
Grid4D
Grid4D DRK
Ours
GT
Figure 4: Qualitative results on the synthetic D-Nerf dataset.
Frequency-aware Gate. A deformation network inherently predicts updates for all Gaussians, which may inadvertently modify points that should remain static. To selectively suppress uwwffreqeency motion while promoting genuine high-frequee freuuerryeencc deformations, that estimates each Gaussian's relative motion state at each time step, Le., whether the point is more dynamic more static compared other Gaussians. The high- tegh-freuueccy Fourier feature ftie is fused with the temporal embedding frem (i.e., the low- sow-freuynccy features), and the resulting representation used predict the deformation parameters via the deformation network Do:
introduce trequency-awand gate
n¹ = nR + T/Tn, S' S
=
Do(frp) in, R T, Ar. As). (8)
where Rg and T₂ denote the predicted rotation and translation, and is the frequency-awarr gate score that modulates the deformation strength at time t. By adaptively weighting the updates, the gate assigns larger values to Gaussians undergoing high-frequency motion, allowing rapid changes in their attributes, while near-static, low-frequency Gaussians receive smaller 7) values, effectively suppressing undesired motion and stabilizing the optimization process.
3.4 OPTIMIZATION
Fourier Frequency Loss. Although the Deformation Network are designed capture high-frequency details and motion, their potential cannot be fully realized without frequency-aware optimization objective. To this end, we introduce a Fourier frequency loss. Specifically, for a rendered image I' and its target image I, we use Fast Fourier Transform (FFT) to obtain the corresponding amplitude spectra lmmp and Lamp- The Fourier frequency loss is then defined as:
Gaussian kernels and the Fourier-
Lio 1/mmp Lampll
Since the phase primarily encodes structural information and the rendered image I' shares highly similar geometry with the target image 7, the differences in phase are minimal; therefore, we only consider discrepancies in amplitude. We integrate Lire with the reconstruction losses used in Grid4D Xu et al. (2024). yielding the final training objective:
CoLL + 02) + orLr + Thrffte
(10)
where de, dr, and The are hyperparameters balancing the contributions of each term. Here, C, denotes the smooth regularization loss used in Grid4D. Following Xu et al. (2024), we keep and consistent with their settings and fix them during training. Similar to prior works Yang et al. (004); Wu et al. (2024),, we initialize with static canonical Gaussians the beginning of training to ensure stable convergence. For Gaussians initialized from SIM Schhoberrgrrr & Frahm (016)). we shorten the static initialization stage for improved efficiency. Moreover, adopt the adaptive density controller and opacity resetting mechanism introduced in Gaussian Splatting Kerbl et al. (2023). The overall pipeline of our FAGS is illustrated in Fig.

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Published as a conference paper at ICLR 2026
Table I: Quantitative results on D-NeRF dataset.
Best
and second- best results are highlighted.
Bouncing Balls SSIM
Hell Warrior
Hook
Jumping Jacks
Model
PSNR
L.ISS.
PSNR
SSIM
[PIPS.]
PSNR
SSIM f
LPIPS
PSNR
SSIM 1
LPIPS]
Tensor-4D"
0.044
31.26
0.925
0.074
0.943
24.20
HoxPlane"
40
0.992
0.031
24.30
0.944
0.073
28.26
0.955
0.052
31.74
0.974
0.036
Voxe
40.28
0.991
0.039
28.30
0.966
0.054
31.86
0.972
0.044
34.77
0,987
0.053
DeformGS
41.62
0.995
0.008
41.09
0.986
0.027
37.06
0.986
0.016
37.06
0,986
0.016
4D-GS
40.77
0.994
0.016
35.37
0.985
0.020
32.90
0.977
0.027
35.37
0,985
0.020
SC-GS
0.022
0.969
0.991
39.80
0.013
Grd4D
42.36
0.995
0.007
42.85
0.990
0.016
38.89
0,990
0.009
39.36
0,993
0.008
GridDDDDRK
40.82
0.995
0.011
41.92
0.989
0.019
36.07
0.983
0.021
37.57
0.991
0.011
0.007
0.991
40.18
0.992
40.52
Model
PSNR
SSIM
Mutant
LPPPS.
PSNR
Standup
SSIM
I.PIS.]
