DeLiVR: Differential Spatiotemporal Lie Bias for Efficient Video Deraining
Authors: Shuning Sun
Jialang Lu
Xiang Chen
Jichao Wang
Dianjie Lu
Guijuan Zhang
Guangwei Gao
Zhuoran Zheng
Venue: ICLR 2026 Poster (2026)
Keywords: Video Restoration
Lie Groups
Positional Bias
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Videos captured in the wild often suffer from rain streaks, blur, and noise. In addition, even slight changes in camera pose can amplify cross-frame mismatches and temporal artifacts. Existing methods rely on optical flow or heuristic alignment, which are computationally expensive and less robust. To address these challenges, Lie groups provide a principled way to represent continuous geometric transformations, making them well-suited for enforcing spatial and temporal consistency in video modeling. Building on this insight, we propose DeLiVR, an efficient video deraining method that injects spatiotemporal Lie-group differential biases directly into attention scores of the network. Specifically, the method introduces two complementary components. First, a rotation-bounded Lie relative bias predicts the in-plane  angle of each frame using a compact prediction module, which normalized coordinates are rotated and compared with base coordinates to achieve geometry-consistent alignment before feature aggregation. Second, a differential group displacement computes angular differences between adjacent frames to estimate a velocity. These biases are combined with temporal decay and a banded attention mask to emphasize short-range reliable relations while suppressing long-range noise. DeLiVR achieves sharper details, fewer rain remnants, and stronger temporal coherence on both synthetic and real rainy benchmarks. The code is publicly available at https://github.com/Shuning0312/ICLR-DeLiVR.

Published as a conference paper at ICLR 2026
DELIVR: DIFFERENTIAL SPATIOTEMPORAL LIE BIAS FOR EFFICIENT VIDEO DERAINING
Shuning Sun Jialang Lu
Xiang Chen'
Jichao Wang'
Dianjie Lu Guijuan Zhang
Guangwei Gao Zhuoran Zheng
UUniversity of Chinese Academy of Sciences "Qilu University of Technology
Hubee University *Nanjing University of Science and Technology
"Shandong Normal University Nanjing University of Posts and Telecommunications
zhengzrênjust jud..uuuuuuunnnn edu.cn
ABSTRACT
Videos captured in the wild often suffer from rain streaks, blur, and noise. In addi- tion, even slight changes in camera pose can amplify cross cross-frame frame mismatches and temporal artifacts. Existing methods rely optical flow heuristic alignment, which are computationally expensive and less robust. To address these challenges, Lie groups provide principled way represent continuous geometric transfor- mations, making them well-suited for enforcing spatial and temporal consistency in video modeling. Building on this insight, we propose DeLiVR, efficient video deraining method that injects spatiotemporal Lie- grour differential biases directly into attention scores of the network. Specifically, the method introduces two complementary components. First, a rotation bounded Lie relative bias pre- dicts the in-plane angle of each frame using a compact prediction module, where normalized coordinates are rotated and compared with base coordinates to achieve ccometry-consisterr alignment before feature aggregation. Second, a differential group displacement computes angular differences between adjacent frames to es- timate a velocity. This bias computation combines temporal decay and attention masks to focus inter-frame relationships while precisely matching the direc- tion of rain streaks. Extensive experimental results demonstrate the effectiveness of our method on publicly available benchmarks. The code is publicly available at htt / /gi thub. com
INTRODUCTION
With the rapid development of mobile terminals and video platforms, outdoor video data inevitably suffers from various adverse weather conditions, among which rain the most common degrada- tion (Yang et al., 2017; Bahnsen & Moeslund, 2019). Raindrops and rain streaks not only severely reduce the visual quality of videos, leading to blurred details and decreased contrast, but more importantly, they significantly affect the performance of downstream high-level computer vision tasks, such as object detection, semantic segmentation, and scene understanding in autonomous driving (Dai et al., 2021; Singha & Bhowmik, 2020). Therefore, developing efficient and robust video deraining algorithms crucial for improving the accuracy of advanced vision tasks such as autonomous driving and robotic navigation.
Early video deraining methods mainly relied on hand-crafted priors, such as applying frequency- domain filtering based the physical characteristics of rain streaks, using sparse coding and Gaussian mixture models for layered modeling (Li et al., 2018). However, these previous models overly simple and often suffered from weak generalization when faced with diverse and dy- namic real rain scenes, which could easily introduce artifacts or lead to oversmoothed details (Wang al., 2022). Later, deep learning-based methods, especially CNN, achieved significant improve- ments through end-to-end learning (Yu et al., 2021: Wang et al., 2020; 2025). Nevertheless, their
"Equal contribution. Corresponding author.

---

Published as a conference paper at ICLR 2026
(a) The Challenge: Spatiotemporal Dynamics of Rain streaks
(b) Our Approach: Geometric Approach with Lie Theory
Frume
Tilted Image Patch
SO(2) Head
Algebr
predict
(c) Failure Case: Corrupted Optical Flow
Lic- equivalent Predictor
AI-
Exponential Map
RC9)
Brightness constuncy assumptiin fails rain
pop (91) emp
- cool
cool
-aise
Figure I: Illustration of the problem and our solution. (a) Challenge: rain streaks show spatiotempo- ral dynamics with varying angles, making aligoment unreliable. (b) Our approach: an SO(2) Head with exponential map ensures geometry-consistee alignment. (c) Failure case: optical flow is cor- rupted as brightness constancy breaks in rain.
exploitation of temporal information remained limited, mostly through simple frame fusion or opti- cal flow alignment, making it difficult effectively handle large-scale motion (Guo et al., 2023).
In recent years, some studies have attempted to introduce more powerful architectures to improve video deraining performance, such adopting Transformers capture long-range spatiotemporal dependencies (Li et al., 2024; Yan et al., 2021; Yang et al., 2022; Wu et al., 2024). However, these methods lack knowledge of geometric alignment and are overly reliant on data-driven knowledge when utilizing inter-fraad frame information. When training data contains complex kinematic features such rotations and rapid movements, these methods often exhibit biased information capture un- der varying rain densities and slight variations in camera pose (Wang et al., 2019; Chan et al., 2022). How to explicitly introduce physically meaningful kinetic knowledge into the network to guide pre- cise video-based rain removal remains key challenge (Rota et al., 2023; Zhou et al., 2022). To address this issue, we propose to explicitly encode geometric priors of the Lie group (Lie & Engel, 1893) into the attention mechanism, enabling the network to leverage physically interpretable mo- tion constraints to distinguish true correspondences from rain noise during cross-framm aggregation (see Figure 4). This design provides explicit geometric guidance for self-attention, thereby signifi- cantly improving alignment robustness under complex motion and subtle camera pose variations.
Specifically, propose efficient video de-raining method named DeLiVR, which introduces a novel differential spatio-temporal Lie Bias to effectively estimate the variation of rain streaks in dynamic scenes. Unlike existing methods that rely on unreliable optical flow unconstrained im- plicit learning, DeLiVR incorporates continuous geometric transformation theory (Lie groups) as strong prior, directly injected into the attention mechanism. Our method contains two comple- mentary components. First, we design rotation-bounder Lie relative bias module, which employs compact prediction network to directly estimate the in-plane rotation angle of each frame, and achieves geometry-consistent coordinate alignment under the Lie-group framework. Second, we introduce differential group displacement to compute angular differences between adjacent frames, thereby estimating angular velocity and providing dynamic information about motion trends. These two biases are ultimately integrated into a unified attention bias, combined with temporal decay and attention mask, guiding the network to estimate the intensity and direction of rain streaks.
The main contributions of this paper are summarized as follows:
We introduce Lie group theory into video deraining for the first time and propose a novel differential spatiotemporal Lie mechanism. This mechanism provides new paradigm based on geometric priors, independent of optical flow, for solving the feature alignment problem in dynamic scenes.
2

