MODEM: A Morton-Order Degradation Estimation Mechanism for Adverse Weather Image Recovery
Authors: Hainuo Wang
Qiming Hu
Xiaojie Guo
Venue: NeurIPS 2025 poster ()
Keywords: Degradation Estimation
Adverse Weather
Image Restoration
Primary area: applications
TL;DR: MODEM tackles tricky weather image restoration by estimating degradation (DDEM) and using it to guide a novel Morton-order state-space model (MOS2D) for adaptive, context-aware cleaning.

Abstract: Restoring images degraded by adverse weather remains a significant challenge due to the highly non-uniform and spatially heterogeneous nature of weather-induced artifacts, \emph{e.g.}, fine-grained rain streaks versus widespread haze. Accurately estimating the underlying degradation can intuitively provide restoration models with more targeted and effective guidance, enabling adaptive processing strategies. To this end, we propose a Morton-Order Degradation Estimation Mechanism (MODEM) for adverse weather image restoration. Central to MODEM is the Morton-Order 2D-Selective-Scan Module (MOS2D), which integrates Morton-coded spatial ordering with selective state-space models to capture long-range dependencies while preserving local structural coherence. Complementing MOS2D, we introduce a Dual Degradation Estimation Module (DDEM) that disentangles and estimates both global and local degradation priors. These priors dynamically condition the MOS2D modules, facilitating adaptive and context-aware restoration. Extensive experiments and ablation studies demonstrate that MODEM achieves state-of-the-art results across multiple benchmarks and weather types, highlighting its effectiveness in modeling complex degradation dynamics. Our code will be released soon.

MODEM: A Morton-Order Degradation Estimation Mechanism for Adverse Weather Image Recovery
Hainuo Wang, Qiming Hu, Xiaojie Gue
College of Intelligence and Computing, Tianjin University, Tinjjn 300350, China hainuo@tju u. edu. en huqimingetju. edu. en xj wwm.a...guu. gax.guummmmal.... com
Abstract
Restoring images degraded by adverse weather remains a significant challenge due to the highly non-uniform and spatially heterogeneous nature of weather-induced artifacts, e.g., fine-gra fine-grained rain streaks versus widespread haze. Accurately estimat- ing the underlying degradation can intuitively provide restoration models with more targeted and effective guidance, enabling adaptive processing strategies. this end, we propose Morton-Oree -ororr Degradation Estimation Mechanism (MODEM) for adverse weather image restoration. Central to MODEM the Corton-Ordde -Seeecive--Seat Module (MOS2D), which integrates Morton-coded spatial dering with selective state-space models to capture long-range dependencies while preserving local structural coherence. Complementing MOS2D, introduce Dual Degradation Estimation Module (DDEM) that disentangles and estimates both global and local degradation priors. These priors dynamically condition the MOS2D modules, facilitating adaptive and context-aware restoration. Extensive ex- periments and ablation studies demonstrate that MODEM achieves state-of-the-art results across multiple benchmarks and weather types, highlighting its effectiveness in modeling complex degradation dynamics. Our code will be released at here.
Introduction
Computer vision systems are increasingly integral to critical applications, such as autonomous driving [ and intelligent surveillance [49 70), demanding reliable performance in diverse envi- ronments. However, their effectiveness deteriorates significantly under adverse weather conditions,
such as rain [16
42 57 758 92], haze 77 21
[83 85), and snow [38 45 59 87 13 12),
which introduce complex visual artifacts and obscure critical scene information. Thus, effectively restoring clear images from such weather-degraded inputs is essential to boost the robustness and safety of modern computer vision technologies in real- wal-world deployments.
largely rely on physical models hand- crafted statistical priors tailored to individual weather phenomena. Due to the limited feature representation capabilities, these schemes
Early task-specific methods 2 4 23 60 61
30
32 90
brittle in the face of complex scenes deviations from assumed degradation patterns. With the advent of deep learning, numerous deep networks have achieved impressive performance
training large-scale datasets for specific tasks such image deraining [6] 42 75) 78 5 41 69 83], dehazing [76] 77 21 62 71 83 85). or desnowing (38 45)
59 87 These models excel at implicitly learning the inverse mapping through extensive supervision. But their highly specialized nature necessitates separate models for each weather condition, severely limiting scalability and practical deployment in unconstrained environments.
