HAIF-GS: Hierarchical and Induced Flow-Guided Gaussian Splatting for Dynamic Scene
Authors: Jianing Chen
Zehao Li
Yujun Cai
Hao Jiang
Chengxuan Qian
Juyuan Kang
Shuqin Gao
Honglong Zhao
Tianlu Mao
Yucheng Zhang
Venue: NeurIPS 2025 poster ()
Keywords: 3D dynamic reconstruction; computer vision
Primary area: deep_learning

Abstract: Reconstructing dynamic 3D scenes from monocular videos remains a fundamental challenge in 3D vision. While 3D Gaussian Splatting (3DGS) achieves real-time rendering in static settings, extending it to dynamic scenes is challenging due to the difficulty of learning structured and temporally consistent motion representations. This challenge often manifests as three limitations in existing methods: redundant Gaussian updates, insufficient motion supervision, and weak modeling of complex non-rigid deformations. These issues collectively hinder coherent and efficient dynamic reconstruction. To address these limitations, we propose HAIF-GS, a unified framework that enables structured and consistent dynamic modeling through sparse anchor-driven deformation. It first identifies motion-relevant regions via an Anchor Filter to suppress redundant updates in static areas. A self-supervised Induced Flow-Guided Deformation module induces anchor motion using multi-frame feature aggregation, eliminating the need for explicit flow labels. To further handle fine-grained deformations, a Hierarchical Anchor Propagation mechanism increases anchor resolution based on motion complexity and propagates multi-level transformations. Extensive experiments on synthetic and real-world benchmarks validate that HAIF-GS significantly outperforms prior dynamic 3DGS methods in rendering quality, temporal coherence, and reconstruction efficiency.

HAIF-GS: Hierarchical and Induced Flow-Guided Gaussian Splatting for Dynamic Scene
Jianing Chen 1.2 Zehao Li Yujum Cai Hao Jiang Chengxuan Qian 4 Juyuan Kang Shuqin Gao Honglong Zhao', Tianlu Mao Yucheng Zhang'
1 Instittte Computing Technology. Chinese Academy of Sciences, ICT University of Chinese Academy of Sciences, UCAS The University of Queensland *Jiangsu University
{chenjiaming23s, jianghao)@ict.eet
Abstract
Reconstructing dynamic 3D scenes from monocular videos remains fundamental challenge 3D vision. While 3D Gaussian Splatting (3DGS) achieves real-time rendering in static settings, extending it dynamic scenes is challenging due to the difficulty of learning structured and temporally consistent motion representations. This challenge often manifests as three limitations in existing methods: redundant Gaussian updates, insufficient motion supervision, and weak modeling of complex non-rigid deformations. These issues collectively hinder coherent and efficient dynamic reconstruction. To address these limitations, we propose HAIF-GS, a unified framework that enables structured and consistent dynamic modeling through sparse anchor-driven deformation. first identifies motion-relevant regions via Anchor Filter to suppress redundant updates in static areas. A self-supervised Induced Flow-Guided Deformation module induces anchor motion using multi- frame feature aggregation, eliminating the need for explicit flow labels. To further handle fine- grainnd deformations, a Hierarchical Anchor Propagation mechanism increases anchor resolution based motion complexity and propagates multi-level transformations. Extensive experiments on synthetic and real- worldw benchmarks validate that HAIF-GS significantly outperforms prior dynamic 3DGS methods in rendering quality, temporal coherence, and reconstruction efficiency.
Introduction
Reconstructing dynamic 3D scenes from monocular video represents a fundamental challenge in computer vision with applications spanning virtual reality [13, 15J and autonomous driving [4, 41, 48]. Unlike static reconstruction, dynamic environments introduce complex deformations time-varying geometry, significantly complicating consistent modeling of both appearance and motion.
While Neural Radiance Fields (NeRF) [27] revolutionized static scene representation, their implicit volumetric nature requires dense sampling, resulting in prohibitive computational costs and slow rendering. 3D Gaussian Splatting (3DGS) [14] has emerged as an efficient alternative, replacing volume integration with explicit 3D Gaussians for high visual fidelity and real-time rendering. However, 3DGS was designed for static scenes, and extending it to dynamic ones remains challenging.
Several recent methods [44, 39, 40, 49] extend 3DGS to dynamic scenes by introducing learned deformation fields. These approaches typically employ MLPs predict time-dependent transforma- tions of Gaussian parameters (e.g. position, quaternion). While effective in capturing motion, they
Corresponding authors
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Ours
SC-GS
Ours
4DGS
D3DGS
2SN
PSNR:26.17
PS.7939.79
PSNR:35.50
PSNR:37.66
(a) NeRF-DS
(b) D-NeRF
Figure The visualization results on (a) NeRF-DS [42] dataset and (b) D-NeRF [31] dataset.
require querying and updating an excessive number of Gaussians at each timestep, which leads to considerable redundancy. To improve efficiency, subsequent methods [12. 5] introduce sparse set of control points to derive transformations of nearby Gaussians via interpolation. However, such strategies often fail to capture fine- are-graided or non-rigid motion. For example, Figure (b) shows hand motion, where the fine-scale appearance and localized movement highlight the challenges of modeling fine-ge one-grained dynamics in dynamic reconstruction. This limitation is mainly due to two factors: (I) Limited expressiveness: Deformation fields typically employ simple MLPs that lack the capacity to model articulated or spatially varying motion, particularly complex real-world scenes. (2) Insufficient motion supervision: Training relies solely on image reconstruction loss, without explicit motion guidance or structural constraints, resulting in temporal inconsistencies and artifacts.
To address this challenge, we propose HAIF-GS (Hierarchically Anchored and Induced Flow- Guided Gaussian Splatting). a unified framework that significantly improves both the efficiency and accuracy of dynamic scene reconstruction. HAIF-GS builds upon sparse motion anchors as the core deformation units, substantially reducing redundant queries over individual Gaussians and forming compact foundation for anchor-driven motion modeling, Building on this foundation, we introduce three complementary modules to further improve the quality of deformation: (1) Unlike prior methods that process the transformation of all Gaussians indiscriminately through deformation fields, we employ an Anchor Filter module that predicts a dynamic confidence score for each anchor, allowing the model to select motion-relevant anchors and concentrate deformation learning on dynamic regions. (2) We introduce the Induced Flow-Guided Deformation (IFGD) module, which leverages fulti--rraee aggregation to induce scene flow in self-supervised manner and uses it to regularize anchor transformations without requiring external flow labels. This design enables more structured supervision for motion learning and improves the temporal consistency of anchor trajectories. (3) To further enhance motion expressiveness, we employ the Hierarchical Anchors Densification (HAD) module, which progressively densifies anchors in motion-complex regions and establishes a layered structure for hierarchical motion propagation. Assigning new anchors to a parent from upper layers allows the model to transfer transformation cues across levels and to capture fine-grained and non-rigid deformations in challenging regions. By integrating these techniques, our HAIF-GS achieves efficient and accurate reconstruction of dynamic scenes with diverse and complex motion patterns, benefiting from the synergy between sparse representation, targeted supervision, and hierarchical motion modeling.
In summary, our contributions are as follows:
We propose HAIF-GS. a unified framework for dynamic scene reconstruction based on sparse motion anchors to reduce redundancy and improve efficiency, while addressing key challenges of temporal inconsistency and local non-rigidity.
We introduce a motion modeling strategy that integrates motion-aware anchor filtering, induced flow-guided deformation, and hierarchical anchor densification, enabling fine-grained, temporally consistent, and structurally adaptive representation of complex dynamics.
Extensive experiments on both real-world (NeRF-DS) and synthetic (D-NeRF) datasets demonstrate that HAIF-GS achieves state-of-the -fee-o-f--hh-t---- performance quantitatively and qualitatively.

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2
Related Work
Dynamic NeRF. Neural Radiance Fields (NeRF) [27] have become a powerful framework for novel view synthesis in static scenes by implicitl modeling volumetric radiance with MLPs, offering an alternative to traditional multi-view stereo (MVS) approaches [45, 46]. A broad range of works [11, 9, 29-9911 7, 43, 36] have extended NeRF to dynamic settings by introducing temporal representations such as deformation fields and canonical mappings. Despite their effectiveness, these methods remain inefficient due to dense ray sampling and costly volume rendering. To address this challenge, numerous improved methods [20, 24, 22, 23, 26,33 37] have been proposed for dynamic scene rendering. leveraging grid structures [24] and multi-view supervision [22, 23] to enhance both efficiency and reconstruction quality, Recent works accelerate dynamic modeling using explicit representations such as multi-plane [3, 8, 33] and grid-plane hybrids [34], which factorize spatiotemporal space but still render slowly. While these methods significantly accelerate training and inference, their performance remains insufficient for real-time applications.
Dynamic Gaussian Splatting. Recently, 3D Gaussian Splatting (3DGS) [14] has gained attention for achieving real-time rendering with explicit point-bascd representations, and has been increasingly adopted in dynamic reconstruction [44] and has shown potential for broader 3D tasks [18, 32, 2]. Several works have extended 3DGS to dynamic scenes by learning time-varying transformations of Gaussians [44, 39, 40, 12, 5, 25, 49, 19]. Early approaches [44] rely on per-Gausiian deformation fields, which often introduce redundant computations and training inefficiencies. To address this, later methods utilize compact structures such as plane encodings [39] or hash-based representations [40] to model deformation more efficiently. Another line of work [12, 5] employs sparse control points to drive Gaussian motion through interpolation, enabling both high-quality rendering and motion editing. However, cxisting approaches still struggle model fine-grained and temporally consistent deformations in a compact and generalizable manner. In contrast, our proposed HAIF-GS intro- duces sparse anchor-based motion modeling with self-supervised flow induction and hierarchical propagation, achieving a better balance between efficiency and expressive motion representation.
Preliminary
Before introducing our approach, briefly review key background concepts, including the 3DGS for static scenes (Section 3.1) and its recent dynamic extensions (Section 3.2).
3.1
3D Gaussian Splatting
3D Gaussian Splatting (3DGS) [14] has emerged powerful technique for real-time rendering of static scenes. In this representation, the scene is modeled as collections of anisotropic 3D Gaussians, each defined by set of continuous attributes: center position μ R covariance matrix Σ E R3x3 opacity a and spherical harmonics (SH) coefficients h for view-dependent appearance modeling.
To enable differentiable rendering, the covariance matrix is parameterized via a rotation-scaling decomposition: Σ = RS R² where is derived from a unit quaternion and is diagonal scaling matrix. Each 3D Gaussian projects onto the image plane through a camera projection matrix W and a local Jacobian J, creating a 2D elliptical footprint with transformed covariance Σ' = JWEWT jr and projected center μd' JW
Rendering performed via a forward splatting process, where Gaussians contribute to nearby pixels via an a-blending- based soft visibility weighting scheme. The color at pixel u is computed by aggregating radiance contributions from overlapping Gaussians as:
C(u)
Σ T.a,SH(h,, (EN(a)
where T; = II - ag)) represents transmittance, a, is derived from the projected Gaussian density, and SH(h, v) evaluates the spherical harmonic function along view direction v.
The Gaussian parameters are optimized via gradient descent using photometric reconstruction loss. Adaptive density control is applied to prune redundant Gaussians and spawn new ones based on the optimization signal, improving convergence and rendering quality.
3