---

Published as a conference paper at ICLR 2026
We design two bias components: rotation- bounded Lie relative bias and differential group displacement. These components explicitly encode inter-frame rotation transformations and angular velocity information into attention, greatly boosting the spatio -patio-temporal mod- eling capability of networks in complex rainy videos.
We conduct extensive experiments on multiple synthetic and real-world deraining bench- marks. The results demonstrate that DeLiVR outperforms existing advanced methods by producing clearer details, more thorough rain removal, and stronger temporal consistency. Moreover, our approach achieves certain degree of improvement in accuracy for advanced visual tasks.
2 RELATED WORKS
Video Deraining. Video deraining seeks recover clear frames from rainy videos where streaks and veiling effects obscure details and introduce spatiotemporal artifacts. Harly approaches relied on handcrafted priors such photometric modeling, frequency-domate filtering, or sparse/low-rank decomposition, which worked in simple cases but easily failed under dense rain or fast motion (Wang al., 2024; Kim et al., 2015; Li et al., 2018). With the rise of deep learning, CNN-, RNN-, and GAN-based models have achieved better restoration by learning semantic and structural cues, yet frame-wise processing and optical-flow alignment remain computationally expensive and fragile, often leading to mismatches and temporal jitter (Wang et al., 2019). More recently, Transformers and diffusion models have exploited non-local dependencies and generative priors to improve de- tail recovery, but without explicit geometric constraints, attention struggles to maintain alignment under camera rotations or shake (Liang et al., 2022; Gao et al., 2025). To address this gap, we develop spatiotemporal Lie-group differential biases directly into the attention score domain, com- relative biases with temporal motion cues, which enhances alignment and stability without relying on fragile optical flow estimation.
bining
Lie-group research focuses on computer vision. Video restoration critically relies on accurate temporal alignment, yet optical-flow-base methods often fail under rain and other degradations, while implicit incention-basee approaches improve robustness but lack interpretability (Wang et al., 2019; Chan et al., 2022). To enhance stability, recent studies incorporate geometric priors into Transformers: from absolute and relative positional encodings (Liu et al., 2021; Su et al., 2024) to Lie-group formulations that model continuous symmetries (Hutchinson al., 2021). However, strict equivariant designs are computationally demanding and struggle with temporal dynamics. Building on these insights, our method injects lightweight Lie-group differential biases into attention, com- bining frame-level rotation priors with temporal displacements to achieve geometry-consisent and efficient alignment rainy videos.
3 METHODOLOGGY
3.1 OVERVIEW
As illustrated in Fig. 2, DeLiVR restores clean video frames by injecting Lie-group spatiotemporal biases into the Transformer backbone. Specifically, each input clip is first divided into patches and embedded into tokens, followed by lightweight SO(2) head that predicts per-frame rotations to capture camera pose variations. These rotations are then used to build two complementary priors: spatial bias that enforces geometry.consisten aligmment across frames, and a temporal bias that reflects relative angular displacements. The two biases are fused with temporal decay and mask- ing strategies to form a unified spatiotemporal bias, which directly added to the self-attention process. Guided by this bias, the Transformer backbone focuses on reliable spatial-temporal corre- spondences, and the attended features are finally decoded to reconstruct the clean video frame.
3.2 SO(2) HEAD
To capture frame-wise wise orientation variations in rainy videos, we design an SO(2) head that predicts in-plane rotations and provides geometry-aware priors for subsequent bias construction.
3

---

Published as a conference paper at ICLR 2026
Patch Embedding
Lie Trunsformnee
Recortuction
Per-Frame Features
Tokens
Rotation Estimation
Linear
Linear
Linear
feat;
Head
Q
K
R
Axis Axis-Angee Angle 0g
Bias Calculation
Final Spatiotemporal Bias
(Ry, Postion)
[Ry]
Relative rotation
Geometric
Softmax
alignment
Angular distance
Spatial Bias
Temporal Bias
'QK" vă
Attention softmax
Blas
Final Bias Fusion
Atlention
Fusion
Temporal
Attended Features
marks
Operation
decay
Figure 2: Overall architecture DeLiVR. The model restores clean video frames by estimating per-frame rotations, constructing spatial and temporal biases, and injecting them into biased self- attention for robust geometry- coossstry and temporally reliable restoration.
Preliminaries on SO(2). The group SO(2) denotes the set of 2 rotation matrices preserving orientation in the plane:
coos 0 sin 0
sin 0 cos 0
SO(2) R(0)
Lie algebra so(2) consists of all 2 x skew-symmetric matrices, parameterized by scalar angle A:
{
0
so
0
The exponential map exp s2()) + SO(() converts an algebra element into a valid rotation matrix:
exp ((o -0-0) )0)==
[cos 0 sin 0
sin cos 0
SO(2) head for bounded rotation prediction. For each frame X,, lightweight SO(2) head pre- dicts a rotation matrix R, E SO(2). The prediction parameterized in the Lie algebra using the axis-angle representation wi IR22 To avoid degenerate solutions, the rotation magnitude is
strained within a bounded range:
R₂ = exp tanh(w:)),
|w, |l S 6max:
(4)
where exp(-) is the exponential map from so (2) to SO(2), and funx specifies the maximum rotation angle. In practice, we use SO(2) rotations by restricting Wa to the z-axis, which efficiently captures in-plane camera motion.
Compared with directly regressing angles, this design is numerically stable, differentiable, and seam- lessly integrates with Lie-theoretic bias construction, which will be detailed in Sec. 3.3.

