Flow Distillation Sampling: Regularizing 3D Gaussians with Pre-trained Matching Priors
Authors: Lin-Zhuo Chen
Kangjie Liu
Youtian Lin
Zhihao Li
Siyu Zhu
Xun Cao
Yao Yao
Venue: ICLR 2025 Poster (2025)
Keywords: 3D Vision
Differentiable Rendering
3D Gaussian Splatting
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: 3D Gaussian Splatting (3DGS) has achieved excellent rendering quality with fast training and rendering speed. However, its optimization process lacks explicit geometric constraints, leading to suboptimal geometric reconstruction in regions with sparse or no observational input views. In this work, we try to mitigate the issue by incorporating a pre-trained matching prior to the 3DGS optimization process. We introduce Flow Distillation Sampling (FDS), a technique that leverages pre-trained geometric knowledge to bolster the accuracy of the Gaussian radiance field. Our method employs a strategic sampling technique to target unobserved views adjacent to the input views, utilizing the optical flow calculated from the matching model (Prior Flow) to guide the flow analytically calculated from the 3DGS geometry (Radiance Flow). Comprehensive experiments in depth rendering, mesh reconstruction, and novel view synthesis showcase the significant advantages of FDS over state-of-the-art methods. Additionally, our interpretive experiments and analysis aim to shed light on the effects of FDS on geometric accuracy and rendering quality, potentially providing readers with insights into its performance.

Published as a conference paper at ICLR 2025
FLOW DISTILLATION SAMPLING: REGULARIZING 3D GAUSSIANS WITH PRE-TRAINED MATCHING PRIORS
Lin-Zhuo Chen Nanjing University
Kangjee Liu Nanjing University
Youtian Lin Nanjing University
Zhihao Li Huawei Noah's 's Ark Lab
Siyu Zhu
Xun Cao
Yao Yao
Fudan University
Nanjing University
Nanjing University
ABSTRACT
3D Gaussian Splatting (3DGS) has achieved excellent rendering quality with fast training and rendering speed. However, its optimization process lacks explicit geometric constraints, leading to suboptimal geometric reconstruction in regions with sparse or no observational input views. In this work, we try to mitigate the issue by incorporating a pre-trained matching prior to the 3DGS optimization process. We introduce Flow Distillation Sampling (FDS), technique that leverages pre-trained geometric knowledge to bolster the accuracy of the Gaussian radiance field. Our method employs strategic sampling technique to target unobserved views adjacent to the input views, utilizing the optical flow calculated from the matching model (Prior Flow) to guide the flow analytically calculated from the 3DGS geometry (Radiance Flow). Comprehensive experiments in depth rendering, mesh reconstruction, and novel view synthesis showcase the significant advantages of FDS over state-of-the-an methods. Additionally, our interpretive experiments and analysis aim to shed light on the effects of FDS on geometric accuracy and rendering quality, potentially providing readers with insights into its performance. Project page: https: jnjunnuu 3dv. github. hotprojects/fadeeeoooooo
INTRODUCTION
3D Gaussian Splatting (3DGS) (Kerbl et al., 2023) has been widely applied to the field of 3D reconstruction and rendering, including novel view synthesis of static scenes (Kerbl et al., 2023; Yu et al., 2024a), mesh surface reconstruction (Guédon and Lepetit, 2024; Yu et al., 2024b), inverse rendering (Liang et al., 2024; Gao et al., 2023), object detection (Cao et al., 2024), and dynamic 3D reconstruction (Wu et al., 2024; Lin et al., 2024), However, in scenarios with less-observed areas, such as indoor scenes and unbounded scenes, radiance field optimization often suffers from overfitting these limited input views (Li et al., 2024), resulting in unreliable and corrupted geometry reconstruction.
To mitigate the issue, recent research efforts (Li al., 2024; Paliwal al., 2024; Turkulainen et al., 2025) have focused on incorporating geometric priors from input views into the training process, thereby regulating the optimization of radiance field represented by 3D) Gaussian points. For instance, DN-Splatter (Turkulainen et al., 2025) integrates sensor depth and normal cues into the reconstruction process. However, sensor depth acquisition is costly, and the depth prior information from pre-trained monocular deep models inevitably suffer from the scale ambiguity (Liu et al., 2023b). While the normal prior provides even better geometric details, the scale ambiguity still exists due to its monocular nature.
In contrast to monocular priors, pairwise matching priors can provide absolute scale information of the scene. In this paper, we introduce Flow Distillation Sampling (FDS), an online method for distilling matching prior from a pre-trained optical flow model into the 3DGS training process. FDS aims to enhance the geometry quality of Gaussian radiance field by leveraging the matching prior
Equal contribution.
Corresponding author.

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Published as a conference paper at ICLR 2025
Input View
Sampled View
Forward
Differentiable Pass
Loss
3D Gaussian Splatting
Image Loss
Rendered Input.