PSNR
SSIM
Trex
[PIPS
PSNR
Average
SSIM
PIPSS
Tensor-4D"
29.11
0.945
0.060
30.56
0.958
0.036
31.25
0.964
0.048
28.50
0.946
0.056
HexPlane"
33.66
0.982
0.028
34.12
0.983
0.019
31.01
0.976
0.028
31.92
0,972
0.038
ToNeuVox.B
0.977
0.030
0.986
32.87
0.978
0.031
DeformGS
42.13
0.994
0.007
43.70
0.994
0.009
37.78
0.993
0,010
40.07
0.991
0.013
4D-GS
37.71
0.988
0.016
37.88
0.990
0.014
34.14
0.985
0.022
36.30
0,986
0.019
SC-GS
42.55
0.995
0.011
46.16
0.997
0.008
39.53
0.994
0.010
41.59
0,394
0.015
Grid4D
43.94
0.996
0.004
46.51
0.997
0.004
40.01
0.994
0,008
41.99
0.993
0,008
GridDD+DRK
0.019
0.992
Ours
44.16
0.997
0.004
47.30
0.997
0.003
40.59
0.995
0.008
42.76
0.995
0.007
Table 2: Quantitative results on Neu3D dataset. The color marks the best and the second best
Coffee Martini
Cook Spinach
Cut Roasted Beef
Model
1
SSIM f
LPIPS.
PSNR
SSIM
LPIPS.
SSIM
LPIPS.)
4D-GS
27.00
0,885
0.189
31.80
0.942
0.159
32.06
0.939
0.167
Grid4D
27.90
0.893
0.179
32.38
0,947
0.144
33.20
0.947
0.157
Ours
0.899
0.179
32.79
0.967
0.145
33.20
0.950
Model
Flame Steak
Sear Steak
Average
PSNR
SSIM 1
LPIPS
PSNR
SSIM
LPIPS.
PSNR
SSIM
LPIPS
4D-GS
30.23
0.945
0.147
32.18
0.958
0.144
30.65
0.934
0.161
Grid4D
32.07
0.942
0.136
32.61
0.955
0.132
31.63
0.937
0,149
Ours
32.95
0.947
0.132
33.58
0.968
0.125
32.18
0.946
0.146
4D-GS
Grid4D
Ours
GT
Figure 5: Qualitative results on the real-world Neu3D dataset.
4 EXPERIMENTS
Datasets, We evaluate FAGS on D-NeRF D-NeRF Pumarola et al. (202I), HyperNeRF Park et al. (2021b), and
Neu3D Li ct al. 2022p. D-NeRF synthetic monocular dataset with accurate time-varying poses.
while Hy and Neu3D contain real-world captures with poses estimated via COLMAP Fisher 2021 Rendering resolutions are 800 x 800, 536 x 960, and 1,352 x 1,024, respectively.
et al.
Baselines.
We compare against of-te--ffthe--eee 4D reconstruction methods Wu et al.
(002aa) ; Yang
al. (202)); Huang et al. (2024); Xu et al. (2024); Fang al. (2022); Shao et al. (2023); Co
Johnson (2023). NeRF-based approaches include Tensor-4D Shao et al. 2023) and TiNeu Vox Fang
et al. (2022) (plane- and grid-based explicit representations). (Gaussian-base models include 4D- GS Wu al. (2024a), DeformGS Yang et al. (2024), and SC-GS Huang et al. (2024). with the latter extending DeformGS via sparse control points. Grid4D Xu et al. (024g) improves deformation control using a 4D decomposed hash encoding with attention.
Implementation Details. Experiments are performed on an NVIDIA 3090 GPU. We train using Adam with a learning rate of 0.002 for À and 3. FAGS is implemented in CUDA/C++ and integrates with Grid4D Xu et al. (224) as the deformation backbone. We set ore = 0.3 as the default hyperparameter. Other settings that follow Xu et 2024'ss work.

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Published as a conference paper at ICLR 2026
Table 3: Quantitative results on wollw HyperNeRE dataset, including rig subsets (Rig) and the 6 interpolation subsets (Interpolation) The color marks the best and the second best
Interpolation (6 scenes)
Rig scenes)
Model
PSNR
SSIM 1 LPIPS &
MS-SSIMP
PSNR
SSIM
LPIPS L
MS MS-SSIMf
Vox
27.11
0,923
24.21
0.836
4D-GS
27.58
0.794
0.315
0.910
24.64
0.665
0.363
0.654
Grid4D
28.59
0.844
0.199
0.993
25.24
0.685
0.319
0.818
Ours
29.02
0.850
0.195
0.994
25.63
0.719
0.269
0.885
4D-GS
Grid4D
Ours
GT
Figure 6: Qualitative results on the real-world HyperNeRF dataset.