Recently, much attention has been directed toward unified or multi-task frameworks designed to
cope with various weather conditions within single model [95] 67
40
55
65 79]. These
"ooresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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(a) Raster Scanning
(b) Continuous Scanning
(c) Local Scanning
(d) Morton Scanning
Figure 1: Comparison of various image scanning methods. (a) Raster Scanning. (b) Continuous Scanning. (c) Local Scanning, (d) Morton Scanning, which can better preserve spatial locality of
neighboring pixels the resulting ID sequence, beneficial for capturing contextual information.
approaches adopt variety of sophisticated strategies, including architecture search for optimal generalization [40], disentanglement of weather-shared and weather-specific representations (95), knowledge distillation and regularization [ЛI. generative diffusion modeling (55], learned priors or codebooks [79], and transformer-based architectures that offer strong global modeling capabil- ities [67 655. Although these models mark notable progress and offer broader applicability, they still struggle with the challenge of modeling the inherently distinct and often highly spatially het- erogencous characteristics of different weather degradations. For example, haze tends to cause smooth intensity attenuation, whereas rain streaks and snowflakes introduce sharp, local occlusions with specific structural patterns. Most existing architectures lack dedicated degradation estimation mechanisms to explicitly model and leverage these fine-grat fine-grained, spatially variant degradation patterns, deployment. Therefore, effective estimation of
which undermines their performance in spatially variant degradation characteristics, encompassing both global trends and local structures, as guidance is critical for adaptive and contexl-aware restoration under dynamic weather conditions.
For an element (e.g., pixel) of a degraded image, its degradation characteristic can be regarded as latent "state" within a degradation space, encapsulating the influence of adverse weather its visual appearance. These states evolve spatially, governed by both local (e.g.. rain streaks) and non-local patterns (e.g., drifting fog). This perspective naturally lends itself to State Space Modeling (SSM) 17 The connection between the image degradation modeling and SSM is formally given in Sec. By treating degradation structured sequence of evolving states, SSM capture long-range contextual dependencies while maintaining sensitivity to local features. When coupled with degradation estimation mechanisms, SSM empowers the restoration process to be contextually aware and spatially adaptive, effectively aligning restoration strategies with the heterogeneous and scene-specific nature of weather-induced artifacts.
Motivated by the above insight, we propose a novel Morton- Degradation Estimation Mecha- nism (MODEM) that estimates degradation state via SSM and guides adaptive restoration in degraded images. At the heart of MODEM lies the Morton-Order 2D-Selective- Scan Module (MOS2D), which integrates SSM with Morton-coded spatial traversal. Unlike conventional raster scanning, the Morton- order scan follows a hierarchical, locality-preservve structured and efficient modeling of both local and long-range dependencies, as shown in Fig. dd). To complement MOS2D, we further introduce a Dual Degradation Estimation Module (DDEM), designed to extract two complementary forms of degradation information from the input: (i) a global degradation representation that encapsulates high-level weather characteristies such as type and sever- ity, and (ii) set of spatially adaptive kernels that encode local degradation structures and variations. These dual degradation representations are then utilized to dynamically modulate the restoration process. Specifically. the global representation adaptively influences feature transformations within MODEM, while the spatially adaptive kernels guide the matrix construction within MOS2D, refining the spatial dependencies captured along the Morton-order sequence. This modulltinn strategy equips the restoration network with both global awareness and local sensitivity, thereby delivering more precise and effective restoration. Our primary contributions can be summarized as follows:
sequence 50 34
53
31
7 54 that enables
We propose novel Morton-Order Degradation Estimation Mechanism that introduces the MOS2D module, which integrates Morton-coded spatial ordering with selective state space modeling to effectively capture spatially heterogeneous weather degradation dynamics.