Input View
Unobserved Sampled View
Pre-trained Matching Model
FDS
3DGS Flow Rasteizzaiinn
Loss
Radiance Flow
Prior Flow
Figure 1. Pipeline of the proposed FDS. For each input view, we apply the FDS camera sampling scheme to generate corresponding unobserved sampled view. We then compute Radiance flow base rendered depth and the Prior flow from matching prior model. Finally the Prior Flow used supervise Radiance flow, which enhances the geometric quality Gaussian Radiance Field.
into the unobserved novel view. Specifically, observe that the flow between the input view and the unobserved view generated by the match prior model (i.e., Prior Flow), can guide and refine the flow analytically caleulated from the 3DGS geometry (i.e., Radiance Flow), improving the 3DGS reconstruction quality. Moreover, better 3DGS scene will lead to more accurate Prior Flow, creating mutually reinforcing effect between radiance field is poorly optimized and the image rendered from the unobserved viewpoint is blurry during training. addition, camera sampling scheme is proposed adaptively control the overlap between input view and sampled view for better Prior Flow calculation, which allows to leverage prior geometric knowledge more profoundly and thereby better enhance the 3DGS reconstruction quality.
computed flow maps. This remains effective even when the
The proposed FDS has been extensively evaluated on MushRoom (Ren et al., 2024), ScanNet (V2) (Dai et al., 2017), and Replica (Straub al., 2019) datasets for the task of geometry reconstruc- tion. apply FDS to two commonly used baseline approaches, namely 3DGS (Kerbl al., 2023) and 2DGS (Huang et al., 2024). The results demonstrate significant improvement in geometry re- construction accuracy. Additionally, we provide interpretive experiments and comprehensive analysis the effectiveness of FDS, shedding light on its influence on the quality of geometric reconstruction and novel-view rendering. Our contributions are summarized as follows:
FDS leverages matching prior information recover absolute scale, significantly enhancing the geometric quality of the Gaussian radiance field.
An adaptive camera sampling scheme is proposed to selectively choose unobserved views with controllable overlap with the input view, further improving the geometric quality the Gaussian radiance field even in less-observed areas.
By employing FDS and the adaptive camera sampling scheme, we bring significant improve- ments state-of-the-art 3D geometry reconstruction approaches.
RELATED WORK
To enhance the geometry of 3DGS representations, some studies (Gao et al., 2024a; Waczyáska et al., 2024; Lyu et al., 2024; Chen et al., 2023) focus on integrating mesh or SDF representations with 3DGS. (Gao et al., 2024a) improve the splitting of 3DGS under the guidance of mesh representation and deformation gradients. A hybrid representation that integrates 3DGS with mesh allowing 3DGS to be modified as a mesh, is introduced in (Wazzyáska et al., 2024). Mani-GS (Gao et al., 2024b) binds Gaussian and shape-aware triangular
Geometry Reconstruction Based on 3DGS:
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mesh to manipulate 3DGS directly. 3DGSR (Lyu al., 2024) combines signed distance field (SDF) network with 3DGS to enhance geometry quality, aligning the SDF network's 's geometry with that of 3DGS. NeuSG (Chen et al., 2023) utilizes point clouds from 3DGS to regulate NeuS, while its normals are also used to refine 3DGS. Additionally, NeuSG includes regularizers to ensure that 3DGS remains close to the surface. Some work (Guédon and Lepetit, 2024; Huang et al., 2024; Yu et al., 2024b; Chen et al., 2024) tends to extract geometry from 3DGS directly, benefiting from its fast training and rendering speed. Sugar (Guédon and Lepetit, 2024) proposes an efficient mesh extraction method from 3DGS, aligned with regularization term during the training process and refinement strategy. 2DGS (Huang et al., 2024) proposed a 2D surface modeling and two regularization losses which can preserve perspective-correet splatting and enchance geometry reconstruction. A ray-tracing-basee volume rendering is introduced GOF (Yu et al., 2024b), allowing the extraction of geometry from 3DGS directly. PGSR (Chen et al., 2024) proposes unbiased depth rendering, combined with singe and multi-view regularization loss to preserve geometric consistency. However, in low-texture and less frequently observed areas, such indoor scenes, 3DGS still tends to overfit to the limited input views, necessitating regulation through additional prior cues.
Prior Regulation for Rendering: Prior information is usually incoporated in ill-posed problems, including sparse view novel view synthesis, dynamic scene reconstruction, and mesh reconstruction. For sparse novel view synthesis tasks, most works utilize the prior depth information (Deng et al., 2022; Roessle et al., 2022; Song et al., 2024; Wang et al., 2023b; Zhu et al., 2023; Xiong et al., 2023; Paliwal al., 2024), semantic information (Jain et al., 2021; Wynn and Turmukhambetov, 2023; Xiong et al., 2023), and matching information (Paliwal et al., 2024; Lao et al., 2024) to constrain the optimization process of 3DGS. Dynamic scene reconstruction another challenging task which requires reconstructing the scene geometry and object motion at the same time. Therefore, optical flow priors are crucial as they can help distinguish between camera motion and object motion (Liu et al., 2023b) while providing motion priors between frames (Liu et al., 2023a; Gao et al., 2021; Li et al., 2023; Wang et al., 2023a; Guo et al., 2023; Tian et al., 2023). For the mesh reconstruction task, geometry quality is also enhanced by depth priors (Wei et al., 2021; Yu et al., 2022; Turkulainen et al., 2025) or normal priors (Yu et al., 2022; Turkulainen et al., 2025). However, using optical flow model priors to obtain metric depth priors to help geometric reconstruction, while leveraging unobserved regions to enhance the quality of limited view reconstruction, has not yet been explored.
