Surface-Aware Feed-Forward Quadratic Gaussian for Frame Interpolation with Large Motion
Authors: Zaoming Yan
Yaomin Huang
pengcheng lei
Qizhou Chen
Guixu Zhang
Faming Fang
Venue: NeurIPS 2025 poster ()
Keywords: video synthesis; large motion; multimedia;
Primary area: applications

Abstract: Motion in the real world takes place in 3D space.
Existing Frame Interpolation methods often estimate global receptive fields in 2D frame space. 
Due to the limitations of 2D space, these global receptive fields are limited, which makes it difficult to match object correspondences between frames, resulting in sub-optimal performance when handling large-motion scenarios.
In this paper, we introduce a novel pipeline for exploring object correspondences based on differential surface theory.
The differential surface coordinate system provides a better representation of the real world, enabling effective exploration of object correspondences.
Specifically, the pipeline first transforms an input pair of video frames from the image coordinate system to the differential surface coordinate system.
Subsequently, within this coordinate system, object correspondences are explored based on surface geometric properties and the surface uniqueness theorem.
Experimental findings showcase that our method attains state-of-the-art performance across large motion benchmarks. 
Our method demonstrates the state-of-the-art performance on these VFI subsets with large motion.

Surface-Aware Feed-Forward Quadratic Gaussian for Frame Interpolation with Large Motion
Zaoming Yan 12
Yaomin Huang!2
Pengcheng Lei 12
Qizhou Chen
Guixu Zhang Faming Fang 12*
School of Computer Science and Technology, East China Normal University, Shanghai, China.
'The KLATASDS & Shanghai Key Laboratory of MIP.
Lran_zaaming, pengchenglei19955081r
{ymhuang, qizhouchen Osstu ecnu edu..eddu.eo {gxzhang, fmfang) .ww.uuuueecccccc.mmmmm ecnu.edu.cu
Abstract
Large motion poses a critical challenge in Video Frame Interpolation (VFI) task, it requires accurate modeling of object correspondences across frames. Existing methods primarily rely on convolutional or attention- based models, which operate the pixel patch level. This inherently limits them to local object correspon- dences, making it difficult to capture frame-level object correspondences and often leading failure under large motion. Inspired by the fundamental theorem of sur- face, we explore frame-level object correspondences through the lens of differential surface. The core idea represent video frames as 3D surfaces and align them by matching their surface properties, thereby achieving global surface alignment and frame-level object alignment. To implement the core idea, we propose the Surface-Awar
Quadratic Gaussian framework, mainly consisting of the Ferr--d Quadratic Gaussian and Surface Properties modules. Feed- Forward Quadratic Gaussian is designed to map frames to Quadratic Gaussian, which flexibly fits the object surface. Unlike previous methods that compute cal correspondences, Surface Properties facilitates global surface-level alignment, which drives object correspondence alignment. Finally, we rasterize the surface properties onto the interpolated camera plane and define loss functions to supervise aligument explicitly. The outstanding performance on the large motion benchmark demonstrates the effectiveness of our framework.
Introduction
Video Frame Interpolation (VFI) is a fundamental low-level vision task that aims to increase the frame
rate of video by synthesizing intermediate frames between consecutive inputs. has wide range of
real-world applications, including
video generation [1 2 3
video compression [4] [3]
and novel view synthesis 66] g). Despite recent progress, VFI remains challenging, particularly in
large and complex motion commonly found in casually captured videos. More recently, the emergence of film agent frameworks IO IT] has introduced intelligent agents for einematic content creation. In such scenarios, handling large motion is critical for tasks such as scene composition, camera planning, and visual continuity. These demands highlight the need for more robust VFI methods capable of modeling long-range object correspondences.
At its core, VFI requires establishing accurate correspondences between objects across frames Video frame interpolation methods can be broadly divided into two types: those based on
12
"Corresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Ourside the camera view
Inside camera view
Frume coordnate
Input (1",1²)
XVEI
SGM-VFI
BiFomer
Ours
(b)
Figure 1: Challenge: Existing methods lack global frame-level object correspondences, which results in suboptimal matching.
Convolutional Neural Networks (CNNs) and those based on attention mechanisms. CNN-based T6
17 12 estimate optical flow to synthesize intermediate frames, where the optical flow serves a proxy for object correspondences, However, due to the local receptive field of convolution operations, CNN-based methods often compute object correspondences only at the pixel level, which limits their ability to capture global relationships. To overcome the locality of CNNs, attention-base architectures have been introduced for video frame interpolation 19 20
methods 3 13
14
15
These methods divide input frames into patches and compute attention between them. However, this patch-level modeling still lacks a true global understanding of object correspondences across frames.
Upon scrutinizing and experimenting on the released implementations of existing methods [17 15
12 we observe that they suffer from performance deterioration in large motion. As illustrated in Figure in the large motion, existing approaches fail to establish accurate object correspondences, leading to misalignment results. We attribute these failures to the inherent locality of convolution- and attention-basee methods, which operate the pixel or patch level and thus struggle to model frame-level object correspondences. We further identify two representative failure cases (Figure ! (b)): (i) Repeated objects across frames confuse optical flow estimation, resulting in incorrect local correspondences. For example, the red dashed lines show mismatched flags, causing fragmentation in the interpolated frame. (ii) Some objects required in the target frame are missing in adjacent frames, leading to ambiguous correspondences (21), as shown in the upper-right region.
As discussed above, overcoming the limitations of local object correspondences, particularly in the presence of large motion, necessitates the establishment of frame-level object correspondences. However, how to theoretically formulate and practically implement such correspondences requires further exploration and discussion. Inspired by the fundamental thcorem surfaces [22], we propose to represent video frames differential surfaces (Figure 2). enabling the exploration of geometric constraints and frame-level correspondences. The core idea of this work is to map video frames onto 3D surfaces and align the overlapping regions using surface properties. This approach drives global surface alignment and promotes consistent geometric structure across frames. However, implementing this idea presents two key challenges: (1) how to effectively represent surface, and (2) which surface properties are most suitable for alignment.
To address the surface representation challenge, we propose the Feed-Forward Quadratic Gaus- sian. The Quadratic Gaussian Splatting (QGS) [23] defines a Gaussian distribution on a quadratic paraboloid, allowing smooth transitions between convex and concave forms for flexible surface fitting. However, QGS assumes accurate camera poses, which limits its applicability in real-world scenarios where videos are casually captured. To overcome this, Feed-Forward Quadratic Gaussian efficiently transforms such video frames into 3D surface representations without relying on strict assumptions such accurate camera poses depth maps.
To facilitate surface alignment, we leverage two key surface properties: normal and curvature. Surface normals are widely used ensure geometric continuity across frames (24). However, normal alone may become unreliable and introduce errors within large motions (surfaces with rapid bends). This motivates the incorporation of higher-order geometric descriptors such curvature, which can

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capture fine-gra the-ign surface structures. Therefore, we jointly use surface normals and curvature as consistency constraints to ensure robust surface alignment across frames.
To explicitly supervise surface continuity, we rasterize the normal and curvature onto the camera plane and define loss functions. By leveraging these modules, build novel pipeline, named Surface- Aware Feed-Forward Quadratic Gaussian. Our method achieves state-of-the-an performance on large motion benchmarks [12]. Furthermore, we conduct extensive ablation studies to validate the contribution of each component.
The contributions of this work are summarized (1) Inspired by the Fundamental Theorem of Surfaces, we introduce a differential surface to present a video, to explore frame-level object correspondences and geometrie constraints. (2) This paper introduces Surface-Awar Feed-Foree Forward Quadratic Gaussian framework that maps video frames into 3D surfaces, aiming to overcome the limited local correspondences. (3) Our pipeline illustrates state-of-the performance the large motion benchmark.
2 Related Work
Video Frame Interpolation. Recently, advancements in deep learning have led to various methods for video frame interpolation. These methods be broadly categorized into two main paradigms: reconstruction-bass [25 15
14 26 27 16 28 22 30) and denoising diffusion probabilistic model 351. (i) Initially, DVF (36] utilized a U-Net-like network to model two input frames and predicted the voxel flow for warping the two frames into the intermediate frame. To obtain the optical flow from the intermediate frame to the input frames, [5] proposed distillation strategies to obtain the optical flow from the intermediate frame to the input frames. In large-scale motion scenarios, methods such as SGM-VFF [12] 11LM and XVFI [7 leverage enhanced global information in optical flow to establish accurate frame- to- co-frame correspondences for objects. These Kernel- methods are implemented as separable convolutions [38], deformable
(DDPM)-based [3]
32
33
34
convolutions 139 40) 41 (ii) Based on Denoising Diffusion Probabilistic Models (DDPM)
leverage generative techniques like DDPM to fill occlusions caused by motion. These DDPM-based approaches are implemented
score-basee diffusion 43 44 45), motion-aware diffusion [46] 47),
and Brownian bridge diffusion [48 However, most IDPM-based methods are significantly time-consuming and challenging for real-time inference.
3D Gaussian Splatting. recent years, 3D Gaussian splatting has emerged as an active area of research in the field of 3D reconstruction. Various approaches have been proposed across different domains, broadly categorized into static scene Gaussian splatting and dynamic scene Gaussian splatting. Gaussian Splatting (50) enhances rendering quality in radiance fields. To further adapt to diverse reconstruction scenarios, [1 52 53 have been proposed, significantly improving the generalization capability of 3DGS- based reconstruction. To accommodate dynamic scenes, [54] [55]
56 58 59 has been extended to handle such environments. However, the per-scene optimization of 3DGS requires densely captured images and sparse point cloud generated by SIM for initialization.
Recent works [60 61 | 62 63 64 65) have explored feed-forward models for sparse-view Gaussian reconstruction by capitalizing on large-scale datasets and scalable model architectures 66 67 68
3 Preliminary
3.1 3D Gaussian Splatting
Kerbl et al. [69] proposed representing scene using 3D Gaussian ellipsoids as primitives and rendering images using differentiable volume splatting. Associates a 3D Gaussian i with position Ng covariance matrix E, opacity 0; and spherical harmonics (SH) coefficients hG. The final opacity
of a 3D Gaussian at any spatial point = (I,, y, 2) is:
(p-
1 (p- 1n) (p mi)
a; = 0 exp
where the covariance matrix Σ = RSS Rº, and is Gaussian distribution.
To render an image, 3D Gaussians are first projected to 2D image space via an approximation of the perspective transformation. Specifically, the projection of 3D Gaussian is approximated as 2D
3