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Anchor
Ilemrthically Deasity
Coams:
Layer
Motion Auchors (x,
Canonical Gausians w/ Trrisl rod A Anchers
Layer
Trans
Deformable MLP
Indured Flow MLP
Pine
Layer
EGenuccical Anchurs
Inducad Plow: Guided Deformation
Coosse
Layer
Pronuy 100
AR5,07'
Mitinn Static Anchues
Fisttmme Extrectin
Grassans
① Aggesgtion
Independent Paramaters
Truny
KNN
IFGD
Deformed Gaussians
Parett Childre Laak
Trumg
Given the canonical Gaussians, we first initialize sparse motion anchors and filter them using confidence-await Anchor Filter. We then aggregate multi-frame features to predict temporally consistent transformations for each anchor. regions with complex motion, hierarchically densify anchors propagate deformations across layers. Finally, we update Gaussian parameters anchor- based interpolation and render images for supervision.
Figure 2.
The overview of our HAIF-GS.
3.2 Dynamic Reconstruction Based on 3DGS
While 3DGS excels at static scene, extending dynamic scenes presents challenges. Recent methods address this issue by extending 3DGS to dynamic settings through explicit motion modeling in the Gaussian representation. A common approach learns deformation field that transforms static Gaussians over time. Specifically, deformation network D inputs Gaussian's 's canonical attributes (center position μı, rotation r, scaling s) along with timestamp and outputs temporal offsets:
(Mi Tt, st) = D(u, r, s,t),
where (Me, Te: st) denote compenstted attributes at time t, enabling the modeling of non non-rigid deformations across frames for dynamic reconstruction.
In practice, deformable 3DGS can be further enhanced by combining motion priors, camera pose refinement, and suduuee-guied correspondence mechanisms. However, existing approaches often struggle to achieve efficient modeling of complex local motion, maintain temporal consistency across frames, and capture heterogeneous motion patterns in real-world scenarios. These limitations motivate the development of more structured and scalable motion representations for dynamic reconstruction.
4 Method
4.1
Overview
Given image sequences { {I+} and corresponding camera poses [Pr} timestamps {t), our goal is to learn representation that can render the dynamic scene from arbitrary viewpoints any time within observed interval. This task presents inherent challenges: efficient updates numerous Gaussians across time; heterogeneous motion patterns in cal-world scenes combining static backgrounds with complex deformations; and modeling detailed non-rigid motion with limited viewpoints.
Our approach addresses these challenges through hierarchical sparse motion representation based on 3D Gaussian Splatting, as illustrated in Figure 2. We represent motion using a sparse set of learnable 3D motion anchors that predict local transformations propagated to Gaussians through spatial interpolation. To enhance temporal consistency and motion prediction, we introduce an induced flow-guie flow-guided deformation module that aggregates multi-frama features to guide anchor transformations without explicit flow supervision. For complex motion regions, we introduce a hierarchical anchor structure that refines predictions with denser anchors at higher resolution. Our method comprises three components: sparse motion anchors and dynamic decomposition (Section 4.2), induced flow-guided deformation (Section 4.3), and Hierarchical Anchor Densification (Section 4.4).

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4.2 Sparse Motion Anchors and Dynamic Decomposition
Motion anchor representation. We represent scene motion using sparse set of learnable 3D points, referred as motion anchors, which serve the primary units for modeling deformation. Instead of directly associating motion parameters with each Gaussian, we predict local transformations from anchors and propagate them to Gaussian through spatial interpolation.
Motion anchors are initialized via farthest point sampling (FPS) in the canonical space to ensure uniform spatial coverage. Each anchor a, is parameterized by 3D position Z; IR3 and learnable influence scale E Rt. The set of all anchors is denoted as A = {(z;, )
For each Gaussian 9j centered at μıj, we select its K nearest motion anchors Aj based on Euclidean distance in canonical space. The influence of each anchor on a specific Gaussian is determined by a normalized Gaussian kernel [6, 28]:
exp
11g x. 122)
Wij E,,,A, exp M4 JA 1P/122)
The spatial interpolation weights Waj are used to aggregate transformations from neighboring anchors to compute the final motion of each Gaussian.
Dynamic-Stati decomposition. To distinguish between dynamic and static motion patterns, we introduce decomposition strategy over the set of motion anchors. Specifically, assign each anchor ag a confidence score a; E [0. 1] that reflects the likelihood of the anchor participating in dynamic motion. Anchors with high confidence treated as dynamic and contribute to deformation modeling, while static anchors are excluded.
Each a; is predicted by an Anchor Filter, lightweight MLP that takes as input the position encoding of the anchor's s spatial and temporal coordinates , rtt). The Anchor Filter is jointly optimized with the the Induced Flow-Guided Deformation module to enable end-to-end training. During training, we adopt a two-stage scheme: in the first stage, all anchors contribute to the deformation field with their predicted transformations modulated by the soft weight a,, allowing gradients to propagate to the Anchor Filter; in the second stage, a hard decomposition is applied by thresholding a; and only dynamic anchors are used for motion modeling.
To regularize the dynamic-static decomposition, we introduce two regularization losses that encourage confident and sparse selection of motion anchors. The details are described in Section 4.5.
4.3 Induced Flow-Guided Deformation
To leverage temporal context, we introduce the Induced Flow-Guided Deformation module, which consists of two key components. The Induced Flow MLP predicts forward and backward scene flows from anchor position and timestamp after position encoding, providing three temporally shifted queries across adjacent frames. The Deformable MLP maps each flow-guided query to feature embedding and then integrates them into a temporally aligned feature, which is used to predict anchor-wiss wise transformations (i.e. rotation and translation) through multiple transformation heads. The induced flows serve as internal guidance signals, facilitating multi-frame feature alignment and thereby promoting temporally consistent motion modeling. Notably, both the dynamic-static separation and flow-based motion learning are induced during scene reconstruction optimization, without requiring external flow supervision.
Induced flow-guided temporal queries and feature aggregation. Given a motion anchor x and time t, after positional encoding, the Induced Flow MLP predicts backward and forward scene flow:
(F' F(+1)= MLP (x. t),
where 1-1 and F++1 represent the anchor displacement from t to t - and + 1, respectively. These flows guide the construction of three temporally shifted queries across adjacent frames:
4t-1 = (x ft t 1), qe = (x. t), 4++1 = (x + F++1 t ++1).
Each flow-guided query is mapped time time-aware feature embedding by a shared Deformable MLP:
pt+i MLP MLPasfom (LL)stom(((c4)) i (-1,0,++1)
5

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These embeddings are aggregated using simple weight to produce a temporally consistent feature:
= (1 2X) *
(4)
where À E 0.5) is fusion weight that emphasizes the reference frame while incorporating motion context from neighboring frames. We set À 0.25 in all experiments.
This temporal aggregation bridges scene flow prediction and scene reconstruction, enabling their joint optimization during training. Embedding temporal consistency into anchor representations enables accurate prediction by sharing information across frames. The flow fields are learned without explicit flow supervision; instead, multi-frame feature aggregation implicitly induces flow prediction to converge toward coherent and consistent motion patterns during scene reconstruction.
Transformation prediction and interpolation. The temporally consistent feature f of anchor a; at timestep is used to predict translation AT; E IR3 and rotation AR E R through multiple independent transformation heads. Given these predicted anchor transformations, our next goal is to drive the motion of individual Gaussian using nearby anchors. For each Gaussian j. we identify set of neighboring motion anchors A, via K-nearest neighbor (KNN) search in the canonical space. The corresponding spatial interpolation weights Wij are computed based on the spatial distance between Gaussian centers and anchors, as defined in Eq. 3. Following the prior dynamic fusion methods [12, 6]. we adopt the linear blend skinning (LBS) strategy [35] to compute the Gaussian deformation Azj. Arj by interpolating the transformations of its neighboring anchors:
Au4
Σ wis (AR - 14) + + AT;), Arj TEA,
Σ iEA,
Way
AR
2 Tr
(5)
where fy and I; denote the centers of Gaussian j and anchor and @ is quaternion multiplication. This interpolation allows each Gaussian's 's deformation to be locally driven by a sparse anchor transformations, enabling compact modeling of dense deformation fields.
Temporal self-supervision. To encourage temporal consistency in motion learning, apply cycle consistency loss on the predicted scene flow. This loss is described in detail in Section 4.5.
4.4 Hierarchical Anchor Densification
While sparse motion anchors efficiently model global motion, they may struggle to capture fine- grained, non-rigid deformations. We address this with a hierarchical anchor structure that introduces finer-resolution anchors in regions of high motion complexity.
identify regions requiring finer-resolution anchors by computing the temporal translation variance for each base-level anchor. Specifically, for each anchor a;, compute the normalized variance var(a.) of its predicted translation AT; across Ne(= 16) randomly sampled timestamps as:
N Σ | -T:I,, where AT: N.
No
(ar(
1
Σ AT. N.
1
(6)
Anchors with variance var exceeding threshold marked for hierarchical refinement. We generate finer-resolution anchors by duplicating each selected anchor with small spatial offsets, forming multi-scale hierarchy that captures progressively finer motion details.
Figure 2 illustrates our hierarchical anchor densification module, which refines motion representations across multiple anchor layers in a coarse-to- fine manner. Each child anchor encodes its own spatial position, timestamp, and the parent translation, enabling cross-level motion propagation. All layers share the deformation MLP while using lightweight, layer-specific feature extractors for efficiency.
For each Gaussian's final transformation, we independently retrieve neighboring anchors from each layer, apply weighted interpolation within layers, and fuse the results using level-specific learned confidence weights. This enables multi-scale motion decomposition with minimal computational overhead, as only regions requiring fine-grad grained modeling incur the cost of additional anchor levels.