METHOD
Our FDS regulates the optimization of Gaussian radiance field by incorporating matching priors from the pretrained deep model. The generation of Radiance Flow and our proposed FDS loss, along with the equipped camera sampling scheme, are detailed in Sec. 3.1 and Sec. 3.2, respectively.
3.1 3D GAUSSIAN SPLATTING AND RADIANCE FLOW
We utilize 3DGS as an example to demonstrate how Radiance Flow is generated. 3DGS (Kerbl et al., 2023) employs collection of 3D Gaussians to represent the 3D scene. The expression of i-th 3D) Gaussian distribution shows below:
( - 1 M1XX-M)">T'' -ms).
(1)
where Σ; = R.S.S? R.. and μ4; represents the position of the Gaussian, which is optimized during training. Both St and R2 are represented by a 3D scaling vector 8; and a quaternion qt. respectively. In addition to the above parameters, each Gaussian P. has extra learnable attributes, including opacity ag and color feature ft.
To render color for pixel æ, volume rendering based method similar to NeRF (Mildenhall et al., 202 1) is adapted:
i-1 ag),
C(x) Σ a
II
(2)
N
j=1
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where O₁ is the color of each Gaussian point, represented by spherical harmonics. is the blending weight for each 2D Gaussian point which is the projection 3D Gaussian points on the image plane. N is the number of Gaussian points. Similarly, the depth of pixel z is rendered using alpha blending.
( EiEN d II (1
Eien di 11;=1 (iz)
where d; is the distance from the target camera the Gaussian Point P.. We can also render Radiance Flow between two views of camera m, using their camera poses and position Gaussian points μig As mentioned above, we can project pixel (u,, U1) in m-th view image the n-th view by its corresponding depth and their pose transformation:
U2
W1
(u2 V2)
U2 1
KT KO-K-WU DD" (u1, U1)
Vi
1
where Tm is the relative transformation from m-th view to nith view, K is the intrinsic matrix, and Dm (u1, 01) the rendered depth of (u1, 81) in m-th view.
Next, we calculate Fmm->"(x) (x) for pixel æ = (u1, v1) from view m to view n:
Fm (x)
U2
U1
(5)
1/2
U1
For other type Gaussian radiance field such as 2DGS (Huang et al., 2024), we only need to replace the alpha blending based depth D(x) with corresponding formulation.
3.2 FLOW DISTILLATION SAMPLING
Given collection of images (T' Gaussian Radiance Field typically employs the following loss function for rendering optimization:
= B
E
1 A)L1 + ALD-SSIM + Anormathns
(6)
where B denotes batch size, and Ln represents the normal consistency loss from (Huang et al., 2024).
However, when N is small, this representation suffers from overfitting (Li et al., 2024; Paliwal et al., 2024).
Point
We propose the Flow Distillation Sampling (FDS) method to incorporate pretrained match- ing priors into the rendering optimization pro- cess, thereby mitigating overfitting and improv- ing rendering performance.
Point 2
Flaw
Flow 2
The camera sampling scheme and loss function design in FDS are introduced in Sec. 3.2.1 and Sec. 3.2.2.
dz
Sample
Sample
3.2.1 CAMERA SAMPLING SCHEME
Sampled View
Sampled View Input View
Input View
Figure 2. Explanation of depth-adaptive translation
During the training process, FDS randomly sam- ples unobserved camera views nearby the input view and then incorporates the matching priors into these views. To utilize the matching prior information between input view and sampled view more profoundly, the geometry the scene while avoiding excessively abrupt motions that could make it difficult for the prior model match.
radius. fixed-radius camera sampling scheme may result in significantly different flow values (Flow and Flow 2) in areas with varying depth (dl and dz).
propose camera sampling scheme that ensures sufficient movement to perceive
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Given the world to camera transformation matrix T" for the i-th input view small translation disturbance t and rotation disturbance R are applied to get the sampled transformation matrix T*, expressed as:
T
E
(7)
where = RR t denotes the transformation matrix from the sampled view to the input view, and t a translation vector satisfying |t] C,, f (f1, f2, t3). indicating that unobserved view is sampled along small spiral circle with radius of éz. As noted in (Bian et al., 2021), the rotation flow in image warping is independent of depth. Therefore, we set rotation part to identity matrix. So that E is pure- translation transformation. For the translation radius εg. illustrated in Fig. 2. using uniform radius for all views leads to varying flows due to the differences in depths; the closer the depth, the larger the flow. To ensure flow consistency across all views while maintaining controllable overlap between the input views and sampled views, we hope to implement a depth-adaptive radius, which can help to preserve the same flow between all input views and their sampled views.