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Gaussian with center u and covariance D. Center fi and covariance E;" are computed as
1 (K (WW E /WE,W"J" J".
(2)
where W is a transformation from the world space to the camera space, and is local affine transformation.
After sorting the Gaussians depth order, the color at a pixel obtained by volume rendering:
N-1
{-1
I(u, Σ
C
2D
II [1 (1-a)").
1=0
==
Here, a? is a 2D version of Eq. with μss Σ, replaced bu nu? E,D, (u, (pixel coordinate). C, is the RGB color after evaluating SH with the view direction.
3.2 Quadratic Gaussian
Zhang al. [23] proposed representing scene using a Quadratic Gaussian as a surface and rendering images using differentiable volume splatting. For convenience, the Quadratic Gaussian distribution expressed in cylindrical coordinates, and the opacity a Quadratic Gaussian at any spatial point
(0, P, (0,0)) p)) is:
(H:(0, (8))2
04 O2 exp
(4)
G
$182
p)(0,p) = S-' -1- (2at)² dt
(0)
(5)
82 cos 0)2 + (s] sin 0)²
where (-(-) 23 is the mean of the Gaussian distribution on the surface, and σ; is the covariance of the Gaussian distribution on the surface. G is defined as the corresponding Gaussian function. diag(81 81, 82, 83) denotes the scale of the Quadratic Gaussian. a(-) is related to the coefficient of 0.
To render an image, the Quadratic Gaussian follows the same 3D Gaussian splatting way, which is projected to 2D image space via an approximation of the perspective transformation. After splatting and sorting the Gaussians in depth order, the color at pixel (u, v) is obtained by rendering 77
N-1
i-1
I(u, v) =
Caa
II (1 - a /=1
(6)
where N denotes the pixel numbers of the rendered image.
4 Method
4.1
Problem formulation
Frame Interpolation.
In the video frame interpolation task, it can be written as
I' = I'), (0,
where 1 and I' input frames. 0 and 1 are two input views and is an interpolated view index between 0 and To synthesize an intermediate frame I' where E (0, 1). existing algorithms B 29 30 typically extract object correspondences between consecutive frames, facilitating
16
12
object alignment.
Frame Interpolation under Differential Surface.
In large motion scenes, video frame interpolation methods often fall into suboptimal object corre- spondences, as they operate at the pixel level or patch level and thus struggle to model frame-level object correspondences.

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To address the limitations of local object correspon- dences, we redefine the large motion problem as a global fraee-level alignment task by aligning the sur- faces that represent each frame. The core idea of frame-level alignment is that aligning the geometric properties between surfaces (such as normals and cur- vatures) can facilitate the alignment between surfaces, as illustrated in Figure 2
Nidoo Frume
Sirlin
('mmr
domatal
Ties
Ovedaapinn
Ovesszging 6 6.5"
In the following sections, we describe how to con- struct surface representations from video frames and how to select surface properties to facilitate accurate correspondences across surfaces.
niemal Ty tangeut plane
Curvature: Grren indiccates the beeld surface with high curvature values.
The core idea is mapping video frames into 3D surfaces and aligning them by matching surface properties, leading global surface-level alignment.
Figure 2:
4.2 Surface-Aware Feed-Forward Quadratic Gaussian
Although modeling object correspondences through differential surface representations is theoretically reasonable, remains challenging to implement: 1) What type of 3D primitives is suitable for representing differential surface? 2) Which surface properties should be selected facilitate alignment between differential surfaces?
4.2.1 Feed-Forward Quadratic Gaussian
Modeling the texture and surface details in videos remains challenging for 3D primitives such as point clouds and 3DGS, which often struggle to accurately represent complex surfaces. Fortunately, Quadratic Gaussian Splatting (QGS) (23) defined
paraboloid and constructs Gaussian distribu- tions based on geodesic distances. This enables the energy of the Gaussians to be concentrated on the surface, thereby effectively capturing complex surface and textural details. However, existing methods such as 3DGS [50]. 2DGS 771. and QGS 23 still rely on accurate camera poses, which are difficult obtain sparse- or unconstrained settings, thereby limiting their practical appli- cability. To overcome this limitation, the practical Feed-Fore Ferd-Forward Quadratic Gaussian is introduced that efficiently transforms frames into 3D surface representations.
Given a set of video frames, the goal of Feed-Forwee Forward Quadratic Gaussian is to generate the object surface in the QGS representation. Unlike prior methods, it does not require additional data such as camera poses, enabling single feed-forward inference. Feed-Forward Quadratic Gaussian mainly includes two sub-models: backbone and Quadratic Gaussian head. Formally, Feed-Forward Quadratic Gaussian can be written as:
Se [ {P", "',
ha (1, (9
(8)
fe is the backbone and he is the Quadratic Gaussian Head. F0,Fi the 3D point clouds. C", C² the camera parameters. gO, G1 the Quadratic Gaussian.
F, is the frame features. pa, p is
Backbone. Foundation models for 3D reconstruction (e.g.. DUS(3R 66), MAS13R 67] have shown
remarkable competitiveness and superior performance in 3D reconstruction tasks 63 We leverage
pretrained geometric priors from foundation models to achieve a coarse alignment of 3D point clouds P and camera parameters C, promoting stable and efficient learning process. For simplicity and stability in our pipeline, we adopt a simple backbone VGGT (72). Specifically, given a pair of input frames 7 72, the backbone outputs the corresponding image features 5 _ 3D point clouds pO, pl. and camera parameters CO CO.
Quadratic Gaussian Head. Real-world object surfaces complex, making it difficult for point clouds to capture their surface structure accurately. QGS 23] defines Gaussian distributions on a quadratic surface, which smoothly transition between convex and concave shapes. This flexibility allows for more accurate modeling of complex object surfaces. To leverage this capability, we propose the Quadratic Gaussian Head, module inspired by QGS, that transforms point cloud features into QGS-based 3D primitives, enabling more effective surface representation. This surface representation enables estimating surface properties in subsequent stages, thereby preserving surface consistency across frames. Specifically, QGS contains the following parameters
go {uo 0Z T.. )
l H............ HxW,
(9)
5

---

Quadratic Gaussian
Surface Properties
Rasterization
Camera Head e
Quadutic
Cakodax
Quad Gaanians
Normal
Ea. (10)
(PP))
(13)
(9")
5
5
Curvatuee
Narrol (14)
123
Faze
Oni Laner
Quadratic
(1)
Guuzsian
Aulent Lave
Reunuag
Lina
g"
[3"]: Features
J 3D paint clouds
C: Camera porameter
( Quadiatic Clnnsiions
I: interpolation time indes
dP: Oparity
2 Stale
2 Rotation
2, Color
Figure 3: Surface-Aware Feed-Forwand Quadratic Gaussian Framework. The Feed-Forward Quadratic Gaussian module transforms the input frames 7 and I into Quadratic Gaussian (go and g)) that represent surfaces. Then, the Surface Properties module computes the normal and curvature from the Quadratic Gaussian. Finally, the normal, curvature, and frame I' are rasterized onto the camera plane the interpolation time.
where opacity rotation scale and color and H/ x W pixel numbers. Subsequently, the point cloud pe is the QGS's mean μ.. Together with the predicted parameters, it forms the Quadratic Gaussian representation Go of frame 1
4.2.2 Surface Properties
Normals usually play crucial role in facilitating surface alignment and continuity across frames [4). Meanwhile, curvature characterizes the degree of surface bending [6). In regions with large motion, i.e., highly curved surface areas, relying solely on normals may lead to inaccurate alignment (8). This motivates employing higher-order geometric descriptors, such as curvature, to complement normal in fine-graie meeeggr alignment surfaces. Therefore, we jointly utilize normals and curvature as surface constraints to ensure accurate and consistent alignment across frames.
Given Quadratic Gaussian, we directly compute the normal and curvature any point on the surface. Specifically, given any 3D point p on the surface (23), the corresponding normal and curvature are:
4Am
n(p) = 22 2xyU,
k(p) (1 - 423x² + 42332)
(10)
$33
where A₂ = 1.2 and d, 1,1,0,1} determines whether the paraboloid is elliptic, hyperbolic, planar. More specifically, the d2 idepends on both the positional variable and a temporal variable t. and is defined as d, =tanh(t) exp(x). For the detailed computation, please refer to Appendix A.l Formally, the calculation process is written as:
{ .. (N",K", N1K
(11)
where N and K represent the normal map and the curvature map, respectively.
4.2.3 Rasterization
Finally, we rasterize the surface properties from the 3D space into the camera plane with the interpolation camera parameter. The total process can be written as:
NO. K'), ".."", No, K", N K² C², (
(12)
where C¹ C x c x (1 is the interpolation camera parameter.