4.1 EXPERIMENTAL RESULTS
We evaluated FAGS against state-of-the-an methods on the synthetic D-NeRF dataset and real- world HyperNeRF and Neu3D datasets. Quantitative metrics include PSNR Fardo SSIM Wang et al. (2003), LPIPS Zhang et al.] (2018), and MS-SSIM Wang et al. (2003) Our Gaussian Kernel and Fourier Deformation Network improve rendering of fine textures and achieve significant quantitative gains (Tab. D Tab. 2 Tab, B Across datasets, our method consistently improves visual fidelity. On D-NeRF (Fig. 4. object boundaries are better preserved, e.g., feet in Hook and hand details in JumpingJacks. In Neu3D (Fig. 5 baselines with non-differemtiated Gaussians often misadjust displacements, causing blurred static backgrounds and loss of high-frequency motion details. In HyperNeRF (Fig. b improper handling of multiple Gaussians leads to artifacts such as disappearing knife tips. By contrast, our FAGS effectively address these issues, demonstrating superior control over both spatial structure and motion details.
(0016).
Trequency-Differnttinn
4.2 ABLATION STUDIES
We present the ablation results of each component in Tab. 4 and Fig. 3 (a) Gaussian Kernels (FDGK). By decoupling Gaussians into high- and low-frequency categories, FDGK reduces redundant stacking and alleviates the deformation network's burden. This specializa- tion enhances the reconstruction of
high-frequency details, evidenced by sharper hand and foot structures in Fig. g Compared to standard 3DGS, FDGK provides greater flexibility and efficiency in representing frequency-aware scene components. (b) High-Frequency Fourier Embed- ding (HFE). HFE injects temporally varying high-frequency signals into each Gaussian, preventing uniformly smooth owwffreueeccy motion. This enables better separation and preservation of fine details, particularly in articulated regions such as fingers and leg joints. (c) Frequency-awand Gate (FG). FG adaptively regulates the deformation strength of each Gaussian based its frequency-aware features. Low- Low-frequenc Gaussians are suppressed to remain stable, while genuine high-frequenc, motions are amplified, improving the network's control over dynamic regions. Unlike hard clamping methods that enforce static bounds, we let 1) smoothly vary, allowing the deformation network to adaptively modulate each Gaussian's 's dynamic behavior at every timestep.
(d) Fourier Frequency Loss (Cire). This loss explicitly regularizes the spectral domain by emphasizing hard-to-optimize high- high-frequency regions. It guides both Gaussians and the deformation network toward precise local fitting, yielding reconstructions closer ground truth with enhanced detail fidelity.
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Table 4: Quantitative ablation results on the synthetic D-NeRF dataset.
Model
Full
w/o FDGK
w/o HFE
w/o FG
w/o Live
w/o (FG + Lit))
w/o FDGK.A
w/o FDGK..3
PSNR
42.76
42.11
42.38
42.70
42.50
42.43
42.30
42.26
SSIM
0.995
0.993
0.994
0.994
0.994
0.994
0.994
0.994
LPIPS
0.007
0.009
0.009
0.008
0.008
0.008
0.008
0.008
w/o HFE Figure 8: Ablation study visualization results D-Nerf dataset.
Ours
w/o Live
GT
Ours
w/o FDGK
w/o PG
4.3 MORE DISCUSSION
High-Low Frequency Gaussians (X's distribution). initialization, all Gaussian kernels are assigned X = 0.5, 3 0.5, which is equivalent to the standard 3D Gaussian kernel. After about 5,000 training steps, the Gaussians clearly bifurcate into two distinct groups corresponding to low- and high-frequency components, with ratio of roughly 3:2, as shown in Fig. [a. More importantly, once this differentiation emerges, the two groups remain stable throughout subsequent training. rreguency-differentttted consistent separation. For more details, please refer to the Appn.
indicating that the frequency differentiated Gaussian kernel can both converge rapidly and maintain
Boundary (3's distribution). The introduced boundary parameter 3 exhibits significant distri- butional shifts in the early stages of training, as shown in Fig. b)). It suggests that the model actively leverages 3 rapidly adapt the differentiated region for better fitting. This highlights the crucial role of 33 in enriching the expressiveness of frequency-differential Gaussian kernel.