---

Published as a conference paper at ICLR 2026
3.3 ROTATION- BOUNDDE LIE RELATIVE BIAS
Building on the predicted rotations from the SO(2) head, we construct rotation rotation-bounder bounded Lie rela- tive bias that explicitly injects geometry information into the attention mechanism.
Coordinate embedding.
We embed spatial locations into normalized 3D coordinate basis:
P= pp Pi E IR, |p:ll = 1,
(5)
where Pi denotes the position of the i-th patch token. For frame the rotated coordinates are obtained as
Pr, RePs.
(6)
with R& provided by the SO(2) head in Sec. 3.2.
Relative spatial bias. The spatial bias between token in frame and token j in frame is defined the inner product of their rotated coordinates:
Bseace [tt, i), (s, (pe. Ps.),
which measures geometry similarity under the predicted rotations.
Bias injection.
The computed spatial bias is added the attention logits:
QK + BBspace
Logits = vd
(8)
This enables the self-attention to explicitly account for frame-wise poses, guiding the network to aggregate features along geometrically aligned correspondences.
3.4 DIFFERENTIAL GROUP DISPLACEMENT
In addition to spatial alignment, temporal consistency is crucial for video restoration. To explicitly capture relative motion between adjacent frames, introduce differential group displacement based on Lie algebra differences.
Lie algebra difference. Given two consecutive frame rotations R Rg E SO(2), their relative motion be represented
AR, = R,-,
We project AR, onto the Lie algebra s2( via the logarithm map:
Ur log(ARt,))
(10)
where log(-) denotes the matrix logarithm and || is the norm measuring the angular displacement. The sequence {vr) can be interpreted as the Lie-velocity of the video.
Pairwise angular difference.
For general frame pairs (t, s), the relative angular difference is
0-11, RR, R.)]|,
(11)
which reflects the rotation magnitude required to align frame t - with frame t.
Temporal bias construction. We convert the angular difference into temporal bias that penalizes pairs with large pose discrepancy:
1, O1-1, K6
B [t
(12)
where x is a scaling constant. This bias is broadcast to the token level and added to the attention logits together with the spatial bias.
5

---

Published as a conference paper at ICLR 2026
Velocity regularization. Lie-velocity sequence:
To further stabilize training, introduce regularization term the
(1- 3) mcan (v)) mcan %)-1)),
(13)
where 3 controls the balance between the overall motion magnitude and smoothness. This regular- izer encourages moderate and smooth inter-frame rotations, preventing unstable predictions.
3.5
SPATIOTEMPORAL LIE-GROUP DIFFERENIAL MECHANISM
The final step is to unify spatial and temporal biases into a single mechanism that governs feature aggregation. We refer this as the spatiotemporal Lie Lie-group differential mechanism, which ensures that both geometric alignment and temporal consistency are simultancously enforced within the attention operation.
Unified bias. Given the spatial bias Bapace (Section 3.3) and the temporal bias Btime (Section 3.4), the total bias added the attention logits is
Biotal (Bspace + B O D @ M,
(14)
where o is scalar balancing temporal bias, D is temporal decay matrix, and M is banded mask.
Temporal decay. The decay matrix D E RxxT is defined as
Dit, s) exp -
(15)
where 7 controls the decay rate. This weighting emphasizes short-range interactions that are more reliable under rain distortions, while gradually suppressing long-range connections.
Banded attention mask. The mask M {0,1) restricts each frame to attend only to local temporal neighborhood:
Mft, s] 1( s| S 6),
(16)
where 8 specifies the temporal bandwidth. This prevents unstable correspondences between frames that are too far apart.
Attention with spatiotemporal Lie.
The attention logits for all tokens finally expressed
QK
Logits
vd Brotal
(17)
with Brotal constructed as in Eq. 14. This operation ensures that spatial alignment (via rotated coordinates) and temporal regularization (via angular differences and decay) tightly coupled inside the same attention layer.
Loss Function DeLiVR is trained end-to-end with a hybrid loss that balances reconstruction fi- delity and geometric regularization. The reconstruction term Lree (L1 loss) ensures pixel-level ac- curacy between the restored and ground-truth frames. To stabilize pose prediction, add rotation magnitude regularizer Ro. which constrains the predicted SO(2) rotations, and Lie-velocity regu- larizer R,, which enforces smooth temporal evolution. The final objective is
L= Lree + Ro + R.
where À9 and X control the trade-off between fidelity and geometric consistency. Based on grid search for optimal performance, we set the hyperparameter weights to X 0.02 and X 0.02 in our experiments.
EXPERIMENTS
4.1 EXPERIMENTAL SETUP
Datasets We conduct a comprehensive evaluation on four benchmark datasets. For synthetic data, use three widely-adopted benchmarks: NTURain (Chen al., 2018), Rain-Syn-Light (Liu al., 2018), and Rain- Rain-Syn-Conn Syn-Complex (Liu et al., 2018). For real-world evaluation, we use the recently proposed WeatherBench (Guan al., 2025) benchmark.