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Table 1. Quantitative comparison NeRF-DS dataset per-scene. We highlight the best second best and
the third best results in each seene. The rendering resolution is set to 480 x 270. DS, HyperNeRF, 4DGS, SC-GS and ours use MS-SSIM/LPPPSS (Alex), while other methods employ SSIM/LPIPS (VGG).
Method
Sieve
PSNRT
MS SSIM
LPIPS1
PSNK1
MS SSIM?
LPIPS1
PSNK1
MS SSIM]
LPPPS.
PSNK1
MS SSIM]
LPPSS.
3008 [14]
23,16
0.2347
21.01
0.7865
22.89
0.2904
HypenNaRF [50]
25.41
0.8798
0.1645
18.93
0.7709
0.3940
23.06
0.3097
0.2052
26.15
0.8897
0. 0.1999
NeRE-DS (42)
25.7M
0.3472
20:54
0.3996
23.19
0.1867
25.72
0.8618
4DGS [39]
26.11
0,9193
0.1107
20.41
0,5311
0.2010
25.70
0,9038
0.1103
26.72
0.9031
0.1301
Defemable SDGS [44]
25.70
0,8715
0.1504
20.48
0.5124
0.2224
25.74
0.5503
0.1533
26.01
0.8666
0.1905
SC-G5 (12)
25.93
0.9187
0.1194
20.17
0.5257
0.2194
25.97
0.1167
26.57
0.1367
Ours
26.51
0,9074
0,0933
20.96
0,5379
0.2181
26.34
0.9522
0.1162
27.05
0.133
0. 1.129
Cup
PSNRT
MS-SSIMT
1JPPS]
PSNR1
MS-SSIMT
LPMPS]
PSNR1
MS-5SIMT
1PPP81
PSNK1
MS-SSIMT
1.MIPS_
SDOS [14]
21.71
0.2548
0.2094
20.29
HypsNNRF [50]
24.99
0,8770
0.1650
25.58
0.3949
0.1777
20141
0.3159
0.1911
23.45
013488
0. 1990
NeRF- DS (42)
24,91
0.1737
25.13
0.3741
19:96
0.1855
23.60
0.1816
4DGS [19]
24.57
0,9102
0.1185
26.30
0,8917
0.1499
19.01
0.8277
0.1631
25.18
0.8845
0.1408
Defoemable SDGS [44]
24,86
0,8908
0.1532
26.31
0.5342
0.3763
19:67
0.7934
0.1901
24.11
0.8524
0.1759
(12)
24.32
0.1207
26.17
19:23
0.1514
24.05
0.1439
Ours
24.72
0,9255
0,1124
26.96
0,9088
0.1247
19.74
0,8893
0. 0.1488
24.63
0.9014
0. 031222
4.5
Optimization
Although our proposed framework can effectively predict Gaussian deformation through anchor- based modeling, it still faces challenges in maintaining flow coherence and controlling the sparsity of motion anchors. To address these challenges, we introduce three additional loss functions.
The cycle consistency loss is specifically designed to enhance bidirectional consistency by encourag- ing the forward flow followed by backward flow to return the original position, in accordance with the physical constraint that holds for most real-world motions:
fayele E.
F!- + Flow(x; F -
11) ,
| + Flow(x; + F ++ 1+)
where Flow is the induced flow MLP defined in Section 4.3. This self-supervision signal is crucial for learning coherent motion patterns without requiring explicit motion annotations.
We also apply two regularization losses on the motion confidence scores or to regularize the dynamic anchors selected by Anchor Filter:
Coparsity = E, [as), Centropy = E. [a:(1 - (x))]
(8)
The sparsity loss Esparsity controls the proportion of dynamic anchors, encouraging the model to explain the scene with few dynamic elements possible, following Occam's 's razor principle that simpler explanations should be preferred. The entropy loss Centropy promotes confident binary decisions in the Anchor Filter by penalizing uncertain scores near 0.5.
In general, our final loss function is formulated as a weighted sum of the LI color loss, the D-SSIM loss, and the three proposed regularization terms, where the photometric losses (Ll and D-SSIM) are similar to those in 3DGS [14] and ensure visual fidelity of the reconstructed scene.
= = + (1 AD + d Leyele + X Ae + x Ay
(9)
where Å1, A2 and A3 are weighting coefficients balaneing the relative contributions of each loss term. We empirically set A=088, \ = 0.01, X2 = 0.2, and λş = 0.5 to prioritize reconstruction quality while ensuring temporal consistency and model parsimony.
5
Experiments
5.1 Experimental Setup
Datasets and Metrics. We evaluate our method on two widely used benchmarks for monocular
dynamic scene reconstruction: NeRF-DS [42] and D-NeRF [31]. For quantitative evaluation,
7

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Table 2.
Quantitative comparison D-NeRF dataset per-scene. We highlight the the best second hest
and the third best results each seene. The rendering resolution is set to 800 x 800.
Jumping SSIMI
Bouncing Balls
Mothod
PSNR1
SSIM?
LPIPS)
PSNR
LPIPS
PSNRT
SSIM1
LPIPS]
PSNR1
SSIM
LPIPS.
TENeuVox [7]
30.51
0,959
0.060
33.46
0.977
0.041
31.43
0.967
0.017
40.28
0.992
0.042
4006 [59]
32.95
0.977
0.027
35.30
0.9%6
0.020
33.95
0.885
0,022
40.77
0.994
0.015
[44]
0.989
SC-GS [12]
38.79
0.990
0.011
39.34
0.992
0.008
39.53
0.991
0.009
11.59
0.995
0.009
Ours
39.38
0.996
0.013
39.79
0.997
0.010
40.27
0.998
0.009
41.63
0.996
0.009
Hell Winiie
Matant
Standup
Moan
Mothod
LPIPS)
PSNRT
SSIM
SSIM1
LPIPS]
SSIM
Vox
0.9664
0.076
32.07
0,880
0.033
31.92
0.038
4DGS [39]
28.80
0,974
0.037
37.75
0.988
0.016
38.15
0,990
0.014
35.41
0.985
0.021
Deformable 3DGS (44]
41.34
0.987
0.024
42.47
0.995
0.005
44.14
0.995
0.007
40.16
0.991
0.012
[12]
Ours
42.50
0.993
0,021
43.65
0.998
0.005
46.83
0.999
0.001
42.00
0.997
0.010
Ground Truth
Ours
SP-GS
SC-GS
3DGS
As
Bell
Press
Sieve
Plate
Figure 3. Qualitative comparison on the NeRF-DS dataset [42]. Compared with other SOTA methods,
method reconstructs finer details and produces structured rendering of the moving objects.
employ three standard metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) [47].
Baselines and Implementation. We compare method with state-of-the-ar art methods in dynamic
scene reconstruction, including NeRF-based methods (TiNeu Vox [7], HyperNeRF [30], and NeRF- DS [42]) and 3DGS-based methods (3DGS [14], Deformable 3DGS [44], 4DGS [39], SC-GS [12], and SP-GS [5]). All implementations are based on PyTorch framework and trained on a single NVIDIA RTX 3090 GPU. For more implementation details, please refer Appendix.
5.2 Comparisons
NeRF-DS Dataset. We evaluate our method on the real-world NeRF-DS dataset. As shown in Table our method outperforms state-of-the-ar baselines across all scenes and metrics. Figure shows that our method captures accurate positions and sharp edges of moving objects in scene like press and sieve, while reducing visual distortions, benefiting from temporal consistency provided by the guidance of induced flow. Moreover, in the scene, our hierarchical anchor design better models the non-rigid deformation of the moving sheet compared the single-layer SC-GS, preserving sinle structure and spatial coherence.

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Ground Truth
Ours
Deformable 3DGS
4DGS
3DGS
HellWantor
Hook
Figure 4. Qualitative comparison on the D-NeRF dataset [31].
Table 3. Ablations on the key components of our pro-
posed framework NeRF-DS dataset [42].
Method
PSNR
MS-SSIM
LPIPS
Truth
w/ HAD
w/o
23.91
0.8629
0.1624
w/o Leycle
24.51
0.8947
0.1437
w/o AF
24.45
0,8802
0.1488
w/o HAD
24.39
0.8774
0.1493
Ours
24.63
0.9014
0.1342
w/ dersify (simple)
densify
Figure 5. Visualization of anchor densify methods.
D-NeRF Datasets. We further validate our method on the synthetic D-NeRF benchmark. The quantitative results summarized in Table 2 show that our approach also achieves the best performance across all evaluated scenes. Figure provides qualitative comparisons, where our method consistently produces more accurate geometry with few artifacts. For example, in hell warrior and jumping jacks scene, our approach better handles body deformation, and recovers coherent limb structures that are distorted or blurred in other methods. These results highlight the effectiveness of our anchor-driven deformation and hierarchical refinement in preserving temporal fidelity and spatial precision.
5.3 Ablation Study
Effectiveness Induced Flow-Guided Deformation. ablate the Induced Flow-Guided Defor- mation module by removing its two core components: the Induced Flow MLP (IF) and the Cycle Consistency Loss (Leycle). As shown in Table (row 1), removing the entire Induced Flow module leads to noticeable drop across all metrics, indicating the importance of multi frame aggregation for temporal consistency. Disabling Lcycle (row 2) slightly reduces PSNR and SSIM, showing its role in guiding consistent motion learning.
Effectiveness of Anchor Filter and Hierarchical Motion Propagation. Removing the Anchor Filter (AF) causes moderate drops (row 3), confirming its role suppressing redundancy. Disabling Hierarchical Anchor Densification (HAD) further reduces performance(row 4), showing its effective- ness in modeling complex motions. Figure 5 compares different densification methods, where our hierarchical design better preserves fine-scale deformation than simple no densification.

---

Conclusion
We presented HAIF-GS, a unified framework for dynamic 3D reconstruction that combines sparse anchor-driven modeling with flow-guided deformation and hierarchical motion propagation. By leveraging sparse motion anchors, our method reduces redundant updates and focuses modeling capacity dynamic regions. The flow-guided component induces temporally consistent anchor transformations through multi-frame aggregation, while the hierarchical propagation module enhances deformation expressiveness in motion-complex areas. Our design addresses key limitations of prior methods by improving temporal consistency, reducing redundancy, and capturing non-rigid motion more effectively. Extensive experiments both synthetic and real-world benchmarks demonstrate that HAIF-GS achieves superior rendering quality, motion fidelity, and efficiency, advancing the state of the art in dynamic scene reconstruction.
Limitations. While HAIF-GS demonstrates strong performance across diverse dynamic scenes, still exhibits limitations. First, although the anchor filtering and hierarchical propagation reduce redundancy, the overall memory footprint remains non-trivial when modeling scenes with highly complex motion dynamics due to anchor proliferation. Second, the self-supervised scene flow is induced implicitly via multi-frame feature alignment, which may be sensitive to significant occlusions regions, potentially affecting transformation stability. Addressing these aspects would further enhance the scalability and generality of our framework.
Acknowledgement
This work was part supported by the Science and Technology Projects of the Ministry of Agriculture and Rural Affairs of China, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No. XDA0450203, and the National Natural Science Foundation of China under Grant 62172392.
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A Technical Appendices and Supplementary Material
This supplementary material provides additional information support the main text. We present ex- tended methodological details in Section A.I, and elaborate implementation aspects in Section A.2. Section A.3 reports additional quantitative and qualitative results, while Section A.4 includes further ablation studies.
A.1 Method Details
Network architecture. Our dynamic MLP model consists of several modular components designed for ppatio-temporal deformation prediction and appearance modeling. The input 3D positions and timestamps are first encoded using positional encoders. Specifically, we use 6 frequency bands for both spatial and temporal encodings on the D-NeRF dataset, and 10 frequency bands on the NeRF-DS dataset, in accordance with the scene complexity and temporal resolution. When the Hierarchical Anchor Densification module is enabled, the encoded features are first processed by a lightweight two-layer MLP for anchor-level feature extraction. Notably, for all hierarchical levels beyond the first, the MLP additionally takes the positional encoding of the parent anchor's 's transformation AT' as input. Each level maintains its own independent MLP parameters without weight sharing. The network then processes the extracted features through three parallel branches: motion mask prediction, scene flow estimation, and deformation modeling.
The motion mask branch consists of a compact three-layer MLP that predicts a soft dynamic confi- dence via sigmoid activation, which modulates the outputs of subsequent branches during training. The scene flow branch is composed of a four-layer MI.P with skip connections and outputs forward and backward displacements support temporal feature aggregation. The core deformation branch consists of an eight-layer MLP with skip connections, followed by three independent prediction heads that separately regress the translation, scaling, and rotation parameters for each Gaussian.
We assign different numbers of motion anchors to each scene based on its motion complexity. For deformation interpolation, the number of nearest anchors is set to K=3. In the Hierarchical Anchor Densification module (Section 4.4), we set the threshold T to 0.75 to achieve optimal performance, and adapt the number of hierarchy levels according to the complexity of each scene.
A.2 More Implementation Details
The NeRF-DS dataset comprises seven stereo video sequences capturing everyday sce- narios with rapidly moving, reflective objects and varying camera viewpoints, presenting significant challenges for dynamic scene reconstruction. We use the default resolution 480x270 for all scenes for training and testing. We train the model using images from the left camera and test it on the right camera. The D-NeRF dataset comprises eight synthetic dynamic scenes with precise camera trajectories and ground-truth deformations. We use the default resolution 800x800 for all scenes for training and testing. Notably, we exclude the Lego scene from our evaluation due to a mismatch between the training and test sets, particularly in the flip angle of the Lego shovel, which has also been recognized in the Deformable 3DGS [44].
Datasets.
Optimization. The scheduler of the learning rate primarily follows Deformable 3DGS [44] and SC-GS [12]. The entire training process is conducted using the Adam optimizer on a single RTX 3090 GPU. The loss weights in Equation 9 are set to À 0.8, A, = 0.01, X2 0.2, and X 0.5. We further evaluate the effect of different weight settings on reconstruction performance in Section 4.5 using the NeRF-DS dataset, and select the optimal configuration based empirical results. We use a simple boddarr--basdd interpolation strategy to adjust loss weights over training steps. Given a list of step-value pairs, each weight is computed via logarithmic interpolation between neighboring landmarks, enabling smooth and stage-aware optimization.
A.3 More Results
We conduct additional quantitative comparisons on the D-NeRF dataset and evaluate all methods using PSNR, SSIM, and LPIPS(VGG) metrics. The results are summarized in Table 4. In addition, we further compare our method with more approaches on the NeRF-DS dataset, and present the quantitative results (PSNR) in Table 5. conduct quantitative comparison additional real-world
14