Frequency-Base -Based Motion Differen- tiation (Gate's distribution). Dur- ing motion learning, we observe that Gaussians are not simply clas-
Param, Distribution
Param, P% Distribution
Gate's Distribution
sified into either completely static or fully dynamic states, as shown
10000
36000
10000
24000
24000
25000
in Fig. Mc). Instead, guided by the Fourier- Deformatinoo Network, each Gaussian is adaptively assigned a rel- ative motion state according to its fre- quency characteristics. A large pro- portion of Gaussians concentrate in the low-frequency regime, while a smaller subset exhibits high-frequency behavior, demonstrating the network's ability capture motion at multiple scales and achieve frequency-based differentiation of Gaussian dynamics.
42003
40000
30000
50200
0.0
3.0
00
0.2
(4)
(b)
(6)
Figure 7: Distributions of reequency-differentiinn parameters
X, B, and the frequency-aware gate across training steps.
FDGK DRK. To thoroughly evaluate reconstruction performance, we integrate the DRK Huang et al. (2025) with the Grid4D Baa44DXueer et al. (2024) deformation network and test on the D-NeRF dataset. Models are trained using the default DRK parameters, and results are shown in Fig. ! Compared to the original Grid4D, the more flexible DRK kernels do not consistently improve reconstruction quality and often degrade in several scenes. We attribute this to the excessive flexibility of DRK, which makes it difficult for the deformation network to control Gaussian deformations across multiple time steps. In contrast, FDGK undergoes clear kernel differentiation carly in training and exhibits stable behavior throughout the optimization process (Fig. which in turn enables more reliable control of temporal deformations.
Reconstruction under Motion Blur. We evaluate FAGS under severe motion blur using the real- world motion blur dataset from BARD-GS Lu et all (025). and directly compare its performance with BARD-GS. In this dataset, the images synthetically blurred for reconstruction, while evaluation

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Published as a conference paper at ICLR 2026
3DGS
DRK
Our FDGK
Figure 9: Qualitative results on the Mip360-NeRF 3D dataset.
BARD-GS
Ours
GT
Figure 10: Qualitative comparisons on the motion-blur dataset.
performed against the sharp ground-truth frames. Quantitative results reported in Tab. and qualitative comparisons are shown Fig. TO Despite the challenging blur and without deblurring pre-processing with MPRNet Mchri et al. (202T)). FAGS remains competitive, often producing substantially sharper and more faithful reconstructions. Applying a pre-processing deblurring step with MPRNet can further improve the results, yielding performance surpassing BARD-GS.
Quantifying High-frequency Motion. In Fig. we show the temporal power spectrum of Gaussian' trajectories in the "Jumpingjackss" sequence. The temporal power spectrum shows that FAGS concentrates substantially more Gaussians in the high-frequency band than Grid4D. This indicates that the FDN ac-
tively induces rapid deforma- tions on many Gaussians, effec- tively capturing high-frequency motion. Furthermore, we pro- vide heatmaps of the temporal second-order finite-difference en- ergy in Fig. 15 Compared to Grid4D, FAGS exhibits stronger contrast between bright and dark regions, indicating that the FDN accurately captures the differ- ences in deformations across consecutive time steps, effectively avoiding overly smooth, global motion. These quantitative results demonstrate that FAGS can precisely model and preserve high- frequency motions, which are essential for accurate dynamic reconstruction.
High
Hightruuu
2003
2130
2009
0.09
675
Log hoghhhhheu Pnorg IPT)
Log Mich-ruuanyy Erango 9911
Grid4D
Ours
Figure 11: Temporal Motion Power Spectrum Gaussians.
5 CONCLUSION
In this paper, we present Frequency-Aware Dynamic Gaussian Splatting (FAGS). principled approach to mitigating motion blur in 4D reconstruction. The blur arises from a spectral conflict in conventional methods that couple high-frequency rendering with high-frequency motion, leading to optimization instability. FAGS resolves this challenge with two complementary innovations. Differentiated Gaussian Kernel refines alpha blending by explicitly decoupling
First, Frequency- Prequency-iifferenttatee opacity from Gaussian shape, allowing Gaussians to specialize in either smooth, low-frequency regions or sharp, high-frequency boundaries. Second, a motion representation by leveraging high-fre sechfreeuency Fourier embeddings and frequency- aware gate, enabling accurate and expressive motion modeling. Extensive experiments on both real and synthetic 4D benchmarks show that FAGS effectively reduces motion blur, sharpens structural details.