---

Published as a conference paper at ICLR 2026
Evaluation Metries We use Peak Signal-to-Noise Ratio, Structural Similarity Index, and Learned Perceptual Image Patch Similarity as the main metrics. Higher PSNR/SSIM and lower LPIPS indi- cate better video restoration quality. For downstream evaluation, adopt mean Average Precision for object detection and mean Intersection over Union for semantic segmentation.
Implementation Details Our DeLiVR model is implemented using the PyTorch framework and trained on NVIDIA 3090 GPUs We use the AdamW optimizer with an initial learning rate of 2 x 10-4, The learning rate is decayed over 5000 epochs using a cosine annealing schedule. We set the batch size to 64. For each input, we randomly sample a window of T" = 5 consecutive frames from the video sequences. Our model is trained with an LI reconstruction loss, aiming to restore the clean center frame from the rainy input sequence.
4.2 COMPARISON WITH STATE-OF-THE-ART METHODS
To comprehensively evaluate the performance of our proposed DeLiVR model, we conduct a com- parison with a range of state-of-the-art (SOTA) video deraining algorithms. The selected baselines cover diverse and prominent technical, including classic CNN-based methods (MFGAN (Yang et al., 2021). S2VD (Yue et al.. 2021)), Transformer- based models (ESTINe (Zhang et al., 2022), ViWS- Net (Yang et al., 2023)), and other recent architectures (ViMP-Net (Wu et al., 2023), rainmanba (Wu et al., 2024), Turtle (Ghasemabadi al.). VDMamba (Sun et al., 2025)).
4.2.1 QUANTITATIVE ANALYSIS
As shown in Table I, DeLiVR consistently achieves the best overall performance across synthetic and real rainy benchmarks. On NTURain, our method ranks second only to VDMamba (CVPR 2025). More importantly, when evaluated on the real-world WeatherBench dataset, VDMamba suf- fers noticeable performance drop (PSNR 23.91, SSIM 0.773). while DeLiVR establishes new statc-of-the- results (PSNR 26.56, SSIM 0.781). This contrast highlights that our Lie-group dif- ferential bias design not only provides competitive results on synthetic benchmarks but also yields superior generalization to challenging real rainy scenarios, demonstrating the practical robustness of our approach.
Table 1: Quantitative comparison on synthetic benchmarks and the real-world WeatherBench dataset. The BeatherBench benchmark included to specifically evaluate the model's general- ization ability to authentic, real-world adverse weather conditions. For PSNR/SSIM, higher is better
(1). For LPIPS, lower is better ()). Best results are in bold, and second-best are underlined.
Method
NTURain
Syn-Light
Syn-Complex
PSNR1
SSIM
LPPPS)]
PSNR
SSIM|
LPIPS.
PSNR1
SSIM
LPIPS]
PSNR1
SSIM
LPIPS.
S2VD (CVPR 21)
32.46
0.953
0.068
25.57
0.833
0.218
16.56
0.524
0.462
26.51
0.827
0.340
MEGAN (TRAMI 22)
33.69
0.950
0.152
22.55
0.839
0.106
21.05
0.763
0.184
20.61
0.707
0.365
(TPAMI
0.950
27.61
0.879
0.169
20.16
0.302
25:22
ViMP-Net (MM 23)
24.86
0.804
0.259
22.32
0.759
0.302
16.42
0.490
0.465
24.04
0.716
0.433
NiWS-Net (ICCV 23)
33.65
(1.49)
0.839
27.70
0.860
0.157
19.13
0,576
0.408
23. 50
(1689
0.381
rainmanba (MM 24)
0.876
0.295
Turtle (NeurlPS 24)
23.15
0.717
0.286
21.16
0.652
0
14.12
0.413
0.511
22.45 32.48
0.462
0.501
VDMamba (CVPR 25)
36.29
0.973
0.010
28.76
0.896
0.157
17.83
0.582
0.376
23.91
0.773
0.344
DeLiVR (Ours)
34.06
0.952
30.53
0.908
0.088
24.68
0.227
26.56
0.781
0.358
4.2.2 QUALITATIVE ANALYSIS
Figure illustrates the visual comparisons on both synthetic and real-world rainy scenes. Compared to other methods, our DeLiVR is capable of generating sharper images with richer details. For instance, methods like MFGAN and S2VD are prone to producing artifacts or over-smoothed back- grounds. While ESTINe and ViWS-Net are strong performers, they still exhibit residual rain streaks and temporal flickering when dealing with dense rain or fast-moving objects. In contrast, by leverag- ing ccometry-consiseee
alignment, DeLiVR not only removes rain streaks more thoroughly but also better preserves object edges and fine textures. It also demonstrates stronger temporal consistency in video sequences, without noticeable flickering artifacts.

---

Published as a conference paper at ICLR 2026
NTU
Light
Complex
Weather Bench
HIL
HIS
HI
HIN
HI
RainManba
MFGAN
ViWS-Net
VDManba
GT
Figure 3: Qualitative comparison with state-of-the-art methods on four benchmarks. From top to bottom, the rows show results on NTU, Rain-Syn- Liigg,, Rain-Syn-Complex, and the real-world WeatherBench dataset. Compared to other methods, our model more effectively removes severe rain streaks and color casts, while better preserving fine background textures and natural colors.
Baseline
Boyace
Full
Figure 4: Visual ablation of different bias components on the NTURain dataset. From left to right: baseline without Lie bias, model with spatial bias only (Bapwz), model with temporal bias only (Brime), and the full DeLiVR with both spatial and temporal Lie-group differential biases.
4.3 ABLATION STUDY
To assess the contribution of each component in DeLiVR, conducted ablation study (Ta- ble 2). Starting from plain spatiotemporal Transformer baseline, adding the spatial bias (Space) via bratton-bounded Lie relative bias improved PSNR by 1.37 dB, confirming the importance of explicit geometric alignment. Incorporating the temporal bias (Time) through differential group displacement further enhanced performance by modeling inter-frame motion. Finally, adding tem- poral decay and banded attention mask (D&M) yielded the best results.
Table 2: Ablation study of different components of DeLiVR on the NTURain dataset. For FVD, lower better (L).
Model Baseline
Bspace
Brime
D&&
PSNRT
SSIM
FVD.
(a)
29.21
0.868
47.25
(b)
32.58
0.927
31.6
(c)
33.14
0.935
22.5
(d)
7
34.06
0.952
18.5
Rotation-Peen Pentuuratottt Study. To directly validate that the proposed Lie-group differential bias im- proves cross-frame alignment, conduct controlled experiment where small in-plane rotations are injected into several frames of the input sequence. This perturbation produces synthetic mis- alignment while keeping scene content unchanged. As shown in Fig. 5, the rotation-aware model exhibits clearer temporal stability. The attention maps further reveal that the rotation-enhanced model captures richer directional dependencies, displaying higher entropy and concentrated
8

---

Published as a conference paper at ICLR 2026
high-valued regions. The creentionddiffernnce visualization highlights that the Lie-group bias pref- erentially strengthens correspondences around motion-sensitive structures, thereby reducing flicker and ghosting. These results provide explicit interpretability evidence that our method addresses cross-frame misalignment beyond improving overall metrics.
Controlled Comparison with Optical Flow Biases. To provide comparison between Lie- group rotation module and optical- saaal-flowbbbseee alternatives, we conducted a strictly controlled exper- iment where all variables except the bias representation were held constant. Specifically, we utilized a 12-layer Transformer backbone and maintained an identical training protocol. For the optical-flow baseline, RAFT flow fields were processed through a small learnable MLP to predict bias maps, mir- roring the structure of our rotation module. This design ensures the only differing factor is the choice of bias representation. Evaluations on the NTU-Rain dataset show our method improves PSNR by +2.43 dB, demonstrating that modeling rain-streak orientation on the SO(2) manifold provides stronger and more stable geometric inductive bias compared with unconstrained optical-flow fields. Visualizations in in Appendix (Fig. 9) and real-world results in Appendix (Fig. 10) further con- firm that our proposed prior excels on benchmarks and transfers robustly to naturally occurring rain conditions.
Attention Demonstrating Additional Information
Rotation
Baceliee Jole dan Maria
kussded Attartion Nedia
100
0005
oocal
Attestie Offineie
Alland Marl-ia
Altertinn Weight
Ellend
22000 5002
0,855
$.109
COLL
25
2.
Figure 5: Attention comparison between the baseline and the rotation-enhanced model. The top row shows full attention matrices for both models under the same input sequence. The sec- ond row visualizes spatial attention maps extracted from representative query positions. The right column reports aggregated attention statistics, including average entropy and maximum attention values. The bottom presents the distribution of attention weights and attention entropy across all heads and layers.
4.4 DISCUSSION
Impact on Downstream Tasks To assess the practical value of our deraining method, we tested its impact on downstream tasks like object detection and semantic segmentation. As visually demon- strated in Figure 6, adverse weather conditions severely degrade the performance of these high-level vision models. The top row shows that the object detector fails on the rainy input, but after pro- cessing with our method, it can accurately localize the targets. Similarly, for semantic segmentation (bottom row), our method helps the model produce a much cleaner and more precise mask com- pared to the corrupted result from the original image. This intuitively proves that method not only enhances visual quality but also acts as a crucial pwppppre-eeeee processing step to improve the reliability of downstream vision systems in real-world scenarios.