According to (4), the pure translation transformation (Bian et al., 2021) between the input view i and its sampled view shown below:
122
Tuj V1
71
D (u2, U2)
U2
D* 01)
K
t2
ta
where K the intrinsic matrix of the camera, after solving the above equation (Bian et al., 2021), we get:
De(m on to Detui, wil Di(un wn Jui jui to Di(0),e1)+ts
U2
U/2
We set 1z in our camera sampling scheme and assume camera intrinsic parameters: fa Jv = The radiance flow F gu1, v1)
U2 21
from the input view i its sampled view is shown
in
below:
Di(ur t1
Fi Fi++s(1 01)
(10)
De(ME,
aim to keep the value of || | Fi agrit*(up (mj U1)lla constant for the pixel x = (w1, v1) during each camera
sampling. By setting Fi (u1, 2n 1| and incorporating this with (10), get:
6, = V G + = Di(ui, v1)
(11)
f
Thus, the radius of translation in camera sampling is defined as De(uu.))) which helps maintain stable flow. The parameter radiance flow between the input view and its sampled view. Given that pixel depths vary within an image, we use the mean depth D; of the image and set the radius of our translation o D.
be tuned hyperparameter, which represents the mean
D. sin(2 D
t
o P cos((2T)
(12)
Where U(0,1) is uniform random value between [0, 1] during training.
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3.2.2 FLOW DISTILLATION SAMPLING LOss
Specifically, to optimize the rendered results of the i-th view, every iteration, we sample an unobserved view near the i-th input training camera to render the color image C The Radiance Flow F (p). guided by Equ. (5), benefits from the introduced matching priors. We define the Prior Flow F as:
=Mo("
(13)
where represents the parameters pretrained network M, I' is the rgb ground truth of view i, and C is the rendered image of sampled view Instead of using C* to generate Prior Flow, find that using Is can help us to remove the floaters in C as shown in Tab. 4. However, both Fi and face challenges:
F
Fi++e derived from Equ. (5), is inaccurate due to the incorrect positioning of Gaussian points.
F derived from Equ. (13), suffers from the blurred rendering quality of C
Despite these inaccuracies, observe that F F++ is more robust and precise during training compared with Fi-+e Motivated by this observation, we aim to utilize F to refine Fi++,, which can make Fi++* more accurate, enhancing the positioning of Gaussian points and subsequently improving the rendering quality of C This process also leads to a more accurate F** Based on these observations, we propose the FDS loss, which distills matching priors from a pretrained deep model through mutual refinement of the two flows:
Lids F F
(14)
Algorithm Flow Distillation Sampling
Input: A batch of input training image: {1 Transformation Matrix: [Ti) Prior Matching M with (ra,t, t., fú, Hi, a4).
Network Mg. Gaussian Points {P.)
Output: Lids
1: for in 21, .I. do
2:
(0, R), I
3:
t - o (2mE), t P cos((2mm)) to + 0
4:
Et R, T + -(T
5:
C² + Render T P)
Di **+ Renderr(T (T P)
6:
7:
X KTęK- DÅ (XXX)Xx/D(XX
8:
Fits x=
FiSS -MolI',
9:
10: Lids + Lidds + 1/B||F* >> 1i
11:
return T.jde
To maintain training stability and reduce computational complexity, we detach F² i from P; when we calculate loss. This prevents the propagation of gradients, as computing them is resource-intensive and time-consuming, as noted in (Poole et al., 2022). Additionally, this helps ensure that F' ii+ not directly influenced by the less reliable Fi++e.
In summary, the procedures of our proposed Flow Distillation Sampling are presented in Algorithm 1. The overall training loss is:
B A)L1 + XLD SSIM + Ln + Ayde
Σ [1
(15)
B

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Published as a conference paper at ICLR 2025
Ingut
3DGS
2DGS
3DGS + FD3
2DGS + FDS
GT (Depth)
Figure 3. Comparison of depth reconstruction Mushroom and ScanNet datasets. The original 3DGS 2DGS model equipped with FDS remove unwanted floaters and reconstruct geometry more preciously.
EXPERIMENTS
4.1 SETUPS
4.1.1
IMPLEMENTATION DETAILS
We apply our FDS method to two types of 3DGS: the original 3DGS, and 2DGS (Huang et al., 2024). The number of iterations in our optimization process is 35,000. We follow the default training configuration and apply our FDS method after 15,000 iterations, then we add normal consistency loss for both 3DGS and 2DGS after 25000 iterations. The weight for FDS, Xyds, is set to 23, and the weight for normal consistency is set to 0.15 for all experiments. We removed the depth distortion loss in 2DGS because we found that it degrades Gaussian point cloud is initialized using Colmap for all datasets. We tested the impact of using Sea Raft (Wang et al., 2024) and Raft (Teed and Deng, 2020) on FDS performance. Due to the blurriness required. Thus, we incorporate normal prior supervision on the rendered normals in ScanNet (V2) dataset by default. The normal prior is predicted by the Stable Normal model (Ye et al., 2024) across all types of 3DGS. The entire framework is implemented in Py PyTorch (Paszke et al., 2019), and all experiments are conducted on single NVIDIA 4090D GPU.