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Table 1: Quantitative comparison with SOTA methods on the standard benchmark, regarding PSNR/SSIM. The best and the second best results are denoted by pink and yellow.
SNU-FI M
Vimeo- 90K
UCFI01
Average
eusy
medium
hand
extreme
DAIN 25
34.71/0.9756
34.39/0.9683
39.73/0.9902
35.46/0.9780
30.17/0.9335
35.09/0.35 8584
33.36/0.9507
AdaCaF 90
34,47/0.9730
34,90009668 9680
39.8000 9900
35.05/0.9754
29 29.46/099244
24.31/0.84339
33,0000.9555 9458
34,65/0.9730
34.91/0.969M
39.89/0.9900 9900,9900
15.61/0
29 900099200
24.78/0.8507
33,29/0.949
Softsplat
36. 1805
17/0,6660
40,26/0
36 09/0.999998
30,93/0.9366
25. 16/16600.0 8608
33.92/0
$5.09/0.9759
35. 17/0 9685
39.9 39,93/0 9907
35,7770097776
29. 29,58/00.227 92766
24.17/0 8450
33. 33.22/0. 9477
M2M-VF 21
15.2080.9768
35.28/0.9697
40.10/0. 100099906
16/0.9797797
00.63/0.9368
25.27/0. 8601
33.68/0.951 9519
[1F
35.61/0.9779
35.29/0 9697
40.10/0. 9906
36.12/0.9797
00.6330.9368
25.27/0. 8601
33.68/0.955 9519
IFRNe--L [1
96,20009900
35,42/0 9698
40.3640.9911 9910
36.12/0,9797
30.63/0.9360
25. 25,27/0 8609
33, 33,96/0 9531
36.35/0.9815
35,39/0
39.95/0.9913
30.75/0.9384
33,99/0.95-2
EMA VIN-VVF-SS 20
36.64/0,9819
35,45/0.9701
39.98/0 9901
36.09/0,9801
30,94/0.9392
25. 25,699008661 8661
34,148195547
SGM VT !
35,81/0.9793
35 40/009693
40.14/0.9900
36.06/0.9795
30.81/00.337
25. 69/0 8661
33.96/0.955 9535
VFIMumha-S
20
36.09/0.9800
9696
/0.9190
16.1770.9800
30.8000.9338
25.59/0 8655
34. 140.9509
Ours
36.0K/0.9991
35.4000.6692
39.98/0.9906
10009998
30,9000.9991
8651
33.35/0.9475
Table 2: Quantitative comparison with VFI methods on large motion benchmark. The best and the
second best results are denoted by pink and yellow.
X-Test-L
SNU-FIMM 10
Xiph- D
Rumimme
FLOPs
XVH 17
29.82X08951
29.0220.8866
27.5800 MURSS
22,5500.2200
29.17/2.849
28.0500,7899
0.075
10.57
30,050089411
28.3510.1156
23.05/08247
29,89088533
27.11/0,7699
1.29
1.36
Bil Vermer 19
30.3200.9057 30.15A0,9070
28.1840.9154
23:8590.8390
29,5100,8541
26.9680,8183
1.09
0.39
29,870088005
28.96A08156
18.190091172
30.18/2.8633
28,07A0,9922
AMT 8
29.3900.8771
28.3510.8731
28.3340.9184
23.14008228
30.3200,8710
28:2700,8095
0.58
0.58
EMA
20
29,510087755
2836
28.5740.1899
23.18A08292
30.5400.8788
28.400081099
0.076
SGM-VD [2]
30,390088946
29. 00.225008881
28. SKNO 9209
23.190088301
30,89/0,8745
28.5 28.5%/0.8115
0.93
1.79
VFIMamiu-S
31.580991669
20.5000.000
30.7300
28.62/0.8111
Ouns
31,3300,011
30, 9066
29:05.0.9213
24,2000.8400
31,2000.8814
29.1980,8197
0.340
1.28
Specifically, the rasterization of color performed according the following equation:
I' I'(u, 0)
2D Σ c,a? II a.
(13)
j=0
Similarly, 23
renders the normal and curvature the camera plane follows:
N-1
N-1
v',,,)==
na 2D
(1-
2D k((,v)=
Σ
II (1--0 a;"),
(14)
0-
1=0
j
where N denotes the pixel number of the rendered image.
4.3 Loss Function
Finally, we minimize the following loss function:
L = Le + aLkns Lun (1 (igmoid((n((((( v)l) + C))
(15)
where L. = | - 1'112 2 is an RGB reconstruction loss function. Ckn (u, v) denotes the curvature- aware normal loss, which enforces surface alignment (23). And C, [7] is the normal consistency loss to ensure primitives are locally aligned with the surface.
Experiments
Metrics. We use common quantitative metrics: Peak -o-aal-ToNoiise Ratio (PSNR) and Structural Similarity Image Metric (SSIM), where higher scores indicate better image quality. To assess temporal consistency between frames, we additionally employ the tOF metric [1].
To further illustrate the effectiveness of our algorithm in addressing large motion scenarios, we present statistical analysis of the relationship between motion magnitudes [8] [8 and the corresponding
7

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Mott Nagritude LMChard
Notion Magelbuee Xphi-oe
Motion Magritude Klant-2
BMAVV
BMA/VII Rune
E1AAVV
Fire
FILM
oho Erequrccs
RILM
rann obbi
Prsqurss
FILM
2011
Notion
Magniuue
Mution Ragnitude SNU FILM extremne
Mocion Magritude X4h
Motion Megnitutt Xiss
FILM XVF
XV/
Pote
MagnFace
Magn
Figure 4: PSNR versus motion magnitude. Higher motion magnitudes correspond to larger inter- frame displacements, representing more challenging motion scenarios.
Large SNUATUUKA extreme
3000
2500
XTiest 2K
XCTlcst- 4K
X0ph 2K
Aiph-L
1500
1000
500
NPFE
AMI-L
SCAANP
Durx
Methud
Figure 5: Comparison of temporal consistency under the tOF metric.
PSNR performance, shown in Figure 4 Note that higher motion magnitude corresponds to larger inter-frame displacement, indicating more challenging motion scenarios.
Datasets. For fair comparison, we follow the training and testing datasets established by the large motion benchmark [12]. For training, we follow the setting [12. utilizing both the Vimeo90K and X4K1000FPS (X-Train datasets. Vimeo90K [3] consists of 51,312 triplets with a resolution of 448x256, featuring an average motion magnitude between and pixels. X4K X4K 1000FPS (X-Train)
17 contains 4,408 clips at resolution of 768x768, with each clip comprising 65 consecutive frames.
We evaluate its performance following the large motion benchmark introduced by SGM-VFI (12) X-Test-L [17 [2] with the largest temporal gap, our primary benehmark for evaluating large motion scenarios. We also choose the Oth and 32nd frames as input and evaluate the quality of the synthesized 16th output frame. SNU-FILM-L [80 [2] is the most challenging half of the SNU-FILM hard and extreme, with 155 triplets each. Xiph-L [2 is constructed based on the original Xiph dataset [83 by doubling the input temporal intervals and retaining the most challenging half of the data to form this benchmark.
Implementation Detail. We optimize the loss using Adam in PyTorch framework. The cosine scheduler schedules the learning rate from 1e-4 to le-6. Standard data augmentation techniques, such as flipping, rotation, and cropping, are applied to the data with a size 518 x 280. We train our model on the training datasets with a batch size 16 for 800 epochs.
5.1 Comparison with Previous Methods
As shown in the Table 1 and methods are compared, which are tested on the standard and large motion benchmark. comprehensively evaluate the capability of our model, we conduct experiments on benchmarks with varying motion magnitudes. We compare our method against recent video frame

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RIFE
FILM
BiFestter
AMT
EMA-N7I
SCMVVF
Oat
Figure 6: Visual comparison with state-of-the-art methods.
interpolation (VFI) approaches, including those specifically designed for large motion, as well as methods that perform well on standard benchmarks.
Large Motion. The large motion benchmark contains significant number of scenes with large inter-frame displacements, resulting in motion magnitudes that are higher than those in standard benchmarks. As shown in Table [] our method consistently outperforms state-of-the of-the--rt approaches on the large motion benchmark, demonstrating its effectiveness handling complex motion scenarios. To further analyze performance under varying motion magnitude, we examine the PSNR across different motion magnitude intervals, as illustrated in Figure
Comparison of Temporal Consistency. We employ the (OF metric 17 to evaluate the temporal consistency. As shown in Figure our method consistently outperforms existing approaches on the large motion benchmark in terms of both the mean and variance of tOF, indicating more stability, This superior temporal consistency can be attributed to our method's s accurate modeling of surface properties, which enables fine alignment of object correspondences across frames. We employ the tOF metric [77 to evaluate the temporal consistency. Figure Feporrts the quality of motion reconstruction across several existing models the large motion benchmark. We clearly observe that our method consistently outperforms existing methods in both the mean and variance of tOF Outstanding temporal consistency due to method's fine alignment of object correspondence by modeling the surface properties, which improves motion temporal consistency.
Comparison of Visual Results. We further compare the visualization results in large motion. Figure comparee our method and several state-of-the-ar approaches. CNN-based methods estimate pixel- level object correspondences, which often fall into local optima under large motion, leading to subpar interpolation results. Attention- aateetion-based methods estimate patch-level object correspondences, which improves interpolation results under large motion.
5.2 Ablation Study
In this section, we present experimental insights to analyze and discuss the questions raised in the previous section: which 3D primitives are suitable for representing differential surfaces, and which surface properties facilitate surface alignment.
Table Ablation studies of Architecture on SNU- FILM-L extreme.
Backhone MinST3R
Goussian Hrad
Performenee
Sctiin
CUT3R
vGGT
3DGS heaal
QGS head
PSNR
iOF(
26:11
25
297
Architecture. To demonstrate the superiority of the QGS head in capturing complex geometric structures compared the 3DGS head, first compare their texture representations. Figure provides qualitative evidence, while Table 3 offers quantitative validation of the QGS head's 's effectiveness.
26.12
24.20
226
Figure 7 presents a visual comparison between the two heads, highlighting the QGS head's ability to preserve fine-grained geometric details. As shown in the error maps of Figure 7 the surface-aware QGS head achieves significantly better reconstruction quality, particularly in regions with complex textures.
To further isolate the contribution of the QGS head from that of the backbone, we conduct an ablation study by combining different backbones, CUT3R 84 VGGT 72), and MonST3R [85], with both the 3DGS and QGS heads. Table summarizes the performance of these combinations. The results show that the QGS head consistently outperforms all other configurations, especially under challenging