Network enhances
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6 ACKNOWLEDGMENT
This work was supported by National Natural Science Foundation of China (62293554, U2336212), National Science and Technology Major Project (20232D0121300), "Pioneer" and "Leading Goose" R&D Program of Zhejiang (2025C02022, Zhejiang Provincial Natural Science Foundation of China (LZ24F020002), Zhejiang Provincial Natural Science Foundation of China under Grant No. LDT23F02023F02. Ningbo Innovation "Yongjiang 2035" Key Research and Development Programme (20247292), and Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), The author gratefully acknowledges the support of Zhejiang University Education Foundation Qizhen Scholar Foundation.
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Reviews:
[{"review_id": "Y1QaiANgy1", "reviewer": "Reviewer_77AF", "summary": "The authors attribute motion blur in prior dynamic Gaussian splatting methods to the inherent difficulty of simultaneously modeling high-frequency rendering details and high-frequency motion. To address this issue, they propose a deformation-field-driven framework that explicitly separates Gaussians into low- and high-frequency components, allowing each group to specialize in reconstructing its respective part before merging. Central to this framework is a Fourier-Deformation Network, which leverages Fourier embeddings to effectively capture fine-grained high-frequency local deformations while suppressing redundant motion in low-frequency regions. In addition, the method introduces a frequency-differentiated Gaussian kernel that adaptively sharpens or smooths Gaussians via learnable parameters, enabling clear separation between high- and low-frequency behavior. Extensive experiments on dynamic scene datasets demonstrate the effectiveness of the approach, supported by thorough ablation studies that validate each proposed component.", "questions": "1. Could you please offer me the training time and evaluation time of the baselines in paper? And could you please tell me how many layers in your MLPs? \n2. Belowing current papers are focusing on dynamic, could you please evaluate your model on blurring dataset to see whether it can reduce heavy motion blur?\n3. Could you select one baseline from the following list of papers and then compare both time metrics and result metrics between that baseline and your approach?\n\n\n[1]. BARD-GS: Blur-Aware Reconstruction of Dynamic Scenes via Gaussian Splatting (Deblurring Method + Blurring Dataset)\n\n[2]. Deblur4DGS: 4D Gaussian Splatting from Blurry Monocular Video (Deblurring Method)\n\n[3]. MoBGS: Motion Deblurring Dynamic 3D Gaussian Splatting for Blurry Monocular Video (Deblurring Method)", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The paper proposes a deformation-field-driven method that is compatible with most existing dynamic 3D Gaussian Splatting approaches and it has a good theoretical explanation of solving motion blur.\n2. The introduction of a frequency-aware deformation field provides a clear and effective strategy for mitigating motion blur in dynamic scenes, especially under novel views.\n3. Experiments demonstrate that the proposed method reduces motion blur compared to prior dynamic Gaussian Splatting methods.", "weaknesses": "1. The paper lacks a clear analysis of the computational overhead introduced by the frequency-aware module, such as runtime or memory usage, especially in comparison to existing baseline methods (In your pipeline, it has 4 MLPs. I think it's necessary to show the training time and evaluation time in your paper).\n2. Although the approach shows that it reduces motion blur with normal input, the paper does not include comparisons with existing approaches that mainly address deblurring. Moreover, it does not evaluate on datasets with motion blur to validate its effectiveness under such conditions.\n3. The description of the formulas are not so clear, e.g. you should clarify the 'g' in expression(2)~(4).", "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": "9V7MSYIRzG", "reviewer": "Reviewer_chQR", "summary": "The paper proposes Frequency-Aware Dynamic Gaussian Splatting, a 4D Gaussian-splatting framework aimed at reducing motion blur in dynamic novel-view synthesis. The authors argue that prior deformation-field-based dynamic Gaussian methods struggle with a *spectral conflict*: they must both (i) stack many soft Gaussians to reproduce high-frequency spatial details, and (ii) drive those same Gaussians along accurate, potentially fast and highly non-smooth temporal trajectories. As a result, the deformation network tends to bias toward globally smooth, low-frequency motion, which causes blurred boundaries and smeared fast-moving parts under novel viewpoints.\n\nTo address this, the paper introduces two technical components.