0.015, the
results in indoor scenes. The
of the ScanNet dataset, additional prior constraints
4.1.2 DATASETS AND METRICS
We evaluate our method for 3D reconstruction and novel view synthesis tasks on Mushroom (Ren et al., 2024), ScanNet (v2) (Dai et al., 2017), and Replica (Straub et al., 2019) datasets, which feature challenging indoor scenes with both sparse and dense image sampling. The Mushroom dataset an indoor dataset with sparse image sampling and two distinct camera trajectories. We train our model on the training split of the long capture sequence and evaluate novel view synthesis on the test split of the long capture sequences. Five scenes are selected to evaluate our FDS, including "coffee room". "honka", "kokko". "sauna", and "vr room". (eanNet(V2) (Dai et al., 2017) consists of 1,613 indoor scenes with annotated camera poses and depth maps. We select 5 scenes from the ScanNet (V2)
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Table 1. 3D Reconstruction and novel view synthesis results on Mushroom dataset. Represents that
FDS uses the Raft model.
Method
Aeci
Comp
CLLT L
NCT
F-Score
Abs Rei
PSNR
SSIM
LPIPS
Time
GOF
0.1812
0.1093
0.1453
0.6292
0.3065
0.2380
21.37
0.7762
0.3132
PGSR
0.0971
0.1420
0.1196
0.7193
0.5105
0.1723
22.13
0.7773
0.2918
1.2h
3DGS
0.1167
0.1033
0.1100
0.7954
0.3739
0.1214
24.18
0.8392
0.2511
sc0.8h
3DGS FDS
1,0569
0.0676
0,0623
0.8105
0.6573
0.0603
24.72
0.8489
0.2379
1=1.3
3DGS FDS
0.0527
0.0565
0.0546
0.8178
0.6958
0.0568
24.76
0.8486
0.2381
2DGS
0.1078
0.0850
0.0964
0.7835
0.5170
0.1002
23.56
0.8106
0.2730
==0.8h
2DGS FDS
0.0689
0.0646
0.0667
0.8042
0.6582
0.0589
23.98
0.8255
0.2621
1113
2DGS FDS
0.0615
0.0534
0.0574
0.8151
0.6974
0.0561
24.06
0.8271
0.2610
s=1.
Table 2. 3D Reconstruction and novel view synthesis results ScanNet dataset.
Method
Acc
Comp
C-L1
NCT
F-Score
Abs Rel
PSNR
SSIM 1
LPIPS
GOF
1,8671
0,0805
0.9738
0.5622
0.2526
0.1597
21.55
0.7575
0.388T
PGSR
0,2928
0.5103
0.4015
0.5567
0.1926
0.1661
21.71
0.7699
0.3899
3DGS
0.4867
0.1211
0.3039
0.7342
0.3059
0.1227
22.19
0.7837
0,3907
3DGS + FDS
0.2458
0.0787
0.1622
0.7831
0.4482
0.0573
22.83
0.7911
0.3826
2DGS
0,2658
0.0845
0.1752
0.7504
0.4464
0.0831
22.59
0.7881
0,3854
2DGS + FDS
0.1457
0.0679
0.1068
0.7883
0.5459
0.0432
22.91
0.7928
0,3800
dataset, uniformly sampling one-tenth of the views, following the approach in (Guo et al., 2022).
To further improve the geometry rendering quality of 3DGS, Replica (Straub et al., 2019) contains small-scale real-world indoor seans. We evaluate our FDS on five scenes from Replica: office0,, officel, office2, office3 and office4, selecting one-tenth of the views for training. The results for Replica are provided in the supplementary materials. To evaluate the rendering quality and geometry of 3DGS, we report PSNR, SSIM, and LPIPS for rendering quality, along with Absolute Relative Distance (Abs Rel) as a depth quality metrics. Additionally, for mesh evaluation, we use metrics including Accuracy, Completion, Chamfer-LI distance, Normal Consistency, and F-scores.
4.2 RESULTS
4.2.1 DEPTH RENDERING AND NOVEL VIEW SYNTHESIS
The comparison results on Mushroom and ScanNet are presented in Tab. I and Tab. 2, respectively, Due to the sparsity of sampling in the Mushroom dataset, challenges are posed for both GOF (Yu et al., 2024b) and PGSR (Chen et al., 2024), leading to their relative poor performance on the Mushroom dataset. Our approach achieves the best performance with the FDS method applied during the training process. The FDS significantly enhances the geometric quality of 3DGS on the Mushroom dataset, improving the "abs rel" metric by more than 50%. We found that Sea Raft (Wang et al., 2024) outperforms Raft (Teed and Deng, 2020) on FDS, indicating that a better optical flow model can lead to more significant improvements. Additionally, the render quality of RGB images shows slight improvement, by 0.58 in 3DGS and 0.50 in 2DGS, benefiting from the incorporation of rross-view consistency in FDS. On the Mushroom dataset, adding the FDS loss increases the training time by half an hour, which maintains the same level as baseline. Similarly, our method shows a notable improvement on the ScanNet dataset as well using Sea Raft (Wang et al., 2024) Model. The "abs rel" metric in 2DGS is improved nearly 50%. This demonstrates the robustness and effectiveness of the FDS method across different datasets.