We design Dual Degradation Estimation Module that jointly estimates global degradation de- scriptors and spatially adaptive kernels. These two complementary representations are used to dynamically modulate MOS2D, allowing contextually aware and spatially adaptive restoration.
2

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Extensive experiments and ablation studies are conducted to demonstrate the effectiveness of the proposed MODEM, and its superiority over other state-of of-the-art competitors in restoring images under diverse and complex adverse weather conditions.
Related Work
This section briefly reviews representative approaches single adverse weather restoration including rain streak removal, raindrop removal, haze removal and snow removal, as well as unified all-in-one models. Additionally, recent advances in SSM-based image restoration techniques are also discussed.
Rain Streak Removal. Traditional rain streak removal methods typically relied on image decomposi- tion [2] or jensor-based priors [30]. With the advent of deep learning. various models have emerged, like the deep detail network for splitting rain details [16], recurrent networks for context aggregation in single images 4T, and spatio-temporal aggregation in videos 4 Further developments include
incertainty-guidee multi-scale designs (78,, density-aware architectures
spatial attention [69]
joint retection-removal frameworks 77,, and -aseb attentive schemes
Raindrop Removal. Early efforts addressed specific scenarios [15 or adherent raindrops in videos 80
Deep learning subsequently provided more generalizable solutions, including learning from synthetic photorealistic data [22], using attention-guided GANs for realistic inpainting [57]. and dedicated networks for visibility through raindrop-covered windows [58]. General restoration architectures like Dual Residual Networks [43] and Adaptive Sparse Transformers [92] are also applicable, with advanced dual attention-in iicntion-in-attennion attention models (86) tackling joint rain streak and raindrop removal.
Haze Removal. Traditional image dehazing methods often utilized statistical priors the Dark Channel Prior (DCP) 23), non-local similarity techniques [4) multi-scale fusion 2 But these approaches faced robustness issues in diverse hazy scenes due to strong underlying assumptions. Deep learning has since become dominant, with methods focusing on estimating transmission and atmospheric light, sometimes using depth awareness (76 or unpaired learning via decomposition 777. Other approaches tackle haze density variations
domain adaptation (62). and contrastive learning (71.
Snow Removal. While specific traditional priors for snow removal are less common compared to other weather conditions, principles from general image restoration were often adapted. Deep learning solutions have gained traction, including powerful general-purpose purpose backbones [13 and more specialized networks. Desnowing-specife models often involve context-aware designs leverage semantic and depth priors [87]. Techniques inspired by classical matrix decomposition and methods for online video processing (38] have also been integrated into deep frameworks.
45
(59
While these specialized models excel under specific weather conditions, their limited generalization requires separate models for each degradation type, hindering real-world practicality.
Unified Adverse Weather Restoration. To mitigate the inefficiency of deploying multiple models for complex weather conditions, unified models have been devised [95] 67 III 40 [5) 65 79). However, these unified ones face fundamental challenge that the degradation space covered by unified models is exponentially larger than that of weather-specific counterparts, substantially increasing the complexity of accurate modeling and generalization. tackle this, existing approaches employ different strategies to learn more generalizable representations. Early efforts included using NAS to find unified structure 40 and leveraging Transformers like Trans Weather (67] for their global context modeling. Others focused on training strategies, such as two-stage knowledge learning with multi-contrastive regularization [1] More recent works have explored disentangling weather-general and weather-specife features (95], adapting powerful generative models like diffusion models (55)), incorporating learned codebook priors (79), and enhancing Transformers with global image statistics like Histoformer [65]. These methods showcase trend towards more sophisticated and adaptive unified restoration. Despite progress, the unified models still struggle to effectively capture the diverse and spatially heterogeneous characteristies of different weather phenomena.
Image Restoration. Recent State Space Models (SSMs) 18
notably Mamba [17
with its selective scan mechanism, offer efficient long-sequence modeling and have rapidly permeated Inspired by these advancements, SSMs are increasingly applied to image restoration. General frameworks like MambalR (20). VMambalR (63] and CU-Mamba [14] demonstrate the potential of Mamba-based models as strong baselines. Specific low-level vision applications have also seen tailored solutions. For example, WaterMamba [19] has been developed
computer vision [52 94
48
64
3

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Output
How the long-runge state ewhres over picels.