\n\n- Frequency-Differentiated Gaussian Kernel (FDGK): Instead of using a fixed isotropic alpha falloff per Gaussian, each Gaussian gets a learnable piecewise alpha modulation ψ(g) with parameters λ (controls sharpness vs smoothness of the opacity profile) and β (controls the spatial extent / boundary of that sharpness). Gaussians can thus specialize as high-frequency (sharp boundaries, for edges) or low-frequency (smooth support for broad regions), reducing the need to stack many Gaussians to recover detail and easing pressure on the deformation network.\n\n- Fourier-Deformation Network (FDN): The deformation network fuses low-frequency spatiotemporal hash encodings with high-frequency temporal Fourier embeddings, whose amplitudes are predicted per Gaussian. A frequency-aware gate η modulates how strongly each Gaussian is allowed to move at each time step, suppressing motion in static/background regions while permitting rapid, localized motion where needed. A Fourier-domain loss on amplitude spectra further emphasizes fitting high-frequency components.\n\nExperiments on D-NeRF, HyperNeRF, and Neu3D show consistent improvements in PSNR / SSIM / LPIPS / MS-SSIM over strong baselines such as 4D-GS, DeformGS, SC-GS, and Grid4D, especially around fast-moving fine structures (fingers, tools, flames). Visualizations of per-Gaussian motion trajectories and ablations suggest that FDGK + FDN reduce drifting / smearing and yield sharper reconstruction of both spatial detail and rapid motion.", "questions": "These are questions where a rebuttal could meaningfully improve my score:\n\n- Can you quantitatively define/measure high-frequency motion?\nFor example, could you report, for baseline vs. your method, the temporal power spectrum or second-order temporal finite-difference energy of a set of tracked Gaussians on fast-moving parts (e.g., fingertips in JumpingJacks)? Right now, high-frequency motion is central but informal.\n\n- Can you give a more concrete analysis supporting the “spectral conflict” claim?\nIn Fig.12, you show that baseline Gaussians drift to other regions to satisfy both detail fitting and motion alignment, which you argue leads to blur. Could you quantify how often this cross-region drift happens, and how it correlates with blur artifacts in novel views? This would turn the nice qualitative story into measurable evidence.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- Clear motivation (motion blur in dynamic GS): The paper focuses on a highly visible failure mode in existing dynamic Gaussian splatting pipelines: smeared or drifting fine details (e.g., fingertips, blades, flames) in novel-view renderings. This is both practically important and easy to judge qualitatively.\n- Theoretically solid contributions: Frequency-Differentiated Gaussian Kernel (FDGK) allows each Gaussian to learn its own alpha profile via λ (sharp vs smooth) and β (boundary span), which lets some Gaussians specialize in high-frequency edges without needing dense stacking, while others handle smooth regions. Fourier-Deformation Network injects explicit high-frequency temporal bases and modulates each Gaussian’s deformation strength with a learned gate η, which is a reasonable mechanism to retain fast, local, non-smooth motion for moving parts while not injecting jitter into the static background.\n- Analysis of parameter distributions: The supplementary shows how λ splits Gaussians into high-frequency vs low-frequency groups during training, and how β adapts boundary spans. The gate η distribution highlights that not all Gaussians become fully dynamic. This supports the claim that the method self-organizes a frequency-aware decomposition.", "weaknesses": "- Core causal story is qualitative, not rigorously established.\nThe paper’s central narrative is that existing methods blur because they cannot jointly model high-frequency spatial detail and high-frequency motion, and that FDGK+FDN resolves this spectral conflict. While the visual evidence is compelling, there is no direct quantitative analysis of temporal frequency content (e.g., Fourier spectrum of per-Gaussian trajectories before/after, or a measure of per-point temporal curvature). Maybe Fig.10 tries to display this point, but there is no sufficient explanation of Fig.10. The argument remains largely anecdotally supported via qualitative trajectory plots and better metrics.\n- Definition of “high-frequency motion” is not clear.\nThe method heavily leans on the dichotomy of “low-frequency global motion” vs “high-frequency local motion,” but never formalizes it (e.g., in terms of time derivatives or spectral energy bands), even though it motivates the design of FDGK, the Fourier embedding, and the gating mechanism. A clearer mathematical definition would make the framing more than just intuitive storytelling.\n- Fourier-Deformation Network assumes a quasi-periodic temporal structure.\nModeling trajectories as Fourier bases with learned amplitudes implicitly assumes motions can be expressed as superpositions of (possibly periodic) sinusoids. From the videos in supplementary materials, most the the shown case can be figured out certain periodic motion pattern. Real-world motion like sudden stops, impacts, or non-repetitive gestures may violate this assumption. The paper does not explore failure cases or quantify when Fourier modes become insufficient.