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Table 4. Additional quantitative comparison on D-NeRE dataset per-scene.
Jumping Jacks
Bouncing Balls
Mathod
PSNR1
SSIM?
1.PPS]]
PSNRT
SSIM
LPIPS
SSIM?
LPIPS]
PSNRT
SSIM
IPIPS..
TENeu [7]
30.51
0,959
0.060
33.46
0.977
0.041
31,43
0,967
0.017
10.28
0.992
0.012
D-NeRF [31]
29.02
0,959
0.054
32.70
0.977
0.038
30.61
0.967
0.053
38.
0.989
0.032
Tensor4D [33)
28.63
0.943
0.063
24.20
0.925
23.86
0,925
0.054
24.47
0.962
0.043
K-Planes [8]
28.12
0.948
0.066
31.11
0.970
0.046
30,45
0,973
0.034
40.05
0.032
SDGS [14]
21.70
0.886
0.104
20.64
0.929
0.106
21.91
0,953
0.055
23.20
0.958
0.060
4DGS [39]
32.95
0.977
0.027
35.50
0.986
0.020
33.95
0,985
0.022
10.77
0.991
0.015
SP-G8 [5]
35.36
0,980
0.018
35.56
0.995
0.024
40.53
Deformblle 3DGS [44]
37.06
0,986
0,016
37.66
0.989
0.015
57.56
0.993
0.010
40.91
0.995
0.009
SC-G8 (12)
38.79
0.990
0.011
99.34
0.992
0.008
39.53
0.994
0.009
41.59
0:995
0.009
0.013
39.79
0.997
0.009
41.63
Hell Warror
Muttntt
Standup
Mean
Mothod
PSNRT
SSIM?
LPPISS
PSNRT
SSIMT
LPIPS
PSNRT
SSIMT
LPPPS1
PSNRT
SSIMT
LPIPS.
TENeuVax [7]
27.29
0,961
0.076
32.07
0.961
0.048
34.46
0,980
0.033
32.78
0.971
0.0:9
D-NeRF [31]
24.06
0.944
0.070
30.31
0.967
0.039
33.13
0,978
0.035
31.14
0.968
0.945
Tensor4D (33)
31.26
0,925
0.073
29.11
0:945
30.56
0,958
0.036
27.44
0.056
K-Plines [8]
24.58
0,952
0.082
32,50
0:971
0.033
33,10
0.979
0.031
31.41
0:969
0.046
3DGS [14]
29.89
0.914
0.111
24.50
0.933
0.058
21.91
0.929
0.089
23.39
0.928
0.083
4DGS [39]
0.037
37.75
0.988
0,990
0.014
35.41
0.021
SP-G8 [S]
40.19
0.989
0.006
39.43
0.9%6
0.016
42,07
0.992
0.000
37:97
0:987
0.915
Detommalle 3DGS [44]
41.34
0,987
0.024
42.47
0.995
0.005
44.14
0.995
0.007
40. 16
0.991
0.012
SC-G8 [12]
42.19 19.19
0,989
0.019
43.43
0.996
0..035
46.72
0.997
0.004
0.991
0.009
Ours
42.50
0.993
0.021
43.65
0.998
0.005
46.83
0.999
0.004
42.00
0.996
0.010
Table 5. Additional quantitative comparison (PSNR1) on NeRF-DS dataset per-scene.
Method
Sieve
Plate
Bell
Press
Cup
As
Basin
Mean
SP-GS [5]
25.62
18.91
25.20
24.34
24.43
24.44
19.09
23.15
SoM [38]
26.32
20.58
25.97
25.41
24.55
26.29
19.66
24.11
MoSca [17]
26.45
21.13
26.11
26.53
24.91
26.17
20.28
24.51
GauFre [21]
24.88
20.00
25.24
25.05
24.04
26.05
19.54
23.64
MoDec-GS [16]
23.48
18.87
22.19
22.87
24.18
24.65
19.57
22.25
Ours
26.61
20.96
26.34
27.05
24.72
26.96
19.74
24.63
datasets: HyperNeRF(misc) [30] and Dycheck [10], and the PSNR results are presented in Table 6 and Table 7.
We report a comparison of average training computational cost between our method and existing approaches on the D-NeRF dataset, including training time, rendering FPS, and memory in Table 8, as well as detailed per-scene results in Table 9, We also report the statisties on NeRF-DS dataset in Table 10.
The additional qualitative results on the NeRF-DS dataset are provided in Figure 6. The additional qualitative results on the D-NeRF dataset are provided in Figure 7.
A.4 More Ablations
We summarize the additional ablation results of different combinations of key components in Table 11. In main paper, we have already provided ablation studies on different densification strategies. Figure presents qualitative results on regions with fine-grained motion, demonstrating that the HAD module effectively improves reconstruction quality in these areas. As shown in Table 1 11, extending the Bascline+IF setup with the HAD module (row 4) results in a noticeable performance gain, further supporting the effectiveness of HAD. And as shown in Table 11, extending the Baseline+IF setup with the AF module (row5) also leads to a performance improvement, indicating that AF effectively guides the Induced Flow MLP and Deformable MLP to focus on dynamic regions, thereby enhancing overall model performance. These ablations validate the design motivation of HAIF-GS.
We conduct additional ablation studies to evaluate the impact of the three loss terms introduced in our framework. The results are summarized in Table 12. It should be emphasized that À denotes the exclusion of the respective loss term.
15

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Table Additional quantitative comparison (PSNR1) HyperNeRF(miss)) dataset per-scene.
Americano
Cross-hands
Espresso
Keyboard
Oven-mitts
Split-cookic
Tamping
4DGS [39]
31.30
28.06
25.82
28.64
27.99
32,64
24.15
28.37
Deformable 3DGS [44]
30.87
27.70
25.47
28.15
27.51
32.63
23,95
28.04
30.94
28.83
26.58
28.54
27.65
33.20
23.79
28.50
Table 7. Additional quantitative comparison (PSNR1)) on Dycheck dataset per-scene.
Method
Apple
Block
Paper-windmill
Space-out
Spin
Teddy
Wheel
Mean
4DGS [39]
15.41
14.44
14.29
14.89
10.53
13.68
Deformable 3DGS [44]
15.61
14.87
14.89
14.59
13.10
11.20
11.79
13.72
Ours
15.51
14.64
16.13
15.45
16.59
12,91
14.12
15.05
Table Overall performance comparison on the D-NeRF dataset, including training time, rendering FPS, and GPU memory.
Method
PSNR
Training Time
FPS
Memory
4DGS [39]
35,41
26 min
134.8
1.1 GB
Deformable 3DGS [44]
40.16
38 min
53.7
4.8 GB
Ours
42.00
29 min
215.4
3.3 GB
Table
Per-scene performance on the D-NeRF dataset.
Scene
PSNRT
Queried Anchors
Training Time|
FPSt
Hook
39.38
604
38 min
211.4
Jumpingjacks
39.79
560
26 min
259.8
Trex
40.27
792
min
165.2
BounsingBalls
41.63
524
min
176.3
Hellwarrior
42.50
568
23 min
236.5
Mutant
43.65
588
35 min
208.8
Standup
46.83
572
27 min
249.5
Mean
42.00
601
29 min
215.4
Table Statistics of Motion Anchors NeRF-DS.
Scene
Sieve
Plate
Bell
Press
Cup
As
Basin
Mean
#Gaussians
114k
119k
185k
114k
118k
113k
130k
127k
#Anchors
3.7k
4.3k
4.4k
3.5k
3.9k
4.1k
4.9k
4.1k
Ratio
0.287
0.314
0.246
0.253
0.279
0.304
0.325
0.287
Table 11. Additional ablation study of key component combinations on NeRF-DS dataset.
Method
PSNR
MS-SSIMI
LPIPSL
Baseline
23.79
0.8513
0.1744
IF (w/o Loyele)
24.15
0.8705
0.1561
IF
24.28
0.8721
0.1505
IF HAD
24.45
0.8802
0.1488
IF AF
24.39
0.8774
0.1493
+ IF (w/o Loyete) + AF HAD
24.51
0.8947
0.1437
Ours (+IF + AF HAD)
24.63
0.9014
0.1342
16

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Table 12. Additional ablation study of the loss weights NeRF-DS dataset.
Aeyele
10
10
10-
10"
10
0
PSNRT
24.53
24.58
24.63
24.60
24.59
24.51
Ammrooy
10
10
10-1
10
10-3
PSNR1
24.58
25.57
24.62
24.60
24.58
24.55
Aquniiyy
10º
10"
10 1
10"²
10
0
PSNRT
24.60
24.63
24.63
24.58
24.58
24.56
Ground Truth
Ours
SP-GS
SC-GS
3DGS
As
Bell
Press
Sieve
Plate
Basin
Cup
Figure Additional qualitative comparison on NeRF-DS datasct [42].
17

---

Ground Truth
Ours
Deformable 3DGS
4DGS
3DGS
Hell Warrior
Jacks
Hook
Mutant:
StandUp
Trxx
Balls
Figure 7. Additional qualitative comparison on the D-NeRF dataset [31].
18