How the local information offects the current stule. Residual Connection.
C ( A
h
x
B
D
Figure 2: Connection between MODEM and SSM.
08
0.0
(a) Input Image
(b) Long Range CAha-1
(c) Local CBa=
(d) Output of MOS2D
Figure 3: With respect to a sample (a), (b)-(d) visualize the long-range CA (c) local C.Eck. and (d) output of MOS2D yk, respectively. More can be found in Appendix A.4
for underwater image enhancement, and IRSRMamba 26 addresses infrared super-resolution. Low- light image enhancement has been tackled by models like RetinexMamba [3] and LLEMamba [89],
while efficient SSM designs have been proposed for image deblurring [35]. In image deraining, notable works include FourierMamba [37] and Mrmba [91]. These efforts underscore growing success of SSMs in addressing image restoration challenges. Our work builds upon this
trend, leveraging SSMs for adaptive modeling of spatially heterogeneous weather degradations.
Bridging Image Degradation Estimation and State Space Modeling
Restoring images corrupted by adverse weather is inherently a highly ill-posed problem. In general, the relationship between an observed degraded image x and its clean version y can be modeled as:
Degrade(y, 0 == 0))
y = Restore(z, 0 == 16c. 01)),
(1)
where Degrade(-, 0) designates complex, often spatially varying weather degradation function parameterized by 0. By considering the spatial influence of degradation, the parameter set (0) can be partitioned into long-range/global degradation (fg. e.g. atmospheric haze) and local one (f2, e-g. rain streak). The objective is to recover the latent clean y from the degraded observation æ. The core challenge lies in the fact that both the degradation process and the artifacts unknown and can vary significantly across scenes and weather types. Thus, estimating the degradation characteristic 0 and central to solving the problem.
constructing the function Restore(-, 0) in Eq.
We propose that State Space Models (SSMs) [17 offer a suitable and robust framework for this degradation estimation task. Recall the core recurrence of discrete-ting SSM:
h Ahe Brg,
Uk Cha +D
(2)
where I&k is the input Morton-order sequence at step kt h4 is the latent hidden state summarizing historical context, and yk is the output. The matrices A, B, and C are learnable parameters that define the SSM's dynamics and output mapping. Please notice that the term Dzg is a practical (non-theoretical) addition for training ease, which analogous residual connection. To better understand how the state dynamics contribute to the output yk. we can analyze the system by omitting the residual Dar and substitute by into the y/ Chu part, follows:
CA CB
By comparing Eq. T with Eq. (3) we interpret SSM components as degradation estimators, as illustrated Fig. 2 The term C'Ahg conceptually models the long-range, spatially propagated degradation context, as shown in Fig. b). The previous hidden state h summarizes accumulated degradation cues (e.g., overall haze level, rain intensity) along the Morton-order scan path. The state transition matrix A then models how these summarized characteristics evolve or persist as the scan progresses spatially (e.g., the smooth attenuation of visibility due to widespread haze or the consistent statistical properties of rain streaks over larger area.). It essentially dictates "how the long-range state evolves over pixels" as noted in Fig. 2 The output matrix C' then translates this evolved context Ahg-1 into contribution to the current output yk. reflecting broader, non-local degradation patterns.

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MBSSL
MDSH
MISSL
Come
Cony
20
DDEM
archirecture propoud
GT Imput
Conv
2
Layeroom
MOSID
Laper/Nem
CAB
MDSL
Linear
Cony Blocks
(c) MOSID DegradntinnAmare Laver (MDSL).
Cony
Blocks
Eitcenr
Sghtt
DWWCom)
Merto
Scantiing
Ss Blnck
LaverNora
Eimaar
Cony
Limear
feature
Degradation Estimation
Morton-Order
2D-Scleetive-enn
(MOS2D). DownSample
Flement-wise product
+
Elementt-wisc
Multiplication
Channdl Concat
LipSomple
Figure 4: (a) Overall architecture of MODEM. (b) The DDEM for extracting global descriptor Zo and adaptive degradation kernel Z₁ degradation priors. (c) The MDSL incorporating the core MOS2D module (d) within a residual block. The blue-colored components indicate elements exclusive to the first training stage. N, .M, M2 denote the number of the corresponding module, respectively.