The qualitative comparisons on the Mushroom and ScanNet dataset are illustrated in Fig. 3. As seen in the first of Fig. 3, both the original 3DGS and 2DGS suffer from overfitting, leading to corrupted geometry generation. Our FDS effectively mitigates this issue by supervising the matching relationship between the input and sampled views, helping to recover the geometry. FDS also improves the refinement of geometric details, as shown in other rows. By incorporating the matching prior through FDS, the quality of the rendered depth is significantly improved.
4.2.2 MESH EXTRACTION
To further demonstrate the improvement in geometry quality, we applied methods used in (Turku- lainen et al., 2025) to extract meshes from the input views of optimized 3DGS and 2DGS. The
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Table 3. Ablation study on geometry priors.
Method
Aoei
Comp
C-LT4
NCT
F-Score
Abs Rel
PSNR 1
SSIM
LPIPS
2DGS
0.1078
0.0850
0.0964
0.7835
0.5170
0.1002
0.2730
Dephh
0,0862
0.0702
0.0782
0.8153
0159665
0.0672
23.92
0.8227
0.2619
2DGS+MVDept
0,2065
0.0917
0.1491
0.7832
0,3178
0.0792
23.74
0.8193
0.2692
IDGSSNNorml
0,0939
0.0637
0.0788
0,8359
0,5782
0.0768
23.78
0.8197
0.2676
2DGS-FDS
0.0615
0.0534
0.0574
0.8151
0.6974
0.0561
24.06
0.8271
0.2610
JDGS+Depph-FDS
0.0561
0.0519
0.0540
0.8295
0.7282
0.0454
24.22
0.8291
0.2570
EDGS-NNrmal-FDD
0.0529
0.0450
0.0490
0,8477
0.7430
0.0443
24.10
0.8283
0.2500
0.0695
0.0513
0.0604
0.8540
0.6723
0.0523
24.09
0.8264
0.2575
2DDGS-DDeplleNNoormlHHHU
0.0506
0,0423
0,0464
0.8598
0.7613
0,0403
24.22
0.8300
0,0403
RF (16000 iters)
RF (20000 itens)
RF (20000 iters)
PF (16000 iters)
PF (20000 ittes)
50
Figure The error map Radiance Flow and Prior Flow. RF: Radiance Flow, PF: Prior Flow, means that there is no FDS loss supervision during optimization.
comparison results are presented in Tab. 1. With the integration of FDS, the mesh quality is signifi- cantly enhanced compared to the baseline, featuring fewer floaters and more well-defined shapes.
4.3 ABLATION STUDY
Ablation study on geometry priors: To highlight the advantage of incorporating matching priors, we incorporated various types of priors generated by different models into 2DGS. These include a monocular depth estimation model (Depth Anything v2) (Yang et al., 2024), a two-view depth estimation model (Unimatch) (Xu et al., 2023), and monocular normal estimation model (StableNor- mal) (Ye et al., 2024). We adapt the scale and shift-invariant loss in Midas (Birkl et al., 2023) for monocular depth supervision and L1 loss for two-view depth supervison. We use Sea Raft (Wang et al., 2024) as our default optical flow model. The comparison results on Mushroom dataset are shown in Tab. 3. We observe that the normal prior provides accurate shape information, enhancing the geometric quality of the radiance field. The multi-view depth prior, hindered by the limited feature overlap between input views, fails to offer reliable geometric information. We test average "Abs Rel" of multi-view depth prior. and the result is 0.19, which performs worse than the "Abs Rel" results rendered by original 2DGS. From the results, can be seen that depth order information provided by monocular depth improves reconstruction accuracy. Meanwhile, our FDS achieves the best performance among all the priors, and by integrating all three components, we obtained the optimal results.
Alltion study on FDS: this section, we present the design of our FDS method through an ablation study on the Mushroom dataset to validate its effectiivness. The optional configurations of FDS are outlined in Tab. 4. Our base model is the 2DGS equipped with FDS, and its results are shown in the first row. The goal of this analysis is to evaluate the impact of various strategies FDS sampling and loss design. We observe that when we replace I, in (13) with C, as shown in the second row, the geometric quality of 2DGS deteriorates. Using T, instead of C, help us remove the

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Published as a conference paper at ICLR 2025
Table 4. Ablation study on FDS strategies.
MolX. C*)
Loss
Metric
X C X
Next Input view
Sampled view
Fixed Sampled view
Abs Rel
F-score
NCT
0.0561
0.6974
0.8151
0.0839
0.6242
0.8030
0.0877
0.6091
0.7614
0.0724
0.6312
0.8015
floaters in C which are also remained in C². We also experiment with modifying the FDS loss. For example, in the third row, we use the next training input view as the sampling view, and replace the render result of next training view with ground truth image of its input view, Due to the significant movement between images, the Prior Flow fails to accurately match the pixel between them, leading further degradation geometric quality. Finally, we attempt to fix the sampling view and found that this severely damaged the geometric quality, indicating that random sampling is essential for the stability of the mean error in the Prior Flow.