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Reviews:
[{"review_id": "rEbyhwRX9w", "reviewer": "Reviewer_be8H", "summary": "This paper proposes a framework, called HAIF-GS, for dynamic 3D reconstruction. The key to the proposed method is: 1) a sparse-anchor based motion representation, 2) a self-supervised induced flow-guided deformation module, 3) a hierarchical anchor propagation mechanism.", "questions": "Can authors provide some results (at least qualitative) for dynamic-static decomposition? (For example, render segmentation maps in novel view synthesis)", "limitations": "Yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strength: \n* The induced flow-guided deformation module is a reasonable design.\n* The proposed method surpasses existing baselines in quantitative evaluation.\nWeakness:\n* The design of sparse and hierarchical anchor-based motion representation has already be seen in existing works, for example: Y. Liang et. al., “HiMoR: Monocular Deformable Gaussian Reconstruction with Hierarchical Motion Representation”, CVPR 2025.", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for recognition of our contributions. We are glad that the reviewer considers “the induced flow-guided deformation module is a reasonable design” and acknowledges that our method “surpasses existing baselines in quantitative evaluation.”\n\n## Q1. Clarification on Relation to HiMoR.\n\nWe thank the reviewer for pointing out the relation to HiMoR [Liang et al., 2025], which also includes a hierarchical anchor design. While this module shares a structural resemblance, our method **follows a fundamentally different formulation and design goal**, addressing key challenges that HiMoR does not explicitly consider:\n\n* **Ensuring temporal consistency.** HiMoR models motion at each frame independently, without enforcing consistency across time. This limits its ability to learn smooth and coherent trajectories. In contrast, we propose an **Induced Flow-Guided Deformation** module that predicts forward and backward flow in a self-supervised manner. Combined with a **cycle consistency loss**, this encourages temporally aligned anchor motion throughout the sequence. We also appreciate that the reviewer recognized this component as a reasonable and well-designed part of our framework.\n\n* **Reducing reliance on external priors.** HiMoR depends on pretrained tracking, segmentation, and monocular depth models to initialize motion bases and guide training. Such reliance may limit its robustness in less controlled settings. Our framework is trained **fully end-to-end** using only photometric and temporal self-supervision, without any external annotations, making it more generalizable and deployment-friendly.\n* **Handling static regions efficiently.** HiMoR applies motion modeling uniformly across the scene, including static backgrounds, leading to unnecessary optimization and redundancy. Our method introduces an Anchor Filter that learns motion confidence for each anchor and filters out static ones, allowing the model to focus computation on dynamic regions and improve efficiency without sacrificing expressiveness.\n\nThese differences reflect a distinct design goal: adaptive, efficient, and self-supervised motion learning, rather than structure-driven modeling under external priors.  \n\nIn addition to the aforementioned contribution differences, we highlight several **methodological distinctions** from HiMoR regarding the sparse and hierarchical anchor design, as well as additional components in our system:\n\n* **Sparse anchors without external initialization.** HiMoR relies on pretrained tracking and depth models to initialize motion bases and nodes, while we adopt a simple FPS-based initialization and fully end-to-end optimization, enhancing generality and ease of use.\n* **Flexible hierarchical modeling.** While both methods use multi-level anchor structures, HiMoR applies a strict tree-structured SE(3) decomposition and recursively composes transformations. In contrast, we adopt layer-wise interpolation and confidence-based fusion, allowing each layer to contribute independently. This flexible design better handles complex motion and avoids the rigidity of explicit trees.\n* **Temporal flow-guided deformation.** HiMoR does not model inter-frame motion explicitly and applies no temporal flow estimation. We introduce a self-supervised flow prediction module that infers forward and backward anchor motion using multi-frame temporal queries, facilitating temporally consistent anchor trajectories and improving motion alignment across frames.\n* **Adaptive hierarchical densification.** HiMoR grows its tree by analyzing per-node neighborhoods, but its densification strategy is hand-designed and not adaptive to local motion complexity. In contrast, we quantify per-anchor motion variance and densify anchors hierarchically only in complex regions. This yields a more targeted and efficient refinement of motion representation.\n\nTo further validate this design, we compare our method with HiMoR on the **Dycheck-iPhone**[Gao et al., 2022] dataset using the same perceptual metric adopted in their paper. As shown in $\\underline{Table\\ 1}$ below, our method achieves a lower LPIPS score (ours: 0.405 vs. HiMoR: 0.463), indicating improved temporal consistency. This supports the effectiveness of our Induced Flow-Guided Deformation and other innovations in addressing the temporal challenges that HiMoR does not explicitly resolve. We have also incorporated a discussion of HiMoR as a recent anchor-based method into the main paper to provide clearer context and positioning.\n\n**Table1. Results(LPIPS↓) on Dycheck-iphone (HiMoR scores from [Liang et al., 2025])**\n\n| Method   | Apple | Block | Paper-windmill | Spin  | Teddy | $\\underline{Mean}$ |\n| -------- | ----- | ----- | -------------- | ----- | ----- | ------------------ |\n| HiMoR    | 0.592 | 0.505 | 0.321          | 0.369 | 0.529 | 0.463              |\n| **Ours** | 0.427 | 0.391 | 0.334          | 0.346 | 0.531 | **0.405**          |\n## Q2. Results for dynamic-static decomposition.\n\nWe appreciate the reviewer’s interest in the dynamic-static decomposition results. While we are unable to include images or external links due to rebuttal guidelines, we provide the following supporting evidence to demonstrate the effectiveness of our motion segmentation:\n\n* **Statistics of Motion Anchors.** We provide $\\underline{Table\\ 2}$ below reporting per-scene anchor-level motion decomposition on the NeRF-DS dataset. Specifically, #Gaussians denotes the total number of 3D Gaussians, #Dynamic Anchors is the number of Motion Anchors, and Dynamic Ratio represents the percentage of anchors predicted as dynamic (i.e., confidence > 0.5). As shown in the table, the predicted dynamic ratio is generally low, which matches the scene composition with mostly static content and limited motion, confirming the effectiveness of our decomposition. In *basin* and *plate*, where dynamic objects are more dominant, the ratio is higher, further supporting the segmentation accuracy.\n* **Spatial distribution of dynamic and static anchors.** We visualized the dynamic and static anchors on the NeRF-DS dataset. While we cannot include these figures here, the results show that dynamic anchors are predominantly concentrated around the central moving objects, whereas static anchors are distributed across the background. This spatial separation provides strong qualitative evidence of accurate dynamic-static decomposition. We have included anchor visualizations in the final version of the paper.\n* **Ablation impact.** As shown in Tab.3 in main paper, removing the dynamic-static segmentation module results in 0.18dB average PSNR drop on the D-NeRF dataset. This suggests that filtering static anchors improves both rendering quality and motion modeling efficiency.\n\n**Table2. Statistics of Motion Anchors on NeRF-DS**\n\n|      Scene       | Sieve | Plate | Bell  | Press | Cup   | As    | Basin | $\\underline{Mean}$ |\n| :--------------: | :---: | :---: | :---: | :---: | ----- | ----- | ----- | ------------------ |\n|    #Gaussians    | 114k  | 119k  | 185k  | 114k  | 118k  | 113k  | 130k  | 127k               |\n| #Dynamic Anchors | 3.7k  | 4.3k  | 4.4k  | 3.5k  | 3.9k  | 4.1k  | 4.9k  | 4.1k               |\n|  Dynamic Ratio   | 0.287 | 0.314 | 0.246 | 0.253 | 0.279 | 0.304 | 0.325 | 0.287              |\n\nWe have included visualization of segmentation masks from novel views in the final version of the paper. These will highlight temporally coherent motion boundaries, consistent with our confidence maps."}, {"review_id": "OrhxyR4S0V", "reviewer": "Reviewer_2Aoj", "summary": "The authors propose HAIF-GS, a sparse anchor-based dynamic Gaussian Splatting algorithm.\nIt separates dynamic and static anchors with an Anchor Filter, a Induced Flow-Guided Deformation module to estimate anchor motion with multi-frame feature aggregation to encourage temporal consistency, and a Hierarchical Anchor Propagation mechanism to help model complex motion with level-of-details.\nExperiments on D-NeRF and NeRF-DS shows superior quality over previous dynamic Gaussian baselines.", "questions": "I would love to see how HAIF-GS performs on more datasets, especially real-world ones with bigger movement like HyperNeRF dataset because a lot of the innovative components could be very sensitive to optimization curve and might fail if not enough multi-view clue is given. It's okay if it fails and the authors can list this as another limitation.\nI would also love to see dynamic results in video format if this is allowed during rebuttal.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\n- The proposed method shows consistent higher performance over other baselines in Table 1 and Table 2.\n- Anchor Filter, Inductive-Flow-Guided Deformation Module and Hierarchical Anchor Propagation mechanism are all novel and effective based on comprehensive ablation study in Table 3 and Figure 5.\n- Hierarchical sparse-anchor idea is novel and intuitive by introducing level-of-details into Sparse-Anchor-based GS.\n- The IFGD module induces forward/backward scene flow does not need ground-truth labels, and HAIF-GS is trained end-to-end in both training stages.\n\n\nWeakness:\n- Efficiency of the proposed method is listed as an advantage (e.g. in Line 43, \" a unified framework that significantly improves both the efficiency and accuracy of dynamic scene reconstruction\"), but no experimental results are yet to support the claim; also memory footprint is listed as a limitation in section A.5.\n- HAIF-GS is qualitatively not necessarily better than 4DGS in Figure 4.\n- SP-GS, as a sparse-anchor based method, is not compared quantitatively in Table 1 and Table 2, as a recent sparse-anchor competitor.\n- Results are only shown in D-NeRF and NeRF-DS dataset, which are from limited scenarios.\n- The paper currently lacks a clear and consistent storytelling trajectory. For example, in abstract, \"This challenge often manifests as three limitations in existing method...\", but in introduction, instead of expanding on the three limitations, the authors start to talk about two factors: \"This limitation is mainly due to two factors...\" \n- Lacking visualization of induced scene flow / static-dynamic separation.\n- The systems have a lot of hyperparameter to tune.", "was_revised": true, "final_justification": "The authors have addressed my major concerns during the rebuttal.", "rebuttal": "We thank the reviewer for the positive feedback. We are glad that the reviewer recognizes our method as “consistently higher performance over other baselines” and finds that “Anchor Filter, Inductive-Flow-Guided Deformation Module and Hierarchical Anchor Propagation mechanism are all novel and effective.”