Concurrettyy, the CB term accounts for the impact of the immediate, local input features Tk. as visualized in Fig. 3(c.. The input matrix determines "how the local information affects the current state" (Fig. 2). allowing features from zą (e.g., local degradation artifacts like dense fog patches, or crucial local image content like fine textures/sharp edges) to directly influence the current hidden state hg. This enables the SSM react to fine-grained local evidence, with C' projecting this locally-informed component into for specific adjustments based on immediate observations.
Morton-Order Degradation Estimation Mechanism
The Morton-Order Degradation Estimation Mechanism (MODEM), depicted in Fig. (a), employs two-stage training strategy designed to accurately leam degradation characteristics.
Stage 1: In the first stage, the Dual Degradation Estimation Module (DDEM), shown in Fig. 4b), is provided with both the degraded image IL and its corresponding ground- truth IGT from the training set. This allows the DDEM explicitly learn the mapping from an image pair to its underlying degradation patterns. It outputs two degradation priors: a global descriptor Zo and a spatially adaptive degradation kernel Z1. These priors, representing the degradation information, into MODEM's main restoration backbone. The backbone itself, comprised of stacked MOS2D Degradation-ANe Aware Layers (MDSLs) detailed in Fig. [[c), only receives the degraded image ToQ and uses these priors to perform adaptive restoration. Each MDSL leverages the Morton-Order 2D-Selective-Sear module (MOS2D), shown in Fig. 4d) and Fig. 5 adaptively modulate features based on the degradation priors Zo and Zi. The degradation representation learned by the DDEM in this stage
then injected
the supervisory target for the Stage 2.
Stage 2: In the second stage, the inputs to both the DDEM and the main backbone consist of only the degraded image ILo- without any GT. The Stage 2 model inherits its parameters from Stage 1, and the DDEM in this stage receives only the degraded image Tuo as input. Simultaneously, there is a frozen DDEM receiving both the GT and the degraded image. The degradation information from this frozen DDEM is then used to supervise the trainable DDEM.
4.1 Dual Degradation Estimation Module (DDEM)
The Dual Degradation Estimation Module (DDEM), shown in Fig. 4 bb), extracts global degrada- tion descriptor Zn and adaptive degradation kernel Z,. In the first stage, DDEM processes the degraded image 40 and ground-truth for. Otherwise, uses only 4to. The input undergoes several
5

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Element-wiic product
Mortin Sean
Libear
56 Block
Element-wihe sam
A.D
Å ==
Mutrippication
DSAM
B (e - -IjA-1B
Fip1
Erpor GT
DOEA
Expend
Softmax
Syea
hy Ahe Deg
Spilt
Ch. DEa
Figure 5: Detailed illustration of the degradation modulation mechanism within a MOS2D module in the main restoration backbone, which employs the Degradation-Adapll Feature Modulation (DAFM) and Degradation Segradation-Selective Attention Modulation (DSAM) to dynamically adjust feature representations based the degradation priors Zo and Z1.
MOS2D Degradation-Awee Layers (MDSLs) to extract degradation feature map F E &RHxWxC, Subsequently, the global descriptor Zo and adaptive kernels Zi derived from F as follows:
2 = MI.P(AvgPoo(FF); Zo = @LLnearr (2), Zi Conv(F) Conv(F)
(4)
where o-)) denotes the SiLU activation function, 2 E RR will be used for degradation supervision. These priors Zo Ca and Zi CR XC22 then guide the main restoration network.
MOS2D Degradation-Aware Layers (MDSL). The iterative application of MDSL enhances sensitivity to degradation patterns, yielding enriched feature maps. For the feature map F; at the i-th MDSL, this process of MDSL can be formulated as:
F (OS)D(LN(FA) F,,
F+11 CAB(Con((LN(E))) F.,
where C-B(.) denotes the Channel Attention Block. LN(.) represents Layer Normalization.