---

Published as a conference paper at ICLR 2026
RainManba
V VDMlnnk
ESTINe
MPGAN
ViWS-Net
Oura
Figure Visual comparison of downstream task performance on the Cain-Syn-Complex dataset.
Efficiency Analysis. In addition to restoration accuracy, efficiency plays crucial role in the practi- cal deployment video deraining systems. Table reports the model size (in terms of parameters) and the average inference time per frame. DeLiVR demonstrates clear advantages over prior meth- ods: it uses significantly fewer parameters and achieves much faster inference, while still delivering competitive or superior restoration quality. This confirms that introducing Lie-group differential biases not only theoretically meaningful and robust, but also lightweight and computationally efficient, making DeLiVR more suitable for real-world applications.
Table 3: Efficiency comparison on the NTURain dataset. Params denote model parameters (in millions). Time denotes average inference time (ms per frame).
Metric
rainmanha
ViMP-Net
Turtle
ViWS-Net
VDMamba
ESTINe
MFGAN
S2VD
DeLiVR (Ours)
Params (M).
38.73
36.63
58.62
57.82
12.70 32,04
29.90
29.47
0.53
2.64
Time (ms))
145.55
130.77
270.54
252.64
175.61
162.81
26.78
82.52
Guidance. We evaluate two representative flow-guided recurrent video restoration models on the WeatherBench dataset:
Comparison with Optical-
Recurrent Video Deraining (Yang et al.. 2019) (PSNR 23.33 / SSIM 0.691 / LPIPS 0.455) and High-Resolutie Optical Flow and Frame-Recurren Network (Fang & Zhan, 2022) (PSNR 24.10 / SSIM 0.716 / LPIPS 0.402). Under the same evaluation setting on an A100 GPU, our rotation- ceniiioo-rediittio--aaae model consistently surpasses both flow-based baselines.
Necessity of Lie Groups. Our design leverages Lie-group theory to ensure valid and continuous ro- tations, provide tangent space for stable optimization, and enable principled definitions of temporal displacement. Although similar effects could be superficially achieved by direct matrix parameter- ization, the Lie-group formulation offers theoretical rigor and extensibility. detailed analysis is provided in Appendix A.
Limitations. Despite its effectiveness, DeLiVR has certain limitations. First, the reliance on votation-centric modeling may not fully capture more complex non-rigid rain dynamics or cam- era motions beyond in in-plane rotations. Second, incorporating Lie-group biases introduces addi- tional computational overhead compared to purely implicit alignment schemes. Addressing these challenges and extending the framework to richer transformation groups (e.g.. SE())SSE(3) are promising directions for future work.
CONCLUSION
We proposed DeLiVR, a video deraining framework that injects Lie-group differential biases into attention to achieve geometry-cconistent alignment and motion-aware temporal modeling. Our method is theoretically grounded through the use of Lie algebra for stable optimization and princi- pled temporal displacement, and empirically validated by extensive experiments. Experimental re- sults demonstrate that DeLiVR not only achieves state-of-the-an -htt performance on real rainy datasets but also enhances downstream tasks such object detection and semantic segmentation. These findings highlight both the superior robustness of DeLiVR compared with existing methods and the practical value of integrating geometric theory into attention for reliable video restoration.
10

---

Published as a conference paper at ICLR 2026
REFERENCES
Chris H. Bahnsen and Thomas B. Moeslund. Rain removal in traffic surveillance: Does it matter? IEEE Transactions on Intelligent Transportation Systems, 20(8):2802-25) 21220022219,,, 2019. doi: 10.1109/
Kelvin CK Chan, Shangchen Zhou, Xiangyu Xu, and Chen Change Loy. Basicvsr++: Improv- ing video super-resolution with enhanced propagation and alignment. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 5972-5981, 2022.
Jie Chen, Cheen-Hau Tan, Junhui Hou, Lap-Pui Chau, and He Li. Robust video content alignment and compensation for rain removal in a enn framework. In Proceedings of the IEEE conference computer vision and pattern recognition, pp. 6286-6299 2018.
Dengxin Dai, Robby Tan, Vishal Patel, Jiri Matas, Bernt Schiele, and Luc Gool. Guest editorial: Special issue "computer vision for all seasons: Adverse weather and lighting conditions".
International Journal of Computer Vision, 129:1-3, 05 2021. doi: 10.1007/s1 10.1007/s1123-000 1263-021-01464-wk
Ning Fang and Zongqian Zhan. High-resolution optical flow and frame- network for video super-resolution and deblurring. Neurocomputiing, 189:128-1333 2022.
Sicheng Gao, Nancy Mehta. Zongwei Wu, and Radu Timofte. Ditvr: Zero-shot diffusion transformer for video restoration. arXiv preprint arXiv:2508.0788 2025.
Amirhosein Ghasemabadi, Muhammad Kamran Janjua, Mohammad Salameh, and Di Niu. Learning truncated causal history model for video restoration. In The Thirty-eighth Annual Conference on Neural Information Processing Systems.
Qiyuan Guan, Qianfeng Yang, Xiang Chen, Tianyu Song, Guiyue Jin, and Jiyu Jin. Weatherbench: A real-world benchmark dataset for all-in-one adverse weather image restoration. arXiv preprint arXiv:2509.11644 11642, 2025.
Yun Guo. Xueyao Xiao, Yi Chang, Shumin Deng, and Luxin Yan. From sky to the ground: A large- scale benchmark and simple baseline towards real rain removal. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 12097-12107, 2023.
Michael J Hutchinson, Charline Le Lan, Sheheryar Zaidi, Emilien Dupont, Yee Whye Teh, and Hyunjik Kim. Lietransformer: Equivariant self-attention for lie groups In International confer- ence on machine learning. pp. 4533 4543. PMLR, 2021.
Jin-Hwan Kim, Jae-Young Sim, and Chang-Su Kim. Video deraining and desnowing using temporal correlation and low-rank matrix completion. IEEE Transactions on Image Processing, 24(9): 2658-2670, 2015.
Boyi Li. Wenqi Ren, Dengpan Fu, Dacheng Tao, Dan Feng, Wenjun Zeng, and Zhangyang Wang. Benchmarking single-image dehazing and beyond. IEEE Transactions on Image Processing, 28 (1):492-505, 2019.
Fengqi Li, Mengehao Guo, Fengqiang Xu, Renxuan Xiong, Xiaohong Yan, Qian Sun, and Deguang Wang. Stformer: Advancing video deraining network integrating with spatial transformers and multiscale feature extraction. In 2024 IEEE International Conference Multimedia and Expo (ICME), pp. 1 1-6. IEEE, 2024.
Minghan Li, Qi Xie, Qian Zhao, Wei Wei, Shuhang Gu, Jing Tao, and Deyu Meng. Video rain streak removal by multiscale convolutional sparse coding. In Proceedings of the IEEE conference computer vision and pattern recognition, pp. 6644-6651 2018.
Jingyun Liang, Yuchen Fan, Xiaoyu Xiang, Rakesh Ranjan, Eddy Ilg, Simon Green, Jiezhang Cao, Kai Zhang, Radu Timofte, and Luc V Gool. Recurrent video restoration transformer with guided deformable attention. Advances in Neural Information Processing Systems, 35:378-393, 2022.
Sophus Lie and Friedrich Engel. Theorie der transformationsgruupenn, volume 3. Teubner, 1893.