\n\n## Q1. Additional evaluation on more challenging real-world datasets.\n We thank the reviewer for the suggestion. We agree that further evaluation on more challenging scenes is important. Our original submission already includes real-world results on the NeRF-DS dataset. In response to the concern regarding potential failure in real-world dynamic scenes with limited multi-view clues, we conduct **additional evaluations on two challenging datasets**:\n* **HyperNeRF (misc)** [29] with topology change and limited multi-view cues;\n* **DyCheck-iPhone** [Gao et al., 2022], featuring large motion and difficult test viewpoints.\n\nAs shown in $\\underline{Table\\ 1\\ and\\ 2}$ below (PSNR↑), our method consistently outperforms D-3DGS and 4DGS on most scenes, especially under severe motion or topology changes. These results conform that the key modules in *HAIF-GS* (anchor filtering, hierarchical motion propagation, and the induced flow-guided deformation) remain stable and effective even under limited multi-view supervision or large non-rigid motion. Despite the potential sensitivity to the optimization process, our experiments show that these components do not collapse or diverge, and can still yield accurate reconstructions across diverse challenging scenes.\nWe have included these additional results and corresponding discussions in the final version of the paper.\n\n**Table1.  Results(PSNR↑) on HyperNeRF (misc)**\n\n|Method|Americano|Cross-hands| Espresso  | Keyboard  | Oven-mitts | Split-cookie |  Tamping  | $\\underline{Mean}$ |\n| :---------: | :-------: | :---------: | :-------: | :-------: | :--------: | :----------: | :-------: | :----------------: |\n|D-3DGS [44] |30.87|27.70|25.47|28.15|27.51|32.63|23.95|28.04|\n|4DGS [38] |31.30|28.06|25.82| **28.64** | **27.99**  |32.64| **24.15** |28.37|\n|**Ours**| **30.94** | **28.83** |**26.58**|28.54|27.64|**33.21**|23.79|**28.50**|\n\n**Table2. Results(PSNR↑) on Dycheck-iphone**\n\n|   Method    |   Apple   |   Block   | Paper-windmill | Space-out |   Spin    |   Teddy   |   Wheel   | $\\underline{Mean}$ |\n| :---------: | :-------: | :-------: | :------------: | :-------: | :-------: | :-------: | :-------: | :----------------: |\n| D-3DGS [44] |**15.61**|**14.87**|14.89|14.59|13.10|11.20|11.79|13.72|\n|  4DGS [38]  |15.41|13.89|14.44|14.29|14.89|12.31|10.53|13.68|\n|  **Ours**   |15.51|14.64|**16.13**| **15.45** | **16.59** |**12.91**|**14.12**|**15.05**|\n## Q2. Experimental evidence for efficiency.\n\nWe thank the reviewer for pointing this out. We now provide experimental results in $\\underline{Table\\ 3\\ and\\ 4}$ to support the efficiency claim. And we have added these results and analyses to the main paper.\n\nAs shown in $\\underline{Table\\ 3}$, our method achieves significantly faster rendering (**215.4 FPS**) than 4DGS (134.8) and D-3DGS (53.7), with a much lighter query structure. Despite the reduced cost, we achieve **higher PSNR (42.00)** than both baselines, owing to the **Induced Flow module**, which enables accurate deformation via sparse anchors. $\\underline{Table\\ 4}$ reports scene-wise statistics. All methods are tested on an RTX 3090 at 800×800 resolution.\n\nAs noted in Section A.5, We acknowledge the relatively larger memory usage due to additional anchor parameters and hierarchy management. However, our model (2.9GB) is still lighter than D-3DGS (4.8GB), striking a good balance between performance and storage. We plan to further optimize memory usage in future work by compressing anchor features or dynamically pruning less-contributing anchors during training.\n\n**Table3. Comparison of efficiency on D-NeRF dataset**\n\n|   Method   |   PSNR↑   | Training Time↓ | Render FPS↑ | Storage↓ |\n| :--------: | :-------: | :------------: | :---------: | :------: |\n|4DGS[38]|35.41|26min|134.8|1.1GB|\n|D-3DGS[44]|40.16|38min|53.7|4.8GB|\n|**Ours**| **42.00** |29min|**215.4**|2.9GB|\n\n**Table4. Evaluation of efficiency on D-NeRF dataset**\n\n|Scene| PSNR↑ | Queried Anchors | Training Time↓ | Render FPS↑ |\n| :----------------: | :---: | :-------------: | :------------: | :---------: |\n| Hook| 39.38 |604|38min|211.4|\n|Jumpingjacks| 39.79 |560|26min| 259.8 |\n|Trex|40.27|792|41min|165.2|\n|BouncingBalls|41.63|524|21min|176.3|\n|Hellwarrior| 42.50 |568|23min|236.5|\n|Mutant|43.65|588| 35min|208.8|\n|Standup|46.83|572|27min|249.5|\n| $\\underline{Mean}$ |42.00|601|29min|215.4|\n\n## Q3. Quantitative comparison with SP-GS.\nWe thank the reviewer for the comment. As shown in $\\underline{Table\\ 5}$, our method outperforms SP-GS[5] on ***NeRF-DS*** (24.63 vs. 23.15) and ***D-NeRF*** (42.00 vs. 37.97; see $\\underline{Appendix\\ A.4}$). Due to space limits, we included only one sparse-anchor baseline in the main paper, choosing the more recent and competitive SC-GS[12] (24.05 / 41.65) over SP-GS.\nWe have added full comparisons in the final version.\n\n**Table5. Comparison(PSNR) with SP-GS on NeRF-DS**\n\n|Method|Sieve|Plate|Bell| Press|Cup|As|Basin| $\\underline{Mean}$|\n| :-------: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :----------------: |\n|SP-GS [5]|25.62|18.91| 25.20 | 24.34 | 24.43| 24.44|19.09 |23.15|\n|**Ours**|26.61| 20.96 | 26.34 | 27.05 | 24.72| 26.96 |19.74|**24.63**|\n\n## Q4. Storyline consistency.\nWe thank the reviewer for the feedback on storyline clarity. To clarify, let us briefly explain the reasoning behind this organization. The three limitations mentioned in the abstract are addressed sequentially: (1) redundant Gaussian updates motivates our sparse anchor design, while (2) and (3) are further analyzed as two underlying challenges —limited expressiveness and insufficient supervision— caused by previous anchor-based methods. Our three modules (Motion Anchors, IFGD, and Hierarchical Anchors) correspond directly to these limitations. We have revised the abstract and introduction to clarify this mapping and ensure better consistency in presentation.\n## Q5. Clarification on Qualitative comparison in Figure 4.\nWe thank the reviewer for the suggestion. The qualitative results in Figure 4 highlight our method’s **superiority in modeling fine-grained details** (red-circled regions) over 4DGS. For instance, in *HellWarrior*, we reconstruct armor rivets and straps missed by 4DGS; in *Hook*, joint textures are sharp, while 4DGS remains vague. These qualitative differences, along with significant PSNR gains (+13.7dB on *HellWarrior*, +6.4dB on *Hook*), demonstrate our strength in capturing local deformations. As D-NeRF scenes are object-centric with simple global structure, performance differences mainly manifest in such fine details—where our method excels.\nWe will consider including more diverse viewpoints in the final version.\n## Q6. Visualization and video results.  \nWe thank the reviewer for the valuable suggestion. Due to the rebuttal policy restricting figures and external links, we are unable to directly provide visualizations of the **induced scene flow**, **dynamic-static separation**, and **video results**. Nevertheless, we have addressed these points indirectly in our response and **will include all three in the final version and on the project page**.\n### 1. dynamic-static separation\nDespite visualization constraints, we provide the following evidence to support the effectiveness of our motion segmentation:\n* **Anchor-level statistics.** $\\underline{Table\\ 6}$ below reports per-scene motion decomposition on NeRF-DS, including total Gaussians, number of dynamic anchors, and the dynamic ratio (anchors with confidence > 0.5). The overall dynamic ratio is low, aligning with the mostly static content of the scenes.\n* **Spatial distribution.** Visualizations (included in the final version) reveal that dynamic anchors cluster around moving objects, while static anchors are background-distributed, qualitatively confirming correct separation.\n* **Ablation results.** Removing this module causes a 0.18dB PSNR drop on D-NeRF (Tab. 3), indicating that filtering static anchors improves both quality and efficiency.\n\n**Table6. Statistics of Motion Anchors on NeRF-DS**\n\n|Scene| Sieve | Plate | Bell|Press | Cup| As|Basin| $\\underline{Mean}$ |\n| :--------------: | :---: | :---: | :---: | :---: | ----- | ----- | ----- | ------------------ |\n|#Gaussians|114k|119k|185k|114k|118k|113k|130k|127k|\n|#Dynamic Anchors| 3.7k|4.3k|4.4k|3.5k|3.9k|4.1k|4.9k|4.1k|\n|Dynamic Ratio| 0.287 |0.314|0.246|0.253|0.279|0.304 |0.325|0.287|\n\n### 2. induced scene flow\nDespite visualization constraints, we clarify that:\n* **Visualization is possible and prepared.** The induced flow can be visualized as 3D vectors at anchor locations. We have produced such visualizations and will release them in the final version and on the project page.\n* **Nature of the induced flow.** The induced scene flow is not a directly supervised or dense optical flow field. Instead, it is a **sparse, anchor-level motion signal** induced implicitly through multi-frame alignment and cycle consistency loss. Its purpose is not to produce explicit flow output, but to **serve as internal guidance** for temporally consistent deformation. While visualizations are possible and will be provided, we believe the most appropriate way to assess its effectiveness is **through its quantitative impact on rendering quality and motion stability**.\n* **Quantitative validation.** As shown in Tab.3 in main paper, removing the induced flow module results in a significant drop in rendering quality (PSNR ↓0.72, LPIPS ↑0.028 on NeRF-DS), confirming its importance in motion modeling.\n### 3. video results\nWe have created a demo video showcasing dynamic reconstruction from novel views on both NeRF-DS and D-NeRF datasets, which will be released on our project page."}, {"review_id": "HJh8Gu046t", "reviewer": "Reviewer_g5h3", "summary": "This work first mentions three limitations in existing monocular dynamic 3DGS methods, i.e. redundant Gaussian updates, insufficient motion supervision, and weak modeling of complex non-rigid deformations. This work further proposes HAIF-GS for these issues, which includes Anchor Filter for identifying motion-relevant regions, Induced Flow-Guided Deformation using multi-frame feature aggregation, and Hierarchical Anchor Densification for progressively modeling fine-grained deformations.", "questions": "* After reviewing the method proposed in this work, I was a little worried about its training and rendering efficiency, but I didn't find relevant descriptions in the submitted manuscript. What is the training and rendering time of the proposed method?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "* Strengths\n  * This work proposes the pipeline HAIF-GS for monocular dynamic 3DGS, which mainly includes motion anchors (the motion basis for modeling motions), an induced flow-guided deformation module, and a coarse-to-fine hierarchical anchor densification strategy. These modules are interesting and make sense.\n\n\n* Weakness\n  * This work mentioned that \"Figure 1 (b) shows hand motion, where the fine-scale appearance and localized movement highlight the challenges of modeling fine-grained dynamics in dynamic reconstruction\". But this claim cannot effectively convince me, since 4DGS and D-3DGS are not designed for the monocular setting. The qualitative experiments shown in Figure 1 can most importantly illustrate that previous multi-view dynamic 3DGS methods cannot be effectively generalized to the monocular setting. By the way, Figure 1 (a) does not appear to be referenced in the main manuscript. \n  * Although this work proposes a series of interesting designs, it lacks sufficient experiments to demonstrate the advancedness and effectiveness of its sophisticated design. Specifically, more quantitative experiments of previous monocular dynamic 3DGS methods are supposed to be implemented, since current reported results of dynamic methods mainly focus on multi-view methods. This work should complement the already open-sourced monocular dynamic 3DGS methods, like Shape of Motion [A] and MoSca [B]. Furthermore, more quantitative experimental results of ablation combinations should be added. At least the baseline (w/o IF, L_{cycle}, AF, HAD) result is supposed to be reported.