Figure 5. Limitation of FDS.
Interpretive Experiments: To demonstrate the mutual refinement of two flows in our FDS, for each view, we sample the unobserved views multiple times to compute the mean error both Radiance Flow and Prior Flow. We use Raft (Teed and Deng, 2020) visualization. The ground truth flow calculated based on Eq. (4) and Eq. (5) utilizing ground truth depth in dataset. We introduce 2DGS. The error maps are shown in Fig. 4. Our analysis reveals that Radiance Flow tends to exhibit significant geometric errors, whereas Prior Flow effectively disregarding errors introduced by floating Gaussian points.
default optical flow model for
FDS loss after 16000 iterations during optimization of
accurately estimate the geometry,
4.4 LIMITATION AND FURTHER WORK
Firstly, our FDS faces challenges scenes with significant lighting variations between different views, as shown in the lamp of first row in Fig. 5. Incorporating exposure compensation into FDS could help address this issue. Additionally, our method struggles with reflective surfaces and motion blur, leading to incorrect matching. In the future, we plan to explore the potential of FDS in monocular video reconstruction tasks, using only single input image at each time step.
CONCLUSIONS
In this paper, we propose Flow Distillation Sampling (FDS), which leverages the matching prior between input views and sampled unobserved views from the pretrained optical flow model, to improve the geometry quality of Gaussian radiance field. Our method can applied to different approaches (3DGS and 2DGS) to enhance the geometric rendering quality of the corresponding neural radiance fields. We apply our method to the 3DGS based framework, and the geometry is enhanced on the Mushroom, ScanNet, and Replica datasets.
ACKNOWLEDGEMENTS
This work supported by National Key R&D Program of China (2023YFB3209702), the National Natural Science Foundation China (62441204, 62472213), and Gusu Innovation & Entrepreneur ship Leading Talents Program (Z.XI 2X22333)3)
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Reviews:
[{"review_id": "cyeWZxVqr3", "reviewer": "Reviewer_GPCw", "summary": "the geometric under-constrain problem of 3D Gaussian Splatting (3DGS) in sparse view setups. By incorporating pre-trained matching priors into the optimization process of 3DGS, this method significantly improves both the geometric accuracy and rendering quality of 3DGS.", "questions": "In the related work section, the review of existing prior art aimed at improving 3DGS performance should be more comprehensive and clearer, particularly concerning the relevant work on optical flow priors. Additionally, in the subsection on Prior Regulation for Rendering, there are sentences with grammatical errors that require careful review and correction.\n\nIn Algorithm 1, there are notation errors that need careful checking and correction.\n\nThe comparison of depth reconstruction experiments needs to be supplemented with results from other methods to validate the superiority of the proposed approach in geometric reconstruction.\n\nIn the dataset section, the paper mentions that the authors have evaluated their method on the Replica dataset, but the experimental results are not presented.\n\nThe authors provide limited comparisons with existing methods; it is recommended that they include more baseline methods for a more robust evaluation.", "limitations": "", "rating": 5, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The method proposed in this paper integrates matching priors derived from a pretrained optical flow model to guide the optimization of 3DGS. This approach effectively enhances both the reconstruction quality and rendering quality of existing 3DGS-based methods.\n\nThe methodology is well-structured, providing clear and detailed explanations of the proposed FDS technique, the adaptive camera sampling scheme, and the associated loss functions.\n\nComprehensive experimental evaluations are conducted across multiple datasets, demonstrating the method's effectiveness and robustness.\n\nAdditionally, the paper includes interpretive experiments to illustrate the mutual refinement process of the flows, thereby enhancing the understanding of the method's capabilities.", "weaknesses": "The results of the proposed method are constrained by the initial quality of the prior flow, however, the reliability of the prior flow cannot be assured under certain sparse viewpoint configurations.\n\nAs noted in the limitations section, the method's reliance on the performance of a pretrained optical flow model restricts its generalizability.\n\nWhile the authors have conducted experiments across multiple datasets, it is important to point out that these datasets are primarily limited to indoor scenes. It is recommended that the authors evaluate their method on a more diverse range of datasets to assess its applicability in various scenarios.\n\nThe paper lacks a discussion on the computational complexity of the method. It is recommended that the authors include a detailed report on the training and inference times of the model in the experimental section, along with comparative metrics against other existing methods.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HK5VV9sLWS", "reviewer": "Reviewer_148K", "summary": "The paper proposes a optical flow based regularization for 3D and 2D Gaussian Splatting. It compares the optical flow output between an input view and a sampled unobserved view to a so-called radiance flow determined from the camera motion and the reconstructed scene. The authors claim that a loss on the difference between the radiance flow an the optical flow results in improved geometry and view synthesis quality. Experiments show improved performance of 3DGS and 2DGS with flow distillation on the SceneNet, Mushroom and Replica dataset.", "questions": "- The Radiance Flow maps pixels from the source view  to the target view. Considering pixels in the target view containing splatted Gaussians that are occlude in the source view, how is the Radiance Flow computed for these regions?