4.2 Morton-Order 2D-Selective-Scan Module (MOS2D)
To effectively model spatially heterogencous degradations in 2D images, our MOS2D employs Morton-Order scan, illustrated in Fig. d)). This converts 2D spatial features into locality- preserving ID sequence, facilitating structured feature interaction and aggregation by SSM.
Specifically, the Morton encoding maps 2D pixel coordinates (i,j), where 0 < i < H, 0 S W. ID index by interleaving the bits of their binary representations. For (in. (In.....fo)) 10)2 and j (J.....,,o)) Jol2, with [log2 (max H, W)) - 1, the encoding 2 is:
interleave(i. (Jn+ 4n In- i............................... J1 i1 Ju, i0)2-
(6)
In the DDEM, Morton-order coding is followed by standard SSM operations to effectively extract global degradation descriptor Zo and adaptive degradation kernel Z,- contrast, in our main restoration backbone, the MOS2D module employs degradation-awanl modulations using Zo and Zi through DAFM and DSAM, detailed Fig. () This dual-modulation ensures that the MOS2D is dynamically conditioned on both long range contextually aware and spatially adaptive restoration.
Degralation-Adaapii Feature Modulation (DAFM). The i-th layer's 's input feature map F; is first modulated by the global degradation descriptor Zp. As shown in Fig. 5 Zo is expanded and split to produce channel-wise adaptive weights Z and biases Z/., which applied to F, using a feature-wise linear modulation operation, thus incorporates global degradation characteristics:
FDAFM = (7) o F.) + Z 7 7 = Split(Linear) (Z)));
where @ denotes element-wise multiplication.
Degradation-Selecinn Attention Modulation (DSAM). To further guide the S6 Block with local degradation information, the spatially adaptive kernel Z, is utilized as follows:
FDSAM W x Softmax(WzZ4,
(8)
where Wr and Wz learnable linear projection matrices.
Degradation Guidedd S6 Block. The core selective sean operation performed by our Degradation- Guided S6 Block. Its parameters dynamically adapted based on the degradation-senniiive features

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(a) Input
(b) WGWSNet (c) WeatherDiff
(d) Histoformer (e) Histoformeri
(f) Ours
Figure 6: Visual comparison on the real world snow dataset
45). Compared to the prior methods
95
55
where "f" denotes the Histoformer [65 for real snow from their official repository, our MODEM achieves superior results without additional training.
651
Table Quantitative comparison with recent state-of-the-an unified methods
40
651
across various datasets. The best and second best results are in bold and underlined, respectively.
Snow 100K-S
Outdoor
RainDrop
Average
Methods
PSNR SSIM
PSNR
SSIM
PSNR
SSIM PSNR
SSIM PSNR
SSIM
All-in-One 40
28.33 0.8820 24.71 0.8980 31.12 0.9268 28.05 0.9023
TransWeather 67
32.51
0.9341
29.31 0.8879
28.83 0.9000 30.17 0.9157
30.21 0.9094
Chen el al. [1]
34.42
0.9469
30.22 0.9071
29.27
0.9147 31.81 0.9309
31.43 0.9249
WGWSNet 955
34.31
0.9460
30.16 0.9007
29.32 0.9207 32.38 0.9378
31.54 0.9263
WeatherDDiffg4
[55]
35.83
0.9566
30.09
0.9041
29.64
0.9312 30.71 0.9312
31.57 0.9308
WeatherDiff 28
[55]
35.02
0,9516
29.58
0.8941
29.72
0.9216 29.66 0,9225
31.00
0,9225
AWRCP 779
36.92
0.9652 31.92
0.9341
31.39
0.9329 31.93 0.9314
33.04
0,9409
Histoformer
665
37.41
0.9656
32.16
0.9261
32.08
0.9389
33.06
0.9441
33.68
0.9437
MODEM (Ours)
38.08
0.9673
32.52
0.9292
33.10
0.9410
33.01 0.9434
34.18
0.9452
FDSAM derived from the DSAM stage. FDSAM is split into three components, which are then linearly transformed to generate the SSM parameters B, C, and A:
Fa, FB, Fc Split(Fbsan))
A WaFa, B= BBFFB, C= WoFc.