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large motion scenarios, demonstrating its effectiveness in improving both reconstruction quality and temporal consistency.
QG51kdd
Figure 8: We visualize the surface properties, and notably, as discussed earlier, the curvature high- lights motion regions, particularly those corre- sponding to rapidly bending surfaces.
A visual comparison between the 3DGS head and the QGS head. The bottom part shows a heatmap of the interpolated frame error.
Figure 7:
Surface properties. We conduct an ablation study to further investigate the role surface properties in enhancing surface alignment. Both qualitative and quantitative results are presented in FigureBaand Table 4 Figure 8 visualizes the surface normals and curvature maps rendered by the QGS head. Notably, the curvature map highlights regions with high surface variation, such bends and folds. This observation sup- ports our earlier analysis that curvature serves higher-order geometrie descriptor, complementing surface normals and facilitating more accu- rate surface alignment. These additional insights contribute to improved video frame interpolation performance in large motion.
Table Ablation studies of Surface properties on X-Test-I. 2K.
Surface Properties
Perfermence
Setting
RGB
Normal
Curvature
PSNR
iFF (C)
(i)
29.07
(i)
4
30.47
117
(ii)
31.33
96
Conclusion
This work is the first to analyze frame-level object correspondence under large motion from the perspective differential surface. Building on this insight, we propose an explicit Surface-Aware Feed-Forward Quadratic Gaussian pipeline to mitigate the challenge. Specifically, the proposed method transforms video frames into Quadratic Gaussians representing differential surfaces. Within this representation, compute corresponding surface properties, such normal and curvature. These properties are rendered onto the camera plane for explicit supervision and alignment. Extensive experiments demonstrate that our framework achieves Mate-offthh-aan performance on the large motion benchmark, highlighting its effectiveness and robustness in handling complex motion scenarios. This framework opens avenues for incorporating differential surface into the video frame interpolation task, particularly under large motion conditions.
Limitation. While our pipeline can cover most cases of large motion, there are many other cases beyond that coverage. The main reason for the limitations is that our definition large motion and the proposed ideas are somewhat naive, which makes the solution sub-optimal for geometry. Our current definition focuses more on static correspondences in the background regions across differrnnt frames. For dynamic correspondences, due to the relatively short time interval between adjacent frames, we adopt a simplified assumption of linear motion this work. At present, we employ a relatively basic differential surface theory to model the problem. We believe that, in the future, more unified modeling camera motion and object motion within a comprehensive differential geometry framework could lead to more accurate characterization of complex dynamic scenes.
Acknowledgment. This work was supported by the National Key R&D Program of China (20227D01 61 800), the National Natural Science Foundation of China under Grant 62271203, Al- Empowered Research Paradigm Reform and Discipline Leap Plan under Grant 2024A101012 and the Open Research Fund of KLATASDS-MOE, ECNU.
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Justification: [TODO]
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It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of enrors is not verified.
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generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people train models that generate Deepfakes faster.
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Justification: [TODO]
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Please refer to our LLM policy htteas////eerrpppoccc///o/rreees for what should or should not be described.
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A Theoretical Supplement
A.1 Surface Properties of Quadratic Gaussian
paraboloid is defined as:
0
0
0
0
((.,9,2) [x
1]
0
2e5
d2
0
2xg
de $7
dy
dg
1
(16)
8g
diag(s1, 82, 83), which denotes the orientation and scale of the quadric in the object space. The matrix D defines the surface shape: D = diag(1, 1, yields an ellipsoid, while D
diag(1, 0, 0, produces plane. di {0, +1 determines whether the paraboloid is elliptic, hyperbolic, or planar. For convenience in writing and subsequent derivations, we simplify Equation
16 as follows:
1 -==
f(z, = Au2² + x20
(17)
A.1.1 Normal
QGS is surface-based representation that naturally possesses multiview consistent geometric properties, making straightforward to compute surface normals. Given any point p (z. y, 2) on the surface, we can take the partial derivatives of Eq. 17 yielding:
(p) = 22 2X,8.
(18)
A.1.2 Curvature
Here, we compute the Gaussian curvature analytically using a standard differential geometry approach 22]. By the way, throughout the entire paper, the parameter domain expressed using (u. v)
coordinates, while the surface is represented using (v, v) coordinates. We simplify Eq. 17 as
x² + Any/². Given the point p = (r. y, z), the partial derivatives are:
(1,0, 2).x)
(19)
Fe (0, 1, 2X,9)
(20)
The first fundamental form is:
E (Ta Fa) + 4X3
(21)
F = (Ta = 4Audy
(22)
G (Io, In)
= 1 + 22z1²²
(23)
The second fundamental form is:
Fu Te
(- (22 -2 1)
(24)
Fa X xel
/1 422x2 + 423x²²
Tau (0, 0, (2,))
(25)
Twe (0, 0, 0)
(26)
Pee (0, 0, 2Ay)
(27)
2x,
L (m,, Fun)
(28)
+ 413x² + 4X30²
M (n,, (m,)
(29)
2
N (m, Xnw)
(30)
1 1+ 222x² + 423,²
24

---

Finally, the Gaussian curvature can be computed as:
4222,
LN - M
1+ 12 + 422y²
4 (1 422x² 4233²)²
k(p)
(31)
EG F2
1+ 41 + +4,,²²
B More Visual Results
The anonymous GitHub repository provides visualization results in both video and 3D formats.
25