\n- In line 267, how does detaching the optical flow influence the overall performance?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper describes an interesting idea on incorporating a flow prior for 3D reconstruction with Gaussian Splatting.\n- The related works contains all relevant geometry reconstruction-based 3DGS works and set them in context to the proposed method.\n- The approach is simple and easy to understand, as Figure 1 and 2 are well done and intuitive.", "weaknesses": "- The experimental evaluation only considered indoor room datasets, MuSHRoom, ScanNet and Replica. Baseline methods usually use more diverse datasets such as DTU [Jensen et al. 2014], Tanks and Tem-\nples [Knapitsch et al . 2017] and Mip-NeRF360 [Barron et al. 2022].\n- The authors found that the depth distortion loss in 2DGS degrades the results. However they do not provide evidence or explanations for that and it is unclear how this influenced the quantitative comparison to 2DGS.\n- The paper solely focus on 3DGS-based methods in the related work and also in the experimental evaluation. Comparisons to neural field based methods such as Geo-NeUS or NeuralAngelo would significantly strengthen the claim of state-of-the-art performance.\n- The overall quality and the presentation should be improved, e.g. the conclusion is unspecific and contains general claims,  inconsistent capitalization of 'Gaussian', no explanation of \\hat{\\alpha} in equation 2.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "cAyYqQNSaP", "reviewer": "Reviewer_w1zd", "summary": "This paper aims to improve the 3D Gaussian Splatting reconstruction quality in regions with sparse or no observational input views, by integrating a pre-trained matching prior into the 3DGS optimization process. The matching prior is incorporated through optical flow from a pre-trained model, which supervises the Radiance Flow calculated using 3DGS-rendered depth. Additionally, the authors introduce a Flow Distillation Sampling scheme to efficiently sample unobserved camera views around the input views. The proposed Flow Distillation Loss effectively avoids the scale ambiguity existing in monocular priors. The authors present clear ablation studies and quanlitative improvements to support their claims.", "questions": "- Given that RAFT is computed at every time step, how does the training time for 2DGS + FDS compare to 2DGS?\n- Why do both monodepth and multi-view depth seem to only worsen the results, as shown in Table 3.?\n- it's said in line 316 that, the normal prior is introduced for evaluation on the ScanNet dataset. But the metrics in Table 2. and Table 3. seem inconsistenct regarding the results of 2DGS + FDS. Does this mean the ScanNet result in Table 2. doesn't use the normal prior?\n- Can 2DGS + FDS outperform 2DGS + Normal in Table 3.?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "- The idea is simple but makes intuitive sense. Matching priors can provide absolute scale information in constrast to monocular priors. This paper offers a promising direction of using pair-wise information prior to advance sparse view reconstruction.\n- This ablation study clearly demonstrates the improvement benefited from using this pair-wise matching prior without scale ambiguity. The quanlitative results shown in Table 3. validate the advatange compared to monocular depth prior, even to multi-view depth prior. A clear visualization of the mutual refinement of two flows is also provided.", "weaknesses": "- This paper lacks evaluation on widely used geometry reconstruction and novel view synthesis benchmarks such as DTU, Tanks and Temples, and MipNeRF 360. The advantages of the proposed method would be more convincing if the authors could present results on one or more of these benchmarks.\n- As mentioned in line 252, both the Prior Flow and Radiance Flow suffer from inaccuracies, raising concerns about the stability of the benefits provided by the proposed Flow Distillation Loss. It is possible that this loss could introduce artifacts or incorrect guidance due to bias. While the metrics in Table 3 appear strong, it’s unclear why the loss significantly outperforms multi-view depth supervision, which does not suffer from inaccurate prior flow. More explanation and analysis are needed to clarify this point.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "qM5sle9zRD", "reviewer": "Reviewer_LTym", "summary": "In this paper, Flow Distillation Sampling (FDS) is proposed to improve the geometric accuracy and rendering quality of  3D Gaussians Splatting.\nFDS first adopts a camera sampling scheme to sample unobserved views near the training views, and then uses the flow predicted by the pre-trained model to guide the flow calculated from the 3DGS geometry.", "questions": "See `Weakness`.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The ideas are intuitive, the paper is well written and easy to understand.\n2. FDS leverages the matching prior mitigate the overfitting problem and enhance the geometry.", "weaknesses": "1. More ablation studies are needed.\n- The depth-adaptive radius is calculated by Eq. (8). How to determine the value of the hyperparameter $\\sigma$? Is FDS robust to different $\\sigma$?\n- Is  FDS must require the normal consistency loss $\\mathcal{L}_{n}$? In Table 3, how is the performance of “2D-GS+FDS”?\n- How to determine the weight for FDS $\\lambda_{fds}$?\n- How to determine the start iteration (e.g., 15,000) of applying FDS?\n\n2 Lack of visual comparison on the ScanNet dataset.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)