---

Published as a conference paper at ICLR 2026
Jiaying Liu, Wenhan Yang, Shuai Yang, and Zongming Guo. Erase or fill? deep joint recurrent rain removal and reconstruction in vidcos. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.
2018.
Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer. Hierarchical vision transformer using shifted windows. In Proceedings of the IEEE/CVF international conference computer vision, pp. 10012-10022, 2021.
Seungjun Nah, Tae Hyun Kim, and Kyoung Mu Lee. Deep multi-scale convolutional neural net- work for dynamic scene deblurring. In The IEEE Conference Computer Vision and Pattern Recognition (CVPR), July 2017.
Claudio Rota, Marco Buzzelli, Simone Bianco, and Raimondo Schettini. Video restoration based on deep learning: a comprehensive survey, Artificial Intelligence Review, 56(6):5317-5364, 2023.
Anu Singha and Mrinal Kanti Bhowmik. Salient features for moving object detection in adverse weather conditions during night time. IEEE Transactions Circuits and Systems for Video Technology, 30(10):3317-333) 2020. doi: 10. 10.109//CSVV222199266666
Jianlin Su, Murtadha Ahmed, Yu Lu, Shengfeng Pan, Wen Bo, and Yunfeng Liu. Roformer: En- hanced transformer with rotary position embedding. Neurocomputing, 568: 127063. 2024.
Shangquan Sun, Wenqi Ren, Juxiang Zhou, Shu Wang, Jianhou Gan, and Xiaochun Cao. Semi- supervised state-space model with dynamic stacking filter for real-world video deraining. In Pro- ceedings of the Computer Vision and Puttern Recognition Conference, pp. 261 14 2-1244,, 2025.
Hong Wang, Qi Xie, Qian Zhao, and Deyu Meng. A model-driven deep neural network for single image rain removal. In Proceedings of the IEEF/CVF conference on computer vision and pattern recognition, pp. 3103-3112, 2020.
Kunyu Wang, Xueyang Fu, Chengzhi Cao, Chengjie Ge, Wei Zhai, and Zheng-Jun Zha. Towards better de-raining generalization via rainy characteristics memorization and replay. arXiv preprint arXiv:2506.00477, 2025.
Shuai Wang, Lei Zhu, Huazhu Fu, Jing Qin, Carola-Bibiane Schönlieb, Wei Feng, and Song Wang. Rethinking video rain streak removal: A new synthesis model and deraining network with video rain prior. In European Conference on Computer Vision, pp. 565-582. Springer. 2022.
Xinrui Wang, Hongyun Zhang, Kecan Cai, Duoqian Miao, Qi Zhang. and Miao Li. Sfformer: Adaptive sparse and frequency-guide transformer network for single image derain. In Chinese Conference on Pattern Recognition and Computer Vision (PRCV), pp. 482-496 Springer, 2024.
Xintao Wang, Kelvin CK Chan, Ke Yu, Chao Dong, and Chen Change Loy. Edvr: Video restoration with enhanced deformable convolutional networks. In Proceedings of the IEFF/CVF conference on computer vision and pattern recognition workshops, pp. 0-0, 2019.
Hongtao Wu, Yijun Yang. Haoyu Chen, Jingjing Ren, and Lei Zhu. Mask-guide progressive net- work for joint raindrop and rain streak removal in videos. In Proceedings of the 3 ACM Inter- national Conference on Multimedia, pp. 7216-7225, 2023.
Hongtao WU, Yijun Yang, Huihui Xu, Weiming Wang, Jinni Zhou, and Lei Zhu. Rainmamba: Enhanced locality learning with state space models for video deraining. In Proceedings of the 32nd ACM International Conference on Multimedia, pp. 7881-7890, 2024.
Wending Yan, Robby Tan, Wenhan Yang, and Dengxin Dai. Self Self-aligned video deraining with transmission-deptl consistency. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition, pp. 11966-11976. 2021.
Wenhan Yang. Robby T. Tan, Jiashi Feng, Jiaying Liu, Zongming Guo, and Shuicheng Yan. Deep joint rain detection and removal from a single image. 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1685-1694, 2017. doi: 10. 10.1109/CPP.2217..0
12

---

Published as a conference paper at ICLR 2026
Wenhan Yang, Jiaying Liu, and Jiashi Feng. Frame- consiseon recurrent video deraining with dual- level flow. Proceedings of the IEEE/CVE conference on computer vision and pattern recogni- tion, pp. 1661-1670, 2019.
Wenhan Yang, Robby Tan, Jiashi Feng. Shiqi Wang, Bin Cheng, and Jiaying Liu. Recurrent multi- frame deraining: Combining physics guidance and adversarial learning. IEEE Transactions on Patlern Analysis and Machine Intelligence, 44(1 (M11)):569-8555 2021.
Wenhan Yang, Robby T Tan, Shiqi Wang, Alex C Kot, and Jiaying Liu. Learning remove rain in video with self-supervision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4663):1378-136, 2022.
Yijun Yang, Angelica Aviles-Rivero, Huazhu Fu, Ye Liu, Weiming Wang, and Lei Zhu. Video hetpeeewwweate--oooeeeeeeee suppression network via weather messenger and adversarial back- propagation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp- 13200-132I0 13210, 2023.
Changfeng Yu, Yi Chang, Yi Li, Xile Zhao, and Luxin Yan. Unsupervised image deraining: Opti- mization model driven deep cnn. Proceedings of the 29th ACM International Conference on Multimedia, pp. 2634-2642, 2021.
Zongsheng Yue, Jianwen Xie, Qian Zhao, and Deyu Meng. Semi-supervised video deraining with dynamical rain generator. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2021.
Kaihao Zhang, Dongxu Li, Wenhan Luo, Wenqi Ren, and Wei Liu. Enhanced nempoll interaction learning for video deraining: faster and better framework. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2022.
Kun Zhou, Wenbo Li, Liying Lu, Xiaoguang Han, and Jiangbo Lu. Revisiting temporal alignment for video restoration. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 6053-6062, 2022.
A APPENDIX
A.1 THEORETICAL ANALYSIS OF LIE GROUP FORMULATION
Although one may use rotation matrices approximate rain streak orientation, here provide theoretical analysis showing why a Lie group formulation is essential for our task.
(i Guaranteed validity of rotations. group:
valid planar rotation must lie in the special orthogonal
SO(2) = {R 2x2 R R = 1, (R) = 1}.
(18)
If R directly parameterized as an unconstrained matrix, optimization may yield invalid results (e.g., det( + 1 or R R & I). Enforcing orthogonality requires either costly projection steps or implicit normalization, which are non-trivial in gradient-baset learning. By contrast, parameterizing in the Lie algebra s2) with exponential mapping
= exp(w),) E so()),
(19)
guarantees R E SO(() by construction. Thus, every predicted transformation remains a mathemat- ically valid rotation.
(ii) Tangent space for stable optimization. The Lie algebra so(2) is the tangent space at the identity, defined as
{ 0 1
52
(20)
This provides linear space for optimization, allowing unconstrained updates R while ensuring stability. Optimization in this Euclidean tangent space avoids the degeneracy and instability of directly manipulating matrix entries subject nonlinear constraints.
13