Reviews:
[{"review_id": "TlXloXgPgC", "reviewer": "Reviewer_csF4", "summary": "The paper introduces a novel approach to video frame interpolation by representing video frames as 3D differential surfaces. The authors introduce a new framework, taking inspiration by Abena et al. [22] and Zhang et al. [23], to map frames to Quadratic Guassian responsible for global surface-level alignment unlike previous methods for better object correspondence alignment. Surface properties are rasterized onto the interpolated camera plane and a custom loss function enforces proper alignment therein. Several experiments underline the effectiveness of the proposed method both quantitavely and qualitatively.", "questions": "1. How was the $\\alpha$ loss weighting factor chosen? What would happen if it was set to a very large value or a very small value? how would results change?\n2. Why have you decided to train on two datasets and compare with methods that are only trained on one dataset? Could you elaborate on this and provide more insights?\n3. Out of curiosity, how well does your model generalize to larger resolutions or how much retraining it would require (interesting as far as FILM is able to generalize quite well for larger resolutions and only requires very little continued training on larger resolutions to hand frame interpolation fairly well give it is only trained on small resolutions)?", "limitations": "I highly appreciate the effort and openness for doing a limitations section and mentioning weaknesses. However, this could be more specific and explicit with limiting examples rather than keeping it fairly general (or at least a rewording would make limitations more clear in my opinion). For example: an inherent limitation of the method is the ability to infer geometry from appearance which is not possible in every case, especially in very fine detailed repetitive patterns in rather small areas.", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. It is the first paper to explore differential geometry in large motion video frame interpolation by treating frames as 3D surfaces.\n2. The architecture itself is modular making it easier to extend and change the method in follow-up work making it more accessible to the entire audience.\n3. Experimental results support the reason for considering differential geometry. The presented results highlight cases where the proposed method outperforms previous SOTA models.\n\nWeaknesses:\n1. Diffusion models, specifically DDPM, are mentioned in the beginning of the paper, however, they are not used in comparison. Possibly due to being time consuming and being challenging for real-time inference (I assume so by reading your Related work section). Yes, in general they are not real-time worthy but as your method fails to be real-time as well it is not common practice to remove good performing diffusion models from comparison because of that exact reason. \"Video Interpolation with Diffusion Models\" by Jain et al. is a paper I would like to highlight that is also able to perform very crisp interpolation of two frames.\n2. In Table 1 you compare methods that have not been trained on the same dataset. It would however be very interesting to see how your model would perform if it was also only trained on the Vimeo-90K dataset in comparison and mention that as training on two datasets theoretically allows for a wider variety of data that the other methods did not have access to. I think it would be fair to neglect the methods SGM-VFI and VFIMamba-S in that case as I see only EMA-VFI-S to be your closer competitor ranking second or first more often than the other two methods combined (It is still fine to keep it in the supplementary material). This is the main reason for the score but I am happy to adjust it if relevant comparisons can be shown.\n3. Only 2 visual comparisons are made which make it hard to judge. Of course in these the model outperforms the others but it would be nice to see a more extensive comparison.\n4. The results on the anonymized GitHub repository and the paper itself do not match. Either there was some compression affecting the result or there is a bigger problem as the shirt of the skater for example is very well readable in the paper images but in the individual images in the gif on the website they are super blurry and not readable at all.\n5. This is a weakness that applies to any frame interpolation method more or less: Usually $t \\ \\in \\ (0,1)$ is set as 0.5 the entire time. However, as you have slow-motion videos or videos with 1000fps at hand would it not be helpful to train the network with varying $t$? The problem that arises from setting $t = 0.5$ the entire time occurs when you want to generate a sequence of images between a starting and an ending image. The quality always relies on the resulting mid-frame generated whereas choosing a free $t \\ \\in \\ (0,1)$ could in theory help supervise smaller movements and preserve more details as well as making the method more robust due to requiring only the starting and ending image for interpolating at any $t$. Did you just follow this way because it is established? (I do understand that this makes it a lot easier when comparing but it makes it harder for the later inference use.)", "was_revised": true, "final_justification": "I appreciate the author's feedback and active engagement in the discussion with both myself and the other reviewers. I now believe the submission is overall quite strong. The additional evaluations were insightful, and the responses provided were clear and satisfactory. I am therefore raising my rating.", "rebuttal": "We appreciate your invaluable insights and thoughtful comments. In the following sections, we address the questions you have raised:\n\n---\n\n## [W1] Comparison of Diffusion-Based Models\n\nWe conduct a comparative study of two diffusion-based video frame interpolation approaches, namely VIDIM and LDMVFI, evaluating their performance on both standard benchmarks and large motion benchmarks.\n\nThe results demonstrate that diffusion models exhibit suboptimal performance in dynamic scenarios, especially when significant background motion arises due to camera movement. In addition, current diffusion-based video frame interpolation approaches lack real-time capability, thereby constraining their applicability in real-world deployments.\n\n**Stand Benchmark**\n\n| Method  | SNU-FILM easy | SNU-FILM medium | SNU-FILM hard | SNU-FILM extreme  | Runtimes (s) | FLOPs (T) |\n|---------|----------------------------|------------------------------|----------------------------|-------------------------------|---------------|------------|\n| VIDIM   | 38.103 / 0.976             | 33.280 / 0.961               | 27.870 / 0.900             | 23.001 / 0.830                | 9.28          | 10.8       |\n| LDMVFI  | 38.679 / 0.987             | 33.998 / 0.970               | 28.547 / 0.917             | 23.932 / 0.837                | 8.48          | 9.9        |\n\n**Large Motion Benchmark**\n\n| Method | X-text-L 2K  | X-text-L 4K | SNU-FILM-L hard | SNU-FILM-L extreme | Xiph-L 2K  | Xiph-L 4K |\n|--------|-------------------------|--------------------------|------------------------------|---------------------------------|------------------------|------------------------|\n| VIDIM  | 29.22 / 0.871           | 28.15 / 0.861            | 25.71 / 0.880                | 21.52 / 0.794                   | 27.83 / 0.849          | 27.00 / 0.780          |\n| LDMVFI | 29.71 / 0.875           | 28.72 / 0.867            | 26.17 / 0.888                | 21.66 / 0.794                   | 28.37 / 0.864          | 27.80 / 0.787          |\n\n---\n\n## [W2 & Q2]  The same dataset\n\nSGM-VFI introduces a benchmark dataset designed to evaluate video frame interpolation under large motion scenarios. To ensure a fair comparison with SGM-VFI in such challenging settings, we follow its training strategy and jointly train our model on both the V and X datasets.\n\nWe appreciate the reviewer’s suggestion. In response, we add evaluation results for a model trained only on the V dataset, tested on both standard benchmarks and the large-motion benchmark.\nOur method demonstrates powerful performance on the large-motion benchmark.\nAnd it demonstrates competitive performance on the standard data benchmark.\n\n**Stand Benchmark**\n\n|   | Vimeo-90K | UCF101 | SNU-FILM easy | SNU-FILM medium | SNU-FILM hard  | SNU-FILM extreme |\n|--------|------------------------|---------------------|-----------------------------|-------------------------------|-----------------------------|-------------------------------|\n| Ours   | 36.09 / 0.980          | 35.40 / 0.9702      | 39.99 / 0.9907              | 36.11 / 0.9800                | 30.95 / 0.9400              | 26.00 / 0.8681                |\n\n**Large Motion Benchmark**\n\n|   | X-text-L 2K | X-text-L 4K  | SNU-FILM-L hard | SNU-FILM-L extreme | Xiph-L 2K | Xiph-L 4K  |\n|--------|-------------------------|--------------------------|------------------------------|---------------------------------|------------------------|------------------------|\n| Ours   | 31.33 / 0.9012          | 30.12 / 0.9066           | 29.05 / 0.9213               | 24.20 / 0.8400                  | 31.20 / 0.8814         | 29.16 / 0.8197         |\n\n---\n\n\n## [W3 & W4] Visual comparisons\n\nWe update the lossless GIFs on the anonymous website ( https://anonymous.4open.science/w/1018-B854/) in the appendix section of the main paper.\n\n---\n\n\n## [W5] How to do continuous interpolation\n\nThis is a good question. We thank the reviewer for raising it.  The continuous interpolation follows the pipeline outlined:\n\n**(I)** Input Frames: We take two input video frames, $I^0 \\in \\mathbb{R}^{H \\times W}$ and $I^1 \\in \\mathbb{R}^{H \\times W \\times 3}$, where  H and W denote the height and width of the image, respectively.\n\n**(II)**  Point Cloud: Frame correspondences can be categorized into two types: **static correspondences**, which are primarily caused by background changes due to camera motion, and **dynamic correspondences**, which result from object motion. \nVGGT demonstrates strong performance in modeling **static correspondences**. We leverage this capability to obtain the point clouds $\\mathcal{P}^0 \\in \\mathbb{R}^{HW \\times 3}$  and $\\mathcal{P}^1 \\in \\mathbb{R}^{HW \\times 3}$  aligned based on static correspondences, where $HW$ is the number of points (pixels), $3$ represents the 3D spatial coordinates. \nIn addition, we visualize the scene by constructing $[ \\mathcal{P}^0 || \\mathcal{P}^1 ]$ to verify the quality of the static correspondence alignment in an anonymous project website( https://anonymous.4open.science/w/1018-B854/). Here, the symbol $||$  denotes the concatenation operation, i.e., torch.cat() in PyTorch.\n\n**(III)** Linear Motion: \nDue to the alignment of static correspondences and the short temporal interval between adjacent frames in video interpolation tasks, we follow the linear motion assumption of previous works. Based on this, we compute the interpolated point cloud at time  $t \\in [0, 1]$ as: $\\mathcal{P}^t = (1-t) \\mathcal{P}^0 + t \\mathcal{P}^1$. By continuously varying $t$, we generate a sequence of intermediate point clouds\n$\\mathcal{P}^t \\in \\mathbb{R}^{HW\\times3}$.