(9)
where Wa. WB, and Wo are learnable linear mappings. We use zero-order hold (ZOH) discretization with timescale A to obtain the discrete matrices A = e and B = (exp( (A)) - -I)AA*B, where is the identity matrix. The S6 Block then processes the Morton-Ordered sequence 2x. which is the Morton-ordered sequence derived from the DAFM features FDAMM- as follows:
y = Chu + DEE, h2 = A + Bæg,
Tg [DA
(10)
where hg is the hidden state at step k. The dynamically generated and C (and A influencing A, B) ensure that the state evolution and output generation are adaptive to the degradation characteristics.
4.3 Loss Function
Our model is trained in two stages. In the first stage, the loss Lauget combines &1 loss and correlation loss Lcor [65] to ensure accuracy and structural fidelity between the output of MODEM Iиo and ground-truth lGT:
Langel
Leor LGT),
(11)
The correlation loss foor (H T
65 is based the Pearson correlation coefficient p(THO: IGr):
pl (Ho TGr)), p(TнO .GT) En (I,,00 THO) Tor)
Coor TGT) = 1
(12)
N N ( (
where N is the total number of pixels, / denotes mean, and (I) denotes standard deviation.
In the second stage, we introduce KL divergence loss fKL to maintain consistency of the degradation representation Ž across stages. Let Zo,st and Zo.s2 be the Ž vectors from the first (fixed) and second stages, respectively. The KL divergence is computed between their softmax distributions o(-):
4C
o 6(Zo, (f)) log (0(Zo.ul (i))
LKL. DKL (d(Zo.u)) || o(Zo.z))
(13)
o5 ((2oz2()))
7

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Table 2: Desnowing Task
Table 3: Raindrop Removal Task
Snow100K-S
-
RainDrop
Methods
Methods
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
SPANet 669
29.92
0.8260
23.70
0.7930
pix2pix
27
28.02
0.8547
JSTASR 10]
31.40
0.9012
25.32
0.8076
DuRN
31.24
0.9259
RESCAN 41
31.51
0.9032
26.08
0.8108
RaindropAttn
588
31.44
0.9263
DesnowNet
45
32.33
0.9500
27.17
0.8983
AttentiveGAN
[57
31.59
0.9170
DDMSNet 87
34.34
0.9445
28.85
0.8772
IDT 73
31.87
0.9313
Restormer 82
36.01
0.9579
30.36
0.9068
MAXIM 666
31.87
0.9352
ConvIR [3
37.98
0.9686
32.11
0.9300
Restormer 82
32.18
0.9408
FSNet 12
37.42
0.9654
31.62
0.9246
AST 92
30.57
0,9333
MODEM (Ours)
38.08
0.9673
32.52
0.9292
MODEM (Ours)
33.01
0.9434
Table 4: Deraining & Dehazing Task
40
Rain
Rain
Snrw
Snow
Outdoor-Ran Rain
INN dincriiio
LSNE dimoriite
Haze
Methods
PSNR
SSIM
CycleGAN 93
17.62
0.6560
-20
pix2pix 27
19.09
0.7100
HRGAN 39
21.56
0.8550
-00
PCNet [29]
26.19
0.9015
L-NE dimemiio
1-SNE dimandon I
MPRNet 81
28.03
0.9192
(g) T-SNE of Histoformer
651
(h) T-SNE of MODEM
NAFNett 9
29.59
0.9027
Figure 7: T-SNE results of Histoformer 65 and MODEM, which
Restormer
82
30.03
0.9215
reflect that MODEM exhibits better clustering of features corre-
MODEM (Ours)
33.10
0.9410
sponding different weather types than Histoformer 665
The total loss for the second stage, Catage2, can be formulated as:
Lstage2 LI(Tio, JCT) + Leor (T1q, JaT) + LiL 70,
(14)
5 Experimental Validation
Our MODEM is implemented in PyTorch [56] and