---

Published as a conference paper at ICLR 2026
(iii) Principled definition of temporal displacement. For temporal modeling, require a sistent notion of relative rotation between frames. Given two orientations Re, Rs E SO()), their relative transformation is
A R R R, E SO(2).
(21)
The logarithm map log S2(() + (2 then yields
ft = (og
(22)
which quantifies the angular displacement as a scalar in the Lie algebra. This is a principled, geomet- rically meaningful notion of motion, while subtracting matrices R. R, provides intrinsic interpretation of displacement.
In summary, while plain rotation matrices can approximate orientation, the Lie group perspective (i) ensures validity of rotations by construction, (ii) offers a tangent space for stable gradient- optimization, and (iii) enables principled temporal displacement via group differences and logarithm mapping. These theoretical properties justify our design choice and highlight why Lie groups are essential modeling spatiotemporal alignment for video deraining.
A.2 CORE PSEUDOCODE OF DELIVR
Algorithm summarizes the overall workflow of our proposed DeLiVR framework. The process begins with patch embedding to obtain tokenized representations, followed by frame-wise rotation prediction through the SO(2) head. The predicted rotations are then used to construct spatial and temporal biases, which are fused into total bias and injected into the attention mechanism. Finally, the updated token states are decoded to reconstruct the clean center frame, with the entire model trained under a joint reconstruction and regularization loss.
Algorithm Core pseudocode DeLiVR
1: Input: Rainy video window X {X,)==
2: Output: Restored center frame Y:
3: Patchify all frames and obtain initial embeddings ())
4: For each frame X₁, use SO(2) head to predict rotation Rç-
5: Construct biases:
1. Rotated coordinates: Pt,i i Rep.
2. Spatial bias: Bspace [t, i), [s. (Pr,s Pa.).
3. Temporal bias: Brime [t, s] = - log R. Rt)l
(.)l/mm K.
4. Fuse: Biotal (Bapace Btime) D O M.
6: Update tokens for = 1....,,..
H((+1) ( Attention(H Brotal).
7: Decode center tokens to obtain Ye.
8: Train with L Lree NoRo R.R
A.3 GENERALIZATION TO DEBLURRING AND DEHAZING
Although our method is introduced primarily for video deraining, the core idea injea-nnectiin a Lie- group differential bias to stabilize cross-frame alignment-is degradattion-agnosiccc To further ver- ify this, we additionally evaluate the model on two representative degradation types: deblurring (trained on the GoPro dataset (Nah et al., 2017)) and dehazing (trained on the RESIDE datasetLi et al. (2019)). As shown in Fig. 7, our method consistently improves geometric stability, reduces temporal flickering, and preserves fine structures across all three tasks (deraining, deblurring, de- hazing). These results demonstrate that the proposed geometric prior captures fundamental motion characteristics rather than degradation-sper specific cues, thereby enabling natural transfer to a broader range of video restoration scenarios.
14

---

Published as a conference paper at ICLR 2026
blur
deblur
haze
dehaze
Figure 7: Generalization to other degradations. Our method consistently produces cleaner struc-
tures and fewer temporal flickers.
raim
derain
Figure 8: Real-world downstream evaluation object detection. We apply off-the-shelf detector to real captured rainy frame (left) and to the derained result produced by our method (right).
A.4 REAL-WORLD DOWNSTREAM EVALUATION
To further validate the practical utility of our method, we test an off-the-shelf object detector on real captured rainy image. As shown in Fig. deraining enables the detector identify an additional pedestrian missed in the rainy input, demonstrating improved reliability for downstream perception.
A.S LARGE VISUALIZATION OF FIGURE 3
To provide clearer view, include the enlarged version of Figure in Appendix.
15

---

Published as a conference paper at ICLR 2026
SPRUCE
SPAUCS
SPRCCE
SPALCE
input
optical flow
work
Figure 9: Visual comparison on the NTU-Rain. From left to right: rainy input, flow-based bias baseline, our Lie Rotation model, and ground-truth.
input
optical flow
our work
Figure 10: Real-world rain removal. From left right: the original rainy input, the flow-based bias baseline. and our Lie Rotation model.
A.6 USE OF LARGE LANGUAGE MODELS
During the preparation of this paper, large language models (LLMs) employed for tex- tual refinement, including grammar checking, clarity improvement, and stylistic polishing of the manuscript.
ETHICS STATEMENT
This work focuses on video deraining, a low-level vision task, and does not involve human sub- jects sensitive personal data. All datasets used in our experiments are either publicly available synthetic datasets or real-world benchmarks that do not contain personally identifiable information. Our method does not introduce risks of privacy leakage misuse beyond the scope of general image
16

---

Published as a conference paper at ICLR 2026
and video restoration. We adhere to the ICLR Code of Ethics, and we believe that contributions advance fundamental research in computer vision without posing foreseeable ethical concerns.
REPRODUCIBILITY STATEMENT
We have made significant efforts to ensure the reproducibility of our work. The paper provides de- tailed descriptions of the proposed architecture, bias formulation, and loss functions in Sections 3, with theoretical derivations further explained in the appendix. Implementation details, training se- tups, and hyperparameters are described in the experimental section and supplementary materials. Pseudocode for the core algorithm is included in the appendix (Algorithm 1), and all datasets used (NTURain, Syn-Light, Syn-Complex, WeatherBench) are publicly available.
17

---

Published as a conference paper at ICLR 2026
GT
Ours
VDManba
TRE THE
RI
ESTINet
RR
ViWS-Net
RR
S2VD
RR
MEGAN
ViMP-Net RainManbu
RH
Turtle
HRU
Imput
Complex
Weather Bench
NTU
Light
Figure 11: Enlarged visualization corresponding to Figure 3.
18