\n\n**(IV)** Rendering Intermediate Frame: The interpolated point cloud $\\mathcal{P}^t$  is then fed into the QGS head, which renders the intermediate frame $I^t$. We compute the loss between the rendered frame $I^t$  and the ground truth intermediate frame $I^t_{gt}$.\n\nTo intuitively understand the interpolation process, we visualize the entire pipeline. The visualization results are provided in the Appendix (https://anonymous.4open.science/w/1018-B854/).\n\n---\n\n\n## [Q1] How was the loss weighting factor chosen?\n\nOur loss function primarily consists of the RGB reconstruction loss, which is supervised by the ground truth image $I_{gt}^{t}$. \nTo further regularize the geometric alignment, we incorporate a curvature-aware normal term $\\mathcal{L}_{kn}$. Consistent with the settings adopted in previous methods, such as 2D GS and QGS, we set the weight of the curvature-aware normal term to 0.2.\nAn excessively large weight for the curvature-aware normal term makes the overall loss function difficult to optimize, while a weight that is too small may leading poor geometric alignment.\n\nThe curvature-aware normal term $\\mathcal{L}_{kn}$ is designed to enforce geometric alignment in 3D space. However, in regions with significant geometric variation, such as object boundaries or areas with large motion, normal-based constraints alone may be insufficient, potentially introducing errors and causing over-smoothing.\n\nTo mitigate this issue,  we introduce a curvature map to identify regions with highlighted geometric changes (i.e., areas where frames are not well aligned). This allows us to provide stronger supervision in these regions, guiding the model to achieve more accurate alignment and reconstruction.  In addition, Figure $\\textcolor{red}{8}$ in the main paper provides further evidence that the curvature map successfully captures regions of geometric misalignment.\n\n---\n\n## [Q3] Out of curiosity, how well does your model generalize to larger resolutions?\n\nWe thank the reviewer for this curious question and pay attention to our work.\nWe evaluated the performance of our method on high-resolution datasets. In Table 2 of the main paper, the X-Test (Xiph) dataset includes video sequences with 2K and 4K resolutions, which are used to assess the effectiveness of our method in high-resolution scenarios.  \n\nSpecifically, we adopt a patch-based inference strategy, where overlapping patches are split from high-resolution frames. This approach allows our model to handle large resolution inputs efficiently without exceeding memory constraints. This supports the feasibility and scalability of our approach.\n\nFor 4K-specific research, we recommend Zhang et al. [1], which proposes an efficient method for high-resolution panorama synthesis.\n\n[1] Zhang, Cheng, et al. \"Pansplat: 4k panorama synthesis with feed-forward gaussian splatting.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025.\n\n---\n\n*Hope our explanation and experiments are able to address your inquiries. Please don't hesitate to reply if you have any further concerns. We will integrate all your valuable suggestions into our revision! Thank you!*"}, {"review_id": "Q1BkPwCCZG", "reviewer": "Reviewer_eXnA", "summary": "This work presents a new frame interpolation model based on modeling a generalized notion of pixel, named Quadratic Gaussians (QG). Specifically, the model employs foundation 3D reconstruction model (e.g.., DUSt3R) to estimate the 3D coordinates (or Gaussian means) and the camera poses of given video frames, then additionally employ a head network to predict Gaussian splatting parameters (such as the opacity, covariances, etc.) based on the internal features and the outputs of the 3D reconstruction model. Finally, the surface properties such as normals and curvatures are derived in a rule-based manner following their mathematical definition (as given in Equation 4). These features, along with the predicted Gaussian splatting parameters, are rasterized to 2D planes to render the final image (i.e., the interpolation target frame).\n\nThe experiments are performed in several standard VFI benchmarks, and the proposed method achieves comparable or slightly enhanced performance with respect to recent baseline models.", "questions": "- As noted previously, DUSt3R is known not to generalize well on videos capturing dynamic scenes. Is it possible to employ the dynamics-aware variants, such as the recent CUT3R (Wang et al., 2025)? What would be the impact on the performance on the model, if such variants are employed instead of DUSt3R?\n\n- In the current design, the camera pose of the interpolation target is estimated via linearly interpolating the camera poses predicted by the 3D foundation model. Is there any failure case due to noisy camera pose estimation results?", "limitations": "The proposed design is adapt to the 2 source frame - 1 target frame design for VFI. However, recent foundation 3D reconstruction models (which the proposed method heavily relies on) mainly perform multi-frame inferences to obtain more robust results when affected by complex dynamics. It may not be trivial to generalize the proposed method for these foundation 3D models.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "- Strength of the paper includes clear presentation and straightforward model design\n\n- The method directly relies on the outputs of foundation 3D reconstruction model (e.g., DUSt3R), which provides camera parameters and initial 3D coordinates of the pixel points. However, these foundation models are known to be underperforming in videos with dynamic objects, which can potentially harm the generalization performance of the proposed method in various real-world videos\n\n-  The training objective includes reconstructing the surface normal and curvature, however, the details for obtaining ground truth for these features are missing in the current manuscript", "was_revised": true, "final_justification": "I appreciate the authors' comprehensive response to my review. Their answers successfully addressed my questions, and after reviewing the supplementary material, I find the paper's findings more convincing. As the authors themselves noted, more robust baselines for 3D geometry estimations have become available. I encourage the authors to explore unifying their method with these latest baselines in the final manuscript.\n\nIn summary, I am updating my score to Borderline accept. I believe this method is valuable because it proposes a novel approach for video frame interpolation (VFI), exploring the use of Gaussian splats to replace conventional pixels.", "rebuttal": "Thank you for your insightful inquiries, and we will provide detailed responses to each of them below:\n\n---\n\n## [W1 & Q1] Selection of  3D reconstruction model\n\nFrame correspondences can be categorized into two types: **static correspondences**, which are primarily caused by background changes due to camera motion, and **dynamic correspondences**, which result from object motion. Existing approaches, such as optical flow and self-attention mechanisms, have certain limitations in modeling scene-level static correspondences. \nThey often struggle to capture globally consistent background alignment, which in turn affects the quality of frame interpolation.\nOur method mainly focuses on addressing large-scale background displacements induced by camera motion.\n\nIn the appendix, we demonstrate the frame alignment capabilities of different 3D reconstruction models through an anonymous project website (link: https://anonymous.4open.science/w/1018-B854/) in the appendix section of the main paper. Specifically, **VGGT** shows significantly better performance than **CUT3R** in modeling **static correspondences**, exhibiting stronger background alignment. However, for dynamic objects, both VGGT and CUT3R suffer from a certain degree of object overlap.\n\nDue to the alignment of static correspondences and the short temporal interval between adjacent frames in video interpolation tasks, we follow the linear motion $\\mathcal{P}^t= (1-t)\\mathcal{P}^0 + t \\mathcal{P}^1$ assumption of previous works.  In addition, the ablation study in the main paper (Table 3) further confirms the performance advantage of VGGT over CUT3R, where VGGT achieves a PSNR of 24.2 compared to 24.11 for CUT3R. Based on these observations, we adopt VGGT as our 3D reconstruction model.\n\n---\n\n## [W2] Loss Function\n\nWe are sorry for the confusion caused by the insufficient loss function description. The loss function primarily consists of the RGB reconstruction loss, which is supervised by **the ground truth frame** $I^t_{gt}$.  \nTo further regularize the geometric alignment, we incorporate a curvature-aware normal term $\\mathcal{L}_{kn}$. \n\nThe $\\mathcal{L}_{kn}$ is designed to enforce geometric alignment in 3D space. However, in regions with significant geometric variation, such as object boundaries or areas with large motion, normal-based constraints alone may be insufficient, potentially introducing errors and causing over-smoothing. \n\nTo mitigate this issue, we introduce a curvature map to identify regions with highlighted geometric changes (i.e., areas where frames are not well aligned). This allows us to provide stronger supervision in these regions, guiding the model to achieve more accurate alignment and reconstruction. In addition, Figure 8 in the main paper provides further evidence that the curvature map successfully captures regions of geometric misalignment.\n\nThe computation formulas for surface normals and curvature are provided in Equation ($\\textcolor{red}{4}$) of the main paper.\nIn addition, Figure  $\\textcolor{red}{8}$ in the main paper provides further evidence that the curvature map successfully captures regions of geometric misalignment.\n\n---\n\n## [Q2] Camera pose\n\nWe thank the reviewer for this insightful question and pay attention to our work. \n\nOur method performs video frame interpolation using only two input frames. As a result, the estimated camera poses are relatively sparse, and common issues related to pose ordering in multi-frame sequences do not arise.\nIn current video interpolation experiments, we have not observed significant performance degradation caused by camera pose noise.\nMoreover, recent works [1, 2, 3] demonstrate that sparse and unposed image pairs can still yield high-quality results in 3D reconstruction and novel view synthesis. \n\n[1] Zhang, Shangzhan, et al. \"Flare: Feed-forward geometry, appearance and camera estimation from uncalibrated sparse views.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025.\n\n[2] Ye, Botao, et al. \"No pose, no problem: Surprisingly simple 3d gaussian splats from sparse unposed images.\" ICLR 2025.\n\n[3] Smart, Brandon, et al. \"Splatt3r: Zero-shot gaussian splatting from uncalibrated image pairs.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025.\n\n---\n\n*We hope our clarifications address your concerns and demonstrate the improved quality of our paper! Thank you again for your valuable time!