\n- Clarity / naming / polish.\nThe paper alternates between **FAGS** and **FDGS**. Fig.10 lacks an explanation. The gating equation (Formula 8) does not have a sufficient explanation. These presentation issues hurt readability.", "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": "qciUzSFrIR", "reviewer": "Reviewer_cavT", "summary": "The authors propose Frequency-Aware Dynamic Gaussian Splatting, or FAGS. FAGS composes of several components: it first intrudes FDGK, which plays on modifying the Gaussian distribution of a GS primitive. FDGK divides the Gaussian distribution into three regions, and modulate the scale and bias of each region, such that the distribution is more peaky or flatter based on optimization. It then introduces additional encoding scheme for the temporal domain, i.e. encoding time into higher dimensions/frequency bands compared to the spatial domain, such that the MLP can disentangle motion better. Frequency gating and a loss in frequency domain is introduced, though their effectiveness is not very evident. Overall, FAGS outperforms previous approach in terms of standard metrics; however, it is unclear to me if this is due to better disentanglement of high frequency detail and motion, or simply a better Gaussian representation capacity.", "questions": "1. WRT the main claim: other than visual quality, is there anything else that proves the predicted motion is now \"higher frequency\" and more accurate, e.g., what is the \"correct\" motion frequency? My impression is that FDGK does improve the representation capacity of individual Gaussians and does improve visual performance; however, its relationship to motion is unclear. I.e., if FDGK is applied to standard 3D reconstruction, will it not improve performance?\n2. Higher dimensional embedding to the temporal axis with Fourier basis: is this related to anything specific about Fourier space, or alternative embedding scheme, e.g. higher dimension hash embedding other implicit neural representation embedding, would achieve similar results?\n3. Are FG and L_fre necessary? Why can frequency-aware gate score behave in the manner that is described? Based on ablation, FG and L_fre contributes very minimally.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "1. FAGS outperforms existing methods on standard 4D reconstruction datasets, particularly on synthetic datasets. Real dataset performances have a smaller improvement, but that seems reasonable given potential noise in real datasets.\n2. The FDGK formulation does seem to improve Gaussian representation capacity and leads to better fitting.", "weaknesses": "I have several issues with this paper, specifically concerning the writing (difficult to read, bold claims without evidence, etc.) and the necessity of multiple parts. I think overall the paper can be more focused on FDGK and better distinguish that contribution. \n\n1. It is hard to follow this work, multiple variables are not defined. E.g. in Eq. (2), g is not defined. D is not defined in Eq. (8), multiple abuse of notation, e.g., where \"MLP\" indicates multiple neural networks with different parameters. The math is unclear, especially Eq. (2). How is this equation related to \"numerical fluctuations\"? While the first part of the Equation makes sense, the second part, where r is said to be able to go to infinity, does not seem mathematically correct. We may be able to scale with r in limited region of the distribution, by certainly not the entire distribution, otherwise opacity can be scaled to infinity. Proper constrains should be stated. I have to reference prior work, e.g., DRK to double-check my understanding. The details on frequency-aware gate score is very sparse, it is unclear to me why this score can do the things that is claimed. All that is conveyed is that this score seems to come out of a neural network. \n\n2. Multiple claims seem to be overboard/abusing concepts that have similar words but not really related. The main claim: \"FAGS can disentangle high freq. detail and high freq. motion\" does not feel properly addressed by FDGK. The FDN introduces higher dimensional embedding to the temporal axis with Fourier basis - I am not sure if this is necessarily related to motion frequency rather than higher dimensional embedding leads to better performance. Similarly, it is unclear to me how the computing the amplitude spectra loss over an image leads to better frequency disentanglement; both FG and L_fre seem to contribute very little based on ablation. \n\n3. It is unclear to me why DRK is not a baseline at least in the ablation study. It seems like this work is closely related to DRK. Despite that DRK does not explicitly address 4D reconstruction, it should be straightforward to add DRK as a kernel representation without affecting