Reviews:
[{"review_id": "C9ij3Lv3mp", "reviewer": "Reviewer_HmPv", "summary": "The paper introduces DeLiVR, a video deraining method that injects spatiotemporal Lie group-based biases into Transformer attention layers, enabling geometry-consistent feature alignment and motion-aware modeling. It achieves strong performance on synthetic and real-world benchmarks, with enhanced efficiency and robustness over prior methods.", "questions": "See above", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Novel Use of Lie Groups in Attention: Introduces a principled and efficient method to incorporate SO(2) Lie algebra into Transformer attention, improving spatiotemporal consistency without optical flow.\n\nStrong Generalization: Achieves SOTA or competitive results on synthetic datasets and real-world benchmarks like WeatherBench, with improved downstream performance.\n\nElegant Design and Efficiency: Uses lightweight geometric predictors instead of full equivariant models, maintaining inference speed and model compactness (2.64M params vs 12–58M in baselines).\n\nThorough Ablation and Theoretical Justification: Detailed experiments, regularization analysis, and Lie group derivations demonstrate rigorous understanding and contribution clarity.", "weaknesses": "SO(2)-only Limitation: The model restricts itself to in-plane rotation (SO(2)) and may underperform on more complex real-world motion (e.g., 3D translations, SE(3)), as briefly acknowledged.\n\nOver-reliance on Geometry: The spatiotemporal bias fusion mechanism may not sufficiently adapt when motion is irregular or scene semantics dominate (e.g., occlusions, deformable objects).", "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": "0GFond9hSW", "reviewer": "Reviewer_ajhU", "summary": "This paper proposes DeLiVR, a method that injects spatiotemporal Lie-group differential biases into Transformer attention scores to achieve geometry-consistent alignment without relying on optical flow. The core contributions include a rotation-bounded Lie relative bias for spatial alignment and a differential group displacement for temporal consistency. Experiments on synthetic and real-world benchmarks demonstrate improved rain removal, detail preservation, and temporal consistency compared to existing methods.", "questions": "-What is the specific connection between the proposed method and rain? Is the predicted rotation that of the camera or the tilt angle of the rain streaks? Overall, what I most want to know is whether the method can transfer to video restoration tasks under other degradations, what its scope of applicability is, and whether it can handle three‑dimensional camera shake.\n\n-The results of this paper require more interpretability validation. I would like to see examples where the proposed method specifically addresses cross frame misalignment and temporal artifacts, rather than only showing improvements in overall metrics.\n\n-Since the authors claim that optical‑flow‑based methods are not robust, they should conduct controlled experiments under the same baseline to demonstrate that the proposed rotation prediction provides more reliable guidance than optical flow. At present, the paper discusses this conclusion only in general terms and lacks strong experimental evidence.\n\n-The paper requires more proofreading and fine‑grained refinement in details, and both the method illustrations and the figures need a more polished presentation.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "-This work addresses a salient problem in video restoration caused by camera rotation, namely spatial and temporal misalignment. The proposed Lie group based in-plane rotation estimation directly targets this challenge, and the method is well motivated with a clear and coherent rationale.\n\n-The proposed method achieves state of the art overall performance on public benchmarks and has an advantage in inference speed.", "weaknesses": "-The in-plane rotation estimation proposed in this paper appears to target only the camera itself. In principle, the scheme applies to any video restoration task and has no obvious relevance to deraining, that is, the authors did not design for the tilt angle of rain. This makes the paper somewhat tenuous as a dedicated video deraining approach.\n\n-Camera shake is inherently 3 dimensional, raising doubts that a in-plane model can resolve the stated issue. The evidence presented in the paper is limited and does not convincingly support claims of mitigating cross frame misalignment and temporal artifacts. Since the method explicitly targets rotation, the evaluation should isolate rotation induced errors and demonstrate corresponding gains; modest and unstable aggregate improvements are not sufficient.\n\n-The authors deny the robustness of optical‑flow approaches and claim that unreliable optical flow will harm such video restoration models. This view should be supported by more solid comparative experiments, given that optical‑flow‑based methods are indeed mainstream in this field. In addition, since the authors introduce physical guidance by embedding a bias for the rotation angle, they should compare with other approaches that use bias modulation. Most straightforwardly, I believe there should be a comparison under the same baseline and modulation scheme between using optical flow for modulation and using the predicted rotation angle, which would directly show that the proposed rotation estimation is more reliable than optical flow.\n\n-The organization and presentation of this paper are not yet at a publishable level. For example, most of Section 3 consists of existing formulas used as background, with few formulas of substantive value that are newly derived by the authors, which makes it hard to grasp the key points. The figures are rather rough (in Fig. 3 many panels do not clearly show differences in details), and some figures do not match their captions (Fig. 4).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PYaRGQ2PN2", "reviewer": "Reviewer_KGvX", "summary": "The paper proposes DeLiVR, a video deraining framework that leverages spatiotemporal Lie-group differential biases to enforce geometric consistency across frames. By embedding Lie-group formulations directly into the attention mechanism, the method effectively models continuous transformations, reducing reliance on optical flow or heuristic alignment. It introduces two key components: (1) a rotation-bounded Lie relative bias for geometry-consistent spatial alignment, and (2) a differential group displacement that captures inter-frame angular velocity to guide temporal attention. Experimental results on multiple benchmarks validate the approach’s superior performance and efficiency compared to existing methods.", "questions": "In Table 3, both the S2VD score (26.78) and the proposed method’s score (82.52) are highlighted in bold. It is recommended to use consistent formatting or clarify the highlighting rule to avoid confusion.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper introduces Lie group theory into video deraining for the first time, providing a principled geometric prior that replaces traditional optical flow with continuous transformation modeling, leading to more robust spatial–temporal consistency.\n2. The proposed differential spatiotemporal Lie Bias, composed of the rotation-bounded Lie relative bias and differential group displacement, is elegantly integrated into the attention mechanism. This design explicitly encodes rotational and velocity information, effectively capturing dynamic rain streak variations in real-world videos.\n3. The paper is clearly written with solid motivation, detailed methodological exposition, and comprehensive experimental validation, making the technical contributions easy to follow and well-justified.", "weaknesses": "1. While the paper introduces Lie group theory as a prior for modeling continuous transformations, the theoretical connection between the proposed Lie biases and actual motion manifolds is not fully discussed. It would be helpful to clarify how the chosen Lie algebra parameterization ensures stability or accuracy under complex non-rigid motion.\n2. The paper claims that VDMamba (CVPR 2025) achieves slightly higher PSNR (36.29 vs. 34.06) and SSIM (0.973 vs. 0.952) but worse perceptual quality (LPIPS 0.010 vs. 0.039). However, the LPIPS metric indicates that VDMamba actually achieves better perceptual results. Therefore, the corresponding discussion in the paper is not rigorous and should be revised to ensure the accuracy of experimental interpretation.\n3. The downstream application evaluation is limited to the Rain-Syn-Complex dataset, which is synthetic. Including evaluations on real captured tasks would make the results more convincing.", "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)