\n  * Typos. \"suppresses\" to \"suppress\" in Line 11.\n\n[A] Wang Q, Ye V, Gao H, et al. Shape of motion: 4d reconstruction from a single video[J]. arXiv preprint arXiv:2407.13764, 2024.\n\n[B] Lei J, Weng Y, Harley A W, et al. Mosca: Dynamic gaussian fusion from casual videos via 4d motion scaffolds[C]//Proceedings of the Computer Vision and Pattern Recognition Conference. 2025: 6165-6177.", "was_revised": true, "final_justification": "I have increased the score to 4(BA). The rebuttal and discussion have addressed most of my concerns, and the proposed method using visual priors shows improvement over MoSca. The reason why I did not give a higher score is that I have comprehensively considered the innovation of this work, the performance reflected by the experiments in the main manuscript, and the experiments supplemented during the rebuttal and discussion. I think the score of 4 (BA) is reasonable.", "rebuttal": "We thank the reviewer for the positive comments. We are glad that the reviewer finds our proposed modules “interesting and make sense,” including the motion anchors, induced flow-guided deformation module, and the coarse-to-fine hierarchical anchor densification strategy.\n\n## Q1. Clarification on Monocular Baselines.\n\nWe appreciate the reviewer’s comments and the suggested works **Shape of Motion(SoM)**[Wang et al., 2024] and **MoSca**[Lei et al., 2025]. \n\nFirst, we would like to clarify that **all baselines** used in Figure 1(b) and our experiments are strong and widely adopted **monocular** methods, and thus all our experimental comparisons and analyses are **fair** and appropriate. We will also explicitly clarify the monocular setting of these baselines in the final version to avoid potential misunderstandings.\n\nIn Figure 1(b), *4DGS*[38] and *D-3DGS*[44] are both widely recognized and frequently used in the monocular dynamic reconstruction literature. **Notably, *SoM* and *MoSca* suggested by the reviewer also adopt these baselines under monocular settings**: SoM compares against D-3DGS, and MoSca includes 4DGS in its main evaluation. This further supports the relevance of using *4DGS* and *D-3DGS* in Figure 1(b) to highlight the limitations of prior approaches in modeling fine-grained, non-rigid motion.\n\nBeyond Figure 1, all baselines used in our experiments (e.g., *SC-GS*[12], *HyperNeRF*[29]) are either designed for or widely used in monocular dynamic reconstruction, and all evaluations are conducted under monocular training settings. Additionally, we have added SoM and MoSca as additional baselines in our main experiments, and we will detail the corresponding results in the response to $\\underline{Q2}$.\n\nWe have also revised the manuscript to reference Figure 1(a) in the introduction.\n\n## Q2. Quantitative Comparison with MoSca/SoM.\n\nWe thank the reviewer for emphasizing the importance of including **additional comparisons with SoM and MoSca**, two recently released monocular methods. Both SoM and MoSca follow the paradigm of end-to-end learning from video data using high-level vision priors, in contrast to our method and prior works such as 4DGS, D-3DGS, and recent CVPR 2025 papers like HiMoR [Liang et al., 2025], which adopt explicit 3D modeling based on deformable Gaussian splatting.\n\nIn response, we conduct additional experiments on the **NeRF-DS** dataset, comparing our method with SoM and MoSca, as shown in $\\underline{Table\\ 1}$ below. These results show that our method outperforms (24.63) both SoM (24.11) and MoSca (24.51) in most scenes, achieving consistently higher reconstruction quality. It is worth noting that **SoM and MoSca rely on pretrained vision foundation models (VFMs) and depth priors**, which offer clear advantages on datasets with available depth. However, NeRF-DS provides no depth prior, making it a more challenging benchmark for evaluating monocular methods. In this setting, our method demonstrates better performance while remaining lightweight and free of external dependencies, such as pretrained models or auxiliary signals.\n\nThis improvement stems from our 3DGS-specific design, including sparse motion anchors, induced flow-guided deformation, and hierarchical anchor densification, which together enable accurate dynamic modeling under purely monocular supervision.\n\nWe have also included MoSca and SoM as comparison baselines in the final version of the paper, further strengthening the completeness of our evaluation.\n\n**Table1. Comparison(PSNR↑) with SP-GS on NeRF-DS**\n\n\n|  Method  | Sieve | Plate | Bell  | Press |  Cup  |  As   | Basin | $\\underline{Mean}$ |\n| :------: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :----------------: |\n|   SoM    | 26.32 | 20.58 | 25.97 | 25.41 | 24.55 | 26.29 | 19.66 |       24.11        |\n|  MoSca   | 26.45 | 21.13 | 26.11 | 26.53 | 24.91 | 26.17 | 20.28 |       24.51        |\n| **Ours** | 26.61 | 20.96 | 26.34 | 27.05 | 24.72 | 26.96 | 19.74 |     **24.63**      |\n\n\n\n## Q3. Additional ablation combinations and baseline without key modules.\n\nWe thank the reviewer for the suggestion. In response, we report additional combinations in $\\underline{Table\\ 2}$ below, including the complete baseline without all key modules (w/o Induced Flow (IF), Cycle Consistency Loss ($L_{cycle}$), Anchor Filtering (AF), and Hierarchical Anchor Densification (HAD)). Our original submission ($\\underline{Appendix A.4}$) also includes an ablation study of loss weights settings.\n\nThe results show that each component contributes to performance, and their combination leads to significant improvements. In particular, removing induced flow and HAD results in clear drops in both reconstruction quality and consistency, confirming their central roles. These ablations validate the design motivation of HAIF-GS.\n\nWe have added the baseline configuration to the main ablation section in the revised paper and included all additional ablation combinations in the supplementary material.\n\n**Table2. Additional ablations on the key components on NeRF-DS.**\n\n|       Method        | PSNR↑ | MS-SSIM↑ | LPIPS↓ |\n| :-----------------: | :---: | :------: | :----: |\n|     w/o **IF**      | 23.91 |  0.8629  | 0.1624 |\n| w/o **$L_{cycle}$** | 24.51 |  0.8947  | 0.1437 |\n|     w/o **AF**      | 24.45 |  0.8802  | 0.1488 |\n|     w/o **HAD**     | 24.39 |  0.8774  | 0.1493 |\n|    w/o **IF+AF**    | 23.84 |  0.8638  | 0.1644 |\n|   w/o **IF+HAD**    | 23.78 |  0.8521  | 0.1749 |\n|    **baseline**     | 23.79 |  0.8513  | 0.1744 |\n|      **Ours**       | 24.63 |  0.9014  | 0.1342 |\n\n\n\n## Q4. Training and Rendering Efficiency.\n\nWe thank the reviewer for the helpful suggestion regarding efficiency. We have conducted extensive evaluations on the D-NeRF dataset (see $\\underline{Table\\ 3\\ and\\ 4}$ below). Our method achieves **real-time rendering speed (215.4 FPS)** while maintaining superior reconstruction quality (**PSNR 42.00**), outperforming both 4DGS and D-3DGS. These results demonstrate that our approach preserves the efficiency advantage of the 3DGS paradigm, while achieving significant gains in reconstruction quality. $\\underline{Table\\ 4}$ presents detailed statistics of our method on each D-NeRF scene. All methods are evaluated on an RTX 3090 GPU at a resolution of 800×800.\n\nWe have included this efficiency evaluation in the final version of the paper to better support the practical value of our method.\n\n**Table3. Comparison of efficiency on D-NeRF dataset**\n\n|   Method   |   PSNR↑   | Training Time↓ | Render FPS↑ |\n| :--------: | :-------: | :------------: | :---------: |\n|  4DGS[38]  |   35.41   |     26min      |    134.8    |\n| D-3DGS[44] |   40.16   |     38min      |    53.7     |\n|  **Ours**  | **42.00** |     29min      |  **215.4**  |\n\n**Table4. Evaluation of efficiency on D-NeRF dataset**\n\n|       Scene        | PSNR↑ | Queried Anchors | Training Time↓ | Render FPS↑ |\n| :----------------: | :---: | :-------------: | :------------: | :---------: |\n|        Hook        | 39.38 |       604       |     38min      |    211.4    |\n|    Jumpingjacks    | 39.79 |       560       |     26min      |    259.8    |\n|        Trex        | 40.27 |       792       |     41min      |    165.2    |\n|   BouncingBalls    | 41.63 |       524       |     21min      |    176.3    |\n|    Hellwarrior     | 42.50 |       568       |     23min      |    236.5    |\n|       Mutant       | 43.65 |       588       |     35min      |    208.8    |\n|      Standup       | 46.83 |       572       |     27min      |    249.5    |\n| $\\underline{Mean}$ | 42.00 |       601       |     29min      |    215.4    |\n\n\n**Typos:** Thank you for pointing this out. We have corrected the typo accordingly."}, {"review_id": "1JucDu9kXg", "reviewer": "Reviewer_CwJy", "summary": "This paper proposes a novel method for monocular dynamic reconstruction, named HAIF-GS, which enhances sparse motion anchor-based deformation with anchor filters, self-supervised induced flow and anchor densify mechanism to capture fine-grained and complex deformation fields. Experimental results show that HAIF-GS achieves state-of-the-art performance across various scenes on two popular datasets, and the visual comparison is convincing.", "questions": "See \"Weakness\"", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:** \n\n1. This paper proposes a novel method for monocular dynamic reconstruction, named HAIF-GS, achieving state-of-the-art performance across various scenes.\n2. The architecture of induced flow-guided deformation as well as the cycle loss, is interesting and intuitive.\n3. The paper is well-written and well-organized.\n\n**Weakness:**\n\nMy major concerns about this paper are the experiment settings, especially the comparison with \"MoSca: Dynamic Gaussian Fusion from Casual Videos via 4D Motion Scaffolds\" / \"Shape of Motion:\n4D Reconstruction from a Single Video\". I've found that when talking about reconstructing dynamic 3D scenes from monocular videos, existing works either follow MoSca/SoM and conduct experiments on DyChek/iphone/DAVIS datasets or compare with 4DGS / Deformable 3D-GS. I believe clarification is needed in the introduction or limitation section. Can this method apply to iphon/DAVIS dataset?  If not, please give some explanation of the limitations and some failure cases. If yes, can you provide some comparison with MoSca/SoM? **I'll raise my rating if this point is well-discussed in the rebuttal.**\n\nHere are some minor concerns, mainly on the readability of this paper.\n1. From lines 184-192, I highly recommend adding more formulas to describe the architecture. Without the help of Figure 2, it's difficult to understand the design of MLPs.\n2. For the ablation studies, can you provide the visual comparison of scene flows with and without $L_{cycle}$ to validate the effectiveness of this loss function?\n3. Also, for the ablation studies, can you provide the visual comparison of anchor points before and after densification to indicate that the densification mainly works on the regions containing complex and fine-grained motions?", "was_revised": true, "final_justification": "While the authors have addressed most reviewer concerns, I remain concerned about the ambiguous relationship between two paradigms: (1) end-to-end learning from video data using high-level vision priors (e.g., MoSca and SoM), and (2) explicit 3D modeling with deformable Gaussian splatting (e.g., Deformable 3D-GS and 4DGS). For monocular video-based 4D reconstruction, it is unclear whether these approaches constitute distinct paradigms given their identical inputs and outputs (the introduction of vision priors makes no difference). If they do not, the method’s limited generalizability is demonstrated by its marginal gains on NeRF-DS and significant performance decline on the iPhone dataset (more challenging and realistic) when compared to MoSca/SoM. Consequently, I maintain my final rating to highlight this issue for all the researchers.