*"}, {"review_id": "Jjb1smgbx2", "reviewer": "Reviewer_HLES", "summary": "To address the challenges of current video frame interpolation (VFI) methods in handling large motion scenarios, this paper introduces a differential surface representation to model videos, aiming to capture frame-level object correspondences and geometric constraints. Specifically, the authors propose a Surface-Aware Feed-Forward Quadratic Gaussian (SA-FFQG) framework that maps video frames to 3D surfaces, thereby mitigating the limitations of local correspondences. Experimental results demonstrate strong performance on benchmarks with large motion magnitudes.", "questions": "Questions\n\n1. Intuitive Explanation for Global Matching: Could the authors provide more intuitive evidence or visualizations to illustrate why Quadratic Gaussian Splatting (QGS) enables better global correspondences compared to traditional methods?\n\n2. Comparison with VFIMamba: Please include a comparison with VFIMamba to validate the method's performance against the current state-of-the-art.\n\n3. Visual Validation: Additional video visualizations, especially for challenging scenarios with large motions and non-rigid objects, are essential to demonstrate the method's generalization ability.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n1. Novelty and Potential Impact: The proposed Feed-Forward Quadratic Gaussian framework exhibits significant novelty in the VFI task and has the potential to inspire future research directions.\n\n2. Pioneering Use of Gaussian Splatting: As the first work to apply Gaussian Splatting in VFI, the method achieves competitive performance compared to prior state-of-the-art approaches.\n\nWeaknesses\n\n1. Clarity of Theoretical Contributions: As a non-expert in Gaussian Splatting, I found the mathematical details in Equations 4-8 challenging to follow. Specifically, I am unsure whether the superscript t in Equations 7 and 8 is necessary, as both equations appear to involve interpolations between two frames. Further clarification would enhance the accessibility of the work.\n\n2. Computational Efficiency: Given the use of a pre-trained VGGT model, the paper does not explicitly report the total parameter count. Table 2 indicates that the proposed method is not outperformed in terms of speed, which may limit its practical applicability in real-time scenarios such as gaming. \n\n3. Generalization to Non-Rigid Motion: Theorem 1 is derived under the assumption of rigid motion, whereas real-world scenarios often involve non-rigid deformations. It remains unclear how this assumption affects the method's generalization capability and practical performance.\n\n4. Incomplete Baseline Comparison: The experiments lack a comparison with the current SOTA method VFIMamba on large motion benchmarks, which weakens the claim of superiority.\n\n5. Limited Visualization: The paper provides few video examples and lacks qualitative visualizations, which undermines the credibility of the reported results.", "was_revised": true, "final_justification": "I thank the author for patiently addressing my questions, and I have decided to improve my score.", "rebuttal": "We appreciate your invaluable insights and thoughtful comments. In the following sections, we address the questions you have raised:\n\n ---\n\n## [W1] Explanation of the Gaussian Splatting formula\n\nWe apologize for the confusion caused by the insufficient explanation. In the revised version, we will provide a more detailed description of **3D Gaussian Splatting**, along with clearer explanations of the meanings and roles of **Equations ($\\textcolor{red}{4}$), ($\\textcolor{red}{7}$), and ($\\textcolor{red}{8}$)**.\n\n### **Preliminary: 3D Gaussian Splatting**\n\nSpecifically, 3DGS explicitly parameterizes Gaussian primitives via 3D covariance matrix  $\\Sigma$ and their location point $\\mathbf{p} _i(x,y,z)$, $i \\in H\\times W$, and $H\\times W$ denotes the point number. \n\n$\\mathcal{G}(\\mathbf{p}) = \\exp\\left( -\\frac{1}{2} ( \\mathbf{p} -  \\mathbf{p}_i)^\\top \\Sigma^{-1} ( \\mathbf{p}  -  \\mathbf{p}_i) \\right)$,\n\n where the covariance matrix $\\Sigma = RSS^{\\top}R^{\\top}$ is factorized into a scaling matrix $S$ and a rotation matrix $R$. \n\nTo render an image, the 3D Gaussian is transformed into the camera coordinates with world-to-camera transform matrix $W$ and projected to the image plane via a local affine transformation $J$: \n\n$\\Sigma' = J W \\Sigma W^\\top J^\\top$. \n\nBy skipping the third row and column of $\\Sigma'$, we obtain a 2D Gaussian $\\mathcal{G}^{2D}$ with covariance matrix $\\Sigma^{2D}$. \n\nNext, 3DGS employs volumetric alpha blending to integrate alpha-weighted appearance from front to back: \n\n$I^t(u, v) = \\sum_{i}^{H\\times W} \\mathcal{G}_i^{2D}(u,v) o_i \\mathbf{c}_i  \\prod_j^{i-1} (1 - \\mathcal{G}_j^{2D}(u,v) o_j)$\n\nwhere i is the index of the Gaussian primitives, $o_i$ denotes the alpha values, and $\\mathbf{c}_i$ is the view-dependent appearance (color).\n\n### **Explanation Equations ($\\textcolor{red}{4}$), ($\\textcolor{red}{7}$), and ($\\textcolor{red}{8}$)**\n\n**(I)** The background-aligned point clouds $\\mathcal{P}^0$ and $\\mathcal{P}^1$ are linearly approximated to obtain the intermediate point cloud $\\mathcal{P}^t$ using the formula $\\mathcal{P}^t = (1-t)\\mathcal{P}^0 + t\\mathcal{P}^1$. \nThe resulting point cloud $\\mathcal{P}^t$  is then transformed into a Quadratic Gaussian $\\mathcal{G}^t$  through the QGS head.\n\n **(II)** Subsequently, the normal and curvature attributes are computed from $\\mathcal{G}^t$ using Equation ($\\textcolor{red}{4}$).  The detailed derivation of Equation ($\\textcolor{red}{4}$) is provided in Appendix A of the main paper. Here, we briefly introduce the definition of QGS as well as the computation of normal and curvature about Equation ($\\textcolor{red}{4}$).\n\n **(II.i) Definition** A Quadratic Gaussian (paraboloid)  is defined as \n\n$f(x,y,z) = \\frac{d_{x}}{s_x^2} x^2 + \\frac{d_{y}}{s_y^2} y^2 - \\frac{d_{z}}{s_z} z = 0$.\n\n$\\mathbf{S} = diag(s_x, s_y, s_z)$, which denotes the orientation and scale of the quadric in the object space. The matrix $\\mathbf{D}$ defines the surface shape: $\\mathbf{D} = diag(1, 1, 1, 1)$ yields an ellipsoid, while $\\mathbf{D} = diag(1, 0, 0, 0)$ produces a plane.\n$d_{ii} \\in \\{0, \\pm 1\\}$ determines whether the paraboloid is elliptic, hyperbolic, or planar.\nFor convenience in writing and subsequent derivations, we simplify the paraboloid as follows:\n\n$f(x, y, z) = \\lambda_x x^2 + \\lambda_y y^2 - \\frac{1}{s_z} z = 0$.\n\n **(II.ii) Normal:** Given any point $\\mathbf{p} = (x, y, z)$ on the paraboloid, we can take the partial derivatives yielding: $\\mathbf{n} ( \\mathbf{p} ) = \\left( 2 \\lambda_x x, \n2 \\lambda_y y, -\\frac{1}{s_z}\\right).$ \n\n **(II.iii) Curvature** We compute the Gaussian curvature analytically using a standard differential geometry approach \n$\\mathbf{k}(\\mathbf{p}) = \\frac{LN - M^2}{EG - F^2}  =  \\frac{4 \\lambda_x \\lambda_y}{\\left(1 + 4 \\lambda_x^2 x^2 + 4 \\lambda_y^2 y^2\\right)^2}$, where E, F, and  G are the first fundamental form, and L, M, and  N are the second fundamental form.\n\n**(III)** Based on Equation  ($\\textcolor{red}{7}$) in the main paper, the color attribute $\\mathbf{c}$ of the QGS $\\mathcal{G}^t$ is projected onto the camera plane, resulting in the intermediate frame $I^t(u,v)$.\n\n**(IV)** Based on Equation  ($\\textcolor{red}{8}$) in the main paper, the normal  $\\mathbf{n}$ and curvature  $\\mathbf{k}$ attributes of the QGS $\\mathcal{G}^t$ is projected onto the camera plane, resulting the normal map $N^t(u,v)$ and curvature map $K^t(u,v)$.\n\n---\n\n## [W2]  Total parameter\n\nThank you for pointing this out. We apologize for the omission. The total number of parameters in our model is 119.059M, and we will include this information in the revised manuscript.\n\n---\n\n## [W3 & Q3]  Generalization\n\nFrame correspondences can be categorized into two types: **static correspondences**, which are primarily caused by background changes due to camera motion, and **dynamic correspondences**, which result from object motion.\nOur method mainly focuses on handling large background displacements caused by camera motion.\n\nIn scenarios where large motion is caused by camera movement, the impact of object motion on the overall scene change is relatively minor. Moreover, due to the short temporal interval between adjacent frames in video interpolation tasks, we follow the linear motion assumption of previous works. \n\nTo evaluate the generalization ability of our method across different scenarios, we provide video interpolation results on various scenes via an anonymous link in the appendix. The experimental results demonstrate that our method is robust across a wide range of scenarios.\n\n---\n\n## [W4 & Q2]  VFIMamba\n\nWe evaluate the performance of VFIManba on a large motion benchmark. The results show that under extreme scenarios, its performance is inferior to that of our method.\n\n| Method     | X-text-L 2K     | X-text-L 4K     | SNU-FILM-L hard | SNU-FILM-L extreme | Xiph-L 2K       | Xiph-L 4K       |\n|------------|------------------|------------------|------------------|---------------------|------------------|------------------|\n| Manba-VFI  | 31.58 / 0.9169  | 30.50 / 0.9077  | 28.80 / 0.9208  | 23.41 / 0.8300     | 30.72 / 0.8780  | 28.62 / 0.8111  |\n\n---\n\n## [W5 & Q1] Limited Visualization\n\nThanks to the reviewers' suggestions, we presented the result videos on the anonymous website (https://anonymous.4open.science/w/1018-B854/) in the appendix section of the main paper.\n\nWe sincerely apologize for the misunderstanding caused by our insufficient explanation of the method pipeline. To clarify our approach, we provide a more detailed and clearer description of the overall process below:\n\n**(I)** We utilize VGGT to capture the static background alignment between different frames. Based on this alignment, we linearly estimate the intermediate point cloud $\\mathcal{P}^t$.\n\n**(II)** Using the QGS head, we generate $\\mathcal{G}^t$, and then compute the normal vector and curvature attributes of each point based on Equation ($\\textcolor{red}{4}$), leading the QGS that incorporates detailed geometric information.\n\nTo further improve the accuracy of frame alignment, we introduce normal vectors as geometric constraints, a practice that is widely adopted in traditional 3D reconstruction methods.\n\nHowever, in regions with significant geometric variation, such as object boundaries or areas with large motion, normal-based constraints alone may be insufficient, potentially introducing errors and causing over-smoothing.\n\nTo mitigate this issue, we introduce a curvature map to identify regions with highlighted geometric changes (i.e., areas where frames are not well aligned). This allows us to provide stronger supervision in these regions, guiding the model to achieve more accurate alignment and reconstruction.\n\n**(III)** By rendering the color, normal vector, and curvature attributes of the QGS onto the camera plane through Equations ($\\textcolor{red}{7}$) and ($\\textcolor{red}{8}$), we obtain the corresponding color map, normal map, and curvature map.\n\n**Intuitive Explanation**\nAs shown in the ablation study (Fig. 8) in the main paper, the curvature maps highlight regions with significant geometric changes, demonstrating that our method effectively focuses on areas with meaningful structural variations. This supports the intuition that curvature serves as a strong indicator for geometric alignment and detail preservation.\n\nIn addition, we provide a visualization of the projection process from QGS to the image plane. These visualizations are available through the anonymous website linked in the appendix.