the motion estimation network too much. Without such experiments, it is unclear to me if FDGK is a simpler variant of DRK with pre-defined regions of Gaussians to optimize. \n\nI overall think this paper has interesting contributions, and would give a borderline accept if FDGK/high frequency detail and motion disentanglement can be more grounded, which may require datasets that have some notion of what \"high/low frequency motions\" are. Given the current state of writing, and the (seemingly) unnecessary components, I vote for borderline reject and think the authors should significantly modify the writing.", "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": "9MmPva5l4i", "reviewer": "Reviewer_UoZA", "summary": "This paper points out the crucial limitations of previous 4D-reconstruction methods: Most of the previous literatures struggle to balance high-frequency rendering details with high-frequency motion, hence resulting in blurred details. This is mainly due to the limited expressiveness of the 3DGS in the dynamic scenes where the standard alpha-blending of 3DGS fails to express modified geometry along the time steps.\n\nTo this end, this paper suggests the novel technique from a frequency perspective where they provide additional learnable parameters into 4DGS pipeline such as $\\lambda$, $\\beta$ and *frequency-aware gate*, enhancing the expressiveness of 3DGS and successfully distinguishing the low-frequency gaussians and high-frequency gaussians.\n\nProposed technique contributes to performance improvement to some extent.", "questions": "**Primary area**: Why is the primary area of this paper indicated as *generative model*?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "This paper addresses the meaningful problem where the limited expressiveness of 3DGS fails to recover the fine-grained details across the time steps due to the lack of clear separation between low-frequency gaussians and high-frequency gaussians. This statement is well introduced in the second paragraph of *Introduction part* which makes their motivation clear.\n\nThe solution suggested by the paper has novelty inside where they improve the expressiveness of 3DGS by introducing the additional learnable parameters from a frequency perspective, clearly separating the gaussians into high-frequency GS and low-frequency GS. Furthermore, ablation studies support the effectiveness of each part where Tab. 4 shows the quantitative improvements and Fig. 7 demonstrates the clear separation of the gaussians into low-frequency and high-frequency components.", "weaknesses": "1. **Marginal performance improvement** \n\n* It seems like the performance improvement in SSIM and LPIPIS is quite marginal (mostly +0.001 in both metrics) compared to the Grid4D while performance in PSNR is relatively clear. Furthermore, in *Trex* scene of Tab. 1, it seems that SC-GS achieves the best result in LPIPS metric while the paper indicates 4DGS and their own method achieves the best scores. \n* Why is LPIPS metric not reported in Neu3D dataset? Also, please report the average scores in Neu3D dataset.\n* In Fig. 6, I failed to find the clear improvement  between Grid4D vs paper's methods, especially in 2nd and 3rd rows. In 2nd row, I think the both of Grid4D and paper's method fail to reconstruct the clear details.\n* The combination of 3 rendering matrices compared to GT (PSNR, SSIM, LPIPS) is sometimes not sufficient to show the effectiveness of the method. It would be better to adopt additional metrics such as MUSIQ [a] and CLIP-IQA [b] to estimate the naturalness of the images since the paper points out the blurred reconstructed details from the previous methods.\n\n2. **Room of improvement in ablation study**\n\n* In Sec. 3.2, paper introduces two learnable parameters, $\\lambda$ and $\\beta$, in the alpha-blending part of the 3DGS to improve the expressiveness of the 3DGS. $\\lambda$ controls the transparency gradient from the projection center, effectively separating the high-frequency GS and low-frequency GS, while $\\beta$ additionally controls the differentiated regions. What will be happened if we remove the $\\beta$? It would be better if the paper reports the performance when they only use one of them ($\\lambda$ and $\\beta$).  \n* Tab. 4 presents the ablation study for each component of FAGS. However, more diverse combinations should be explored.\n\nConsidering the contributions and weaknesses of this paper, I would like to recommend the score between 6 to 8 which is around 7.\n\n---\n\n**References**\n\n[a] Junjie Ke, Qifei Wang, Yilin Wang, Peyman Milanfar, and Feng Yang. Musiq: Multi-scale image quality transformer. In Proceedings of the IEEE/CVF international conference on computer vision, pages 5148–5157, 2021.\n\n[b] Jianyi Wang, Kelvin CK Chan, and Chen Change Loy. Exploring clip for assessing the look and feel of images. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 2555–2563, 2023", "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)