\n\nHaving seen the supplementary experimental results, which largely address my concerns about this method, I'll raise my rating to 4. Borderline Accept.", "rebuttal": "We thank the reviewer for the encouraging feedback. We are glad that the reviewer finds our method “achieving state-of-the-art performance across various scenes,” and considers the design of the induced flow-guided deformation and cycle loss to be “interesting and intuitive.”\n\n## Q1. Discussion on Method Paradigms and Our Positioning. \n\nWe thank the reviewer for raising this important question regarding our relation to **MoSca**[Lei et al., 2025] and **Shape-of-Motion(SoM)**[Wang et al., 2024]. As the reviewer pointed out, recent dynamic 3D reconstruction approaches tend to follow two distinct paradigms:\n\n1. **end-to-end learning from video data using high-level vision priors**, as in *MoSca* and *SoM*; \n\n2. **explicit 3D modeling based on deformable Gaussian splatting**, as in *Deformable 3D-GS(D-3DGS)*[44], *4DGS*[38], as well as recent CVPR 2025 papers *HiMoR* [Liang et al., 2025] and *MoDec-GS* [Kwak et al., 2025]. \n\nOur work clearly belongs to the latter, where we build structured, interpretable deformation fields over explicit Gaussian representations. This difference in paradigm reflects fundamentally different design principles—our method favors geometric control and weak supervision, whereas MoSca/SoM rely on pretrained vision foundation models (VFM) and additional external signals.\n\n## Q2. Applicability to iPhone Dataset and Comparison with MoSca/SoM.\n\nIn response to the reviewer’s suggestion,  we have conducted **supplementary experiments on the DyCheck-iPhone dataset**, also used by MoSca and SoM. Our method is fully compatible with this dataset and achieves **higher PSNR (15.05) than 4DGS(13.68) and D-3DGS(13.72)**, though **lower than MoSca(19.32) and SoM(17.32)**, as shown in the $\\underline{Table\\ 1}$ below.\n\nWe emphasize, however, that this performance gap is understandable due to the fundamentally different paradigms and resulting experimental settings.\n\n* **Challenging properties of the iPhone dataset.** It involves strong non-rigid motion, large camera baselines, and noisy depth priors—all of which are known challenges in dynamic 3D reconstruction, especially when no auxiliary supervision is used.\n* **Heavy reliance on pretrained vision foundation models.** MoSca leverages powerful pretrained components (e.g., BootsTAPIR) to obtain high-quality optical flow and depth, which significantly improve reconstruction but come with high computational cost and less interpretability.\n* **Access to ground-truth depth during training.** MoSca further utilizes the iPhone dataset’s provided depth maps as ground-truth supervision, while our method operates **entirely without depth supervision**, making it applicable to real-world settings where such data is unavailable.\n\nDespite these differences, our approach achieves strong performance on the iPhone dataset and **outperforms prior explicit modeling methods (4DGS, D-3DGS)**, validating its effectiveness within its paradigm. Its lightweight and interpretable design makes it more suitable for general deployment compared to end-to-end alternatives. \n\nWe really appreciate the reviewer for pointing out this important connection. We have revised the final version of the Introduction to include a discussion on MoSca/SoM-style approaches and clarified the paradigm-level distinctions between methods.\n\n**Table1. Results(PSNR↑) on Dycheck-iphone dataset**\n\n| Method | Apple | Block | Paper-windmill | Space-out | Spin  | Teddy | Wheel | $\\underline{Mean}$  |\n| :---------------------: | :---: | :---: | :------------: | :-------: | :---: | :---: | :---: | :----------: |\n| MoSca[Lei et al., 2025] | 19.40 | 18.06 | 22.34| 20.48| 21.31 | 15.47 | 18.17 | **19.32**|\n| SoM[Wang et al., 2024]  | 18.57 | 17.41 | 18.14| 16.85| 19.35 | 13.69 | 17.21 | 17.32|\n| D-3DGS [44] | 15.61 | 14.87 | 14.89| 14.59|13.10|11.20| 11.79 | 13.72|\n| 4DGS [38]| 15.41 | 13.89 | 14.44| 14.29|14.89|12.31| 10.53 | 13.68|\n| **Ours** | 15.51 | 14.64 | 16.13 | 15.45 |16.59|12.91| 14.12 | **15.05** |\n\nFurthermore, this discussion inspires an exciting direction for future work. With the rapid advances of vision foundation models (VFMs), such as the recent VGGT [Wang et al., 2025], we recognize the growing potential of incorporating VFM-derived signals to address long-standing challenges in the 3DGS-based paradigm, including inaccurate camera poses and inefficient prior point cloud initialization. A promising research avenue lies in bridging the two paradigms, aiming to combine the controllability and efficiency of explicit Gaussian modeling with the powerful priors and robustness offered by VFMs.\n\n\n\n## Q3. Formalization of Temporal Feature Aggregation.\n\nWe appreciate the reviewer for the helpful suggestion. While the original text describes the core idea of temporal aggregation (Lines 184-192), we agree that presenting the information flow more formally would further enhance clarity and self-containment, especially without relying on Figure 2.\n\nBelow we provide a more structured and formalized version of this part, which we will include in the final camera-ready version.\n\n1. Given a motion anchor $x$ at timestamp $t$, the Induced Flow MLP predicts forward and backward flows:\n$$\nF^{t-1},\\ F^{t+1} = \\\\text{MLP}_{\\\\text{flow}}(x,\\ t)\n$$\n2. These flows define three temporally shifted queries:  \n$$\nq_{t-1} = (x + F^{t-1},\\ t{-}1),\\quad \nq_t = (x,\\ t),\\quad \nq_{t+1} = (x + F^{t+1},\\ t{+}1)\n$$\n\n3. Each query is passed through a shared Deformable MLP to extract a time-aware feature embedding: \n(Due to rendering issues on OpenReview, we temporarily replace $q_{t-1}$ and $q_{t+1}$ with $q1$和$q2$ below)\n\n$$\nf_{t-1} = \\\\text{MLP}_{\\\\text{deform}}(q1)\n$$\n\n$$\nf_t = \\\\text{MLP}_{\\\\text{deform}}(q_t)\n$$\n\n$$\nf_{t+1} = \\\\text{MLP}_{\\\\text{deform}}(q2)\n$$\n\n4. The final temporally aggregated feature is computed as: \n(Due to rendering issues on OpenReview, we temporarily replace $f_{t-1}$ and $f_{t+1}$ with $f1$和$f2$ below)\n$$\n\\\\tilde{f}_t = \\\\lambda f_1 + (1 - 2\\\\lambda) f_t + \\\\lambda f_2\n$$\n\nThis formalization makes the process more transparent and easier to follow without relying on Figure 2. We appreciate the reviewer’s suggestion and will incorporate this revision into the main paper.\n\n## Q3. Visualization of scene flow and anchor densification.\n\nWe thank the reviewer for the valuable suggestion. Due to the rebuttal policy restricting figures and external links, we are unable to directly provide visualizations of the **induced scene flow** and **anchor densification**. Nevertheless, we have addressed these points indirectly in our response and **will include both two in the final version and on the project page**.\n\n### 1. Scene flow without Cycle Consistency Loss.\n\nWe thank the reviewer for the suggestion and understand the motivation behind visualizing the induced scene flow with and without the cycle consistency loss ($L_{cycle}$) to better illustrate the ablation effects. Such visualizations can indeed be provided.\n\nHowever, it is important to note that in our framework, the induced flow is not defined at the Gaussian level, but is instead computed **at the anchor level** and serves as an **internal supervisory signal** to guide motion learning. Since it is generated in a **frame-specific and anchor-driven** manner, the visualized flow field may not directly reflect global motion or deformation patterns. As a result, while the flow visualizations can highlight certain local differences (e.g., smoother or more consistent directions), their overall interpretability may be limited compared to direct **quantitative comparisons**.\n\nThat said, we have examined the induced scene flow qualitatively on D-NeRF. Without $L_{cycle}$, we observe:\n\n* **asymmetric forward and backward flows**, failing to form closed temporal paths;\n* **increased noise** in motion vectors, especially near thin or fast-moving regions (e.g., limbs, fingers);\n* **temporal jitter** in dynamic parts of the flow field, disrupting inter-frame coherence.\n\nThese artifacts result in degraded deformation quality and ultimately lower rendering performance. We believe the most appropriate way to assess the effectiveness of $L_ {cycle}$ is through its quantitative impact on rendering quality and temporal consistency. As shown in the ablation study in Table 3 of the main paper, removing $L_{cycle}$ leads to a 0.12 PSNR drop, indicating its contribution to learning temporally coherent deformations.\n\n### 2. Visual Comparison of Anchor Points Before and After Densification.\n\nWe thank the reviewer for the suggestion and understand the motivation to verify whether densification focuses on regions with complex and fine-grained motion. Such visualizations can be provided, and we will include them in the final version as well as on our project page.\n\nWe visualize anchor positions on D-NeRF scenes by rendering them together with the novel-view images. In *JumpingJacks*, densified anchors appear around limb-related parent anchors, with finer anchors added at the fingers. In *Hook* and *HellWarrior*, densification mainly occurs at joint regions with fine-grained deformations. These patterns match the areas where our method shows clearer motion reconstruction in Fig. 4 of the main paper, confirming that our hierarchical anchor densification (HAD) adaptively refines motion-complex regions rather than uniformly increasing anchor count. This is also supported by the ablation in Fig. 5 of the main paper.\n\n### Reference\n\n[1] Yiming Liang, Tianhan Xu, and Yuta Kikuchi. Himor: Monocular deformable gaussian\nreconstruction with hierarchical motion representation. In Proceedings of the Computer Vision\nand Pattern Recognition Conference, pages 886–895, 2025. 17\n\n[2] Sangwoon Kwak, Joonsoo Kim, Jun Young Jeong, Won-Sik Cheong, Jihyong Oh, and Munchurl\nKim. Modec-gs: Global-to-local motion decomposition and temporal interval adjustment for\ncompact dynamic 3d gaussian splatting. In Proceedings of the IEEE/CVF Conference on\nComputer Vision and Pattern Recognition (CVPR), 2025. 17"}]

Author rebuttal:

Meta-review: The paper receives 1 borderline reject and 3 borderline accept. Initially, the reviewers have various concerns about some technical clarity and mainly experimental results (more datasets, comparisons to other methods, ablation study, efficiency analysis). During and after the rebuttal, there were extensive discussions on these points, especially the comparisons with MoSca/SoM using the stronger priors, in which two reviewers were finally satisfied with the additional results and thus raised the rating. The AC closely checks the paper, reviews, rebuttal, and the discussed points, and agrees with the assessment from the majority of reviewers (in which the reviewer be8H who remains negative has not participated in the discussion after rebuttal). Therefore, the AC recommends the acceptance rating and encourages the authors to incorporate the suggestions and additional results raised by the reviewers in the final version, as well as releasing the model and code for reproducibility.
Decision: Accept (poster)