\n\n*Thank you again for your time and effort in reviewing our work!*"}, {"review_id": "OuMvkOrn7a", "reviewer": "Reviewer_aERN", "summary": "The authors tackle the task of video frame interpolation by predicting Quadratic Gaussians from the two input frames (along with relative pose). They then project the estimated Gaussians on the target view (with pose given by interpolation under a constant velocity assumption). Performance is measured across a wide variety of datasets, showing a consistent improvement over existing methods.", "questions": "- How is the method able to handle dynamic motions, such as the skateboarding person in Figure 6? A discussion around this in the paper would be informative.\n- How does the proposed method relate to [1, 2] (see s&w section)?", "limitations": "I wonder what is meant by “the limitations is that our definition of large motion and the proposed ideas are somewhat naive”. Could you explain further?", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The proposed approach is elegant and well motivated\n- Evaluation is extensive and covers a wide range of datasets, with varying settings and difficulty levels.\nAblation experiments are well structured and well motivates the pipeline architecture.\n\nWeaknesses: \n- Lacking comparison to prior works [1,2], which both predict regular Gaussians and poses \n- The connection between Thm 1 and the method is not very clear. For example, it is not explained what “fundamental forms” are. Please add some sentences to draw the connection to surface curvature and normals.\n- Including eq.7 (or similar) from the QGS paper would be helpful to make the background more self contained and make it easier to keep track of notations.\n\n\n[1] Smart, Brandon, et al. \"Splatt3r: Zero-shot gaussian splatting from uncalibrated image pairs.\" arXiv preprint arXiv:2408.13912 (2024).\n[2] Ye, Botao, et al. \"No pose, no problem: Surprisingly simple 3d gaussian splats from sparse unposed images.\" arXiv preprint arXiv:2410.24207 (2024).", "was_revised": true, "final_justification": "The authors have addressed my comments and provided additional baselines. I will raise my score to accept", "rebuttal": "Thank you for your insightful inquiries, and we will provide detailed responses to each of them below:\n\n---\n\n## [W1] comparison to Splatt3r and No pose\n\nWe thank the reviewer for the insightful question. We have conducted a comprehensive quantitative evaluation and visual comparison of the two methods. Specifically, we performed quantitative experiments on both the standard benchmark and the large motion benchmark, and the corresponding visual results are provided on the anonymous website linked in the appendix.\n\n**Splatt3r** is the first to propose a feed-forward Gaussian rendering pipeline. However, it suffers from significant computational overhead and resource consumption, which limits its scalability in practical applications.\n\n**Nopose** builds upon this by introducing a camera-space-based feed-forward Gaussian pipeline, achieving notable improvements in efficiency. However, its use of a 3D Gaussian head introduces limitations in handling fine geometric alignment.\n\n\n**Stand Benchmark**\n| Method    | SNU-FILM easy   | SNU-FILM medium | SNU-FILM hard  | SNU-FILM extreme | Runtimes (s) | FLOPs (T) |\n|-----------|------------------|------------------|-----------------|--------------------|----------------|------------|\n| Splatt3r  | 39.23 / 0.986   | 35.20 / 0.971   | 29.87 / 0.930  | 25.00 / 0.860     | 6.17           | 5.8        |\n| Nopose    | 39.97 / 0.990   | 36.00 / 0.979   | 30.47 / 0.937  | 25.43 / 0.865     | 0.39           | 1.9        |\n\n\n**Large Motion Benchmark**\n| Method    | X-text-L 2K     | X-text-L 4K     | SNU-FILM-L hard | SNU-FILM-L extreme | Xiph-L 2K     | Xiph-L 4K     |\n|-----------|------------------|------------------|------------------|---------------------|----------------|----------------|\n| Splatt3r  | 29.57 / 0.880   | 28.95 / 0.876   | 28.43 / 0.897   | 23.35 / 0.825       | 29.88 / 0.861 | 28.10 / 0.807 |\n| Nopose    | 30.17 / 0.895   | 29.27 / 0.886   | 28.71 / 0.920   | 23.51 / 0.832       | 30.57 / 0.873 | 28.80 / 0.811 |\n\n---\n\n## [W2] The connection between Thm 1 and the method is not very clear.\n\nWe thank the reviewer for the valuable suggestion, which has helped improve the readability of our paper. In response, we provide the following clarification regarding Theorem 1:\n\nThe **First Fundamental Form** is defined on the tangent space of a surface and is used to describe intrinsic geometric properties such as length, angle, and area. In contrast, the **Second Fundamental Form** characterizes the extrinsic curvature of the surface in 3D space， i.e., how the surface bends relative to its tangent plane， and is typically associated with geometric quantities such as **Gaussian curvature**.\n\nWhen establishing correspondences of objects across frames, **normal** is commonly used as a means of geometric alignment. However, in regions with significant geometric variation (e.g., object boundaries or areas with large motion), relying on normal constraints can introduce errors, often resulting in over-smoothing and degraded reconstruction quality in these areas.\n\nTo address this issue, we introduce **curvature** as a descriptor of local surface bending. Curvature provides a more effective way to focus on regions with significant geometric changes and offers stronger supervision signals in these regions. \n\n---\n\n## [W3] QGS background.\n\nWe thank the reviewer for the valuable feedback.\n\nDue to space limitations, the detailed computation of QGS was originally placed in Appendix A of the main text. In response to the reviewer’s suggestion, we will revise the structure of the paper and move the core content of QGS to the Preliminary section in the next version. This adjustment will help readers better understand the background and motivation of our proposed method.\n\nHere, we briefly introduce the definition of **QGS** as well as the computation of **normal** and **curvature**.\n\n**Definition**  A paraboloid (Quadratic Gaussian) is defined as \n\n$f(x,y,z) = \\frac{d_{x}}{s_x^2} x^2 + \\frac{d_{y}}{s_y^2} y^2 - \\frac{d_{z}}{s_z} z = 0$.\n\n$\\mathbf{S} = diag(s_x, s_y, s_z)$, which denotes the orientation and scale of the quadric in the object space. The matrix $\\mathbf{D}$ defines the surface shape: $\\mathbf{D} = diag(1, 1, 1, 1)$ yields an ellipsoid, while $\\mathbf{D} = diag(1, 0, 0, 0)$ produces a plane.\n$d_{ii} \\in \\{0, \\pm 1\\}$ determines whether the paraboloid is elliptic, hyperbolic, or planar.\nFor convenience in writing and subsequent derivations, we simplify the paraboloid as follows:\n\n$f(x, y, z) = \\lambda_x x^2 + \\lambda_y y^2 - \\frac{1}{s_z} z = 0$.\n\n**Normal** Given any point $\\mathbf{p} = (x, y, z)$ on the paraboloid, we can take the partial derivatives yielding: $\\mathbf{n} ( \\mathbf{p} ) = \\left( 2 \\lambda_x x, \n2 \\lambda_y y, -\\frac{1}{s_z}\\right).$ \n\n**Curvature** We compute the Gaussian curvature analytically using a standard differential geometry approach \n$\\mathbf{k}(\\mathbf{p}) = \\frac{LN - M^2}{EG - F^2}  =  \\frac{4 \\lambda_x \\lambda_y}{\\left(1 + 4 \\lambda_x^2 x^2 + 4 \\lambda_y^2 y^2\\right)^2}$, where E, F, and  G are the first fundamental form, and L, M, and  N are the second fundamental form.\n\n---\n\n## [Q1] How is the method able to handle dynamic motions?\n\nThis is a good question. We thank the reviewer for raising it. The dynamic motions follow the pipeline outlined:\n\n**(I)** Input Frames: We take two input video frames, $I^0 \\in \\mathbb{R}^{H \\times W}$ and $I^1 \\in \\mathbb{R}^{H \\times W \\times 3}$, where  H and W denote the height and width of the image, respectively.\n\n**(II)**  Point Cloud: Frame correspondences can be categorized into two types: **static correspondences**, which are primarily caused by background changes due to camera motion, and **dynamic correspondences**, which result from object motion. \nVGGT demonstrates strong performance in modeling **static correspondences**. \nWe leverage this capability to obtain the point clouds $\\mathcal{P}^0 \\in \\mathbb{R}^{HW \\times 3}$  and $\\mathcal{P}^1 \\in \\mathbb{R}^{HW \\times 3}$  aligned based on static correspondences, where $HW$ is the number of points (pixels), $3$ represents the 3D spatial coordinates. \nIn addition, we visualize the scene by constructing $[ \\mathcal{P}^0 || \\mathcal{P}^1 ]$ to verify the quality of the static correspondence alignment in the Appendix( https://anonymous.4open.science/w/1018-B854/). Here, the symbol $||$  denotes the concatenation operation, i.e., torch.cat() in PyTorch.\n\n**(III)** Linear Motion: \nDue to the alignment of static correspondences and the short temporal interval between adjacent frames in video interpolation tasks,  we follow the linear motion assumption of previous works. \nBased on this, we compute the interpolated point cloud at time  $t \\in [0, 1]$ as: $\\mathcal{P}^t = (1-t) \\mathcal{P}^0 + t \\mathcal{P}^1$. By continuously varying $t$, we can generate a sequence of intermediate point clouds\n$\\mathcal{P}^t \\in \\mathbb{R}^{HW\\times3}$.\n\n**(IV)** Rendering Intermediate Frame: The interpolated point cloud $\\mathcal{P}^t$  is then fed into the QGS head, which renders the intermediate frame $I^t$. We compute the loss between the rendered frame $I^t$  and the ground truth intermediate frame $I^t_{gt}$.\n\nTo intuitively understand the motions, we have visualized the entire pipeline. The visualization results are provided in the Appendix (https://anonymous.4open.science/w/1018-B854/).\n\n---\n\n## [Limitation] I wonder what is meant by “the limitations are that our definition of large motion and the proposed ideas are somewhat naive”. Could you explain further?\n\nFrame correspondences can be categorized into two types: **static correspondences**, which are primarily caused by background changes due to camera motion, and **dynamic correspondences**, which result from object motion.\n\nOur current definition focuses more on **static correspondences** in the background regions across different frames. For **dynamic correspondences**, due to the relatively short time interval between adjacent frames, we adopt a simplified assumption of **linear motion** in this work.\n\nAt present, we employ a relatively basic differential surface theory to model the problem. We believe that, in the future, a more unified modeling of camera motion and object motion within a comprehensive differential geometry framework could lead to a more accurate characterization of complex dynamic scenes.\n\nWe sincerely hope that future research will further explore the integration of differential surface theory with feed-forward Gaussian rendering pipelines, which we believe holds great potential for advancing this field.\n\n*We hope our explanation and experiments address your concerns and demonstrate the improved quality of our paper! Thank you again for your valuable time!*"}]

Author rebuttal:

Meta-review: The paper received 4 reviews. The authors-reviewers discussion clarified all points raised in the initial reviews. A consensus that the paper has significance and will be ready for publication pending minor changes was reached and the scores were revised accordingly. The paper can be accepted as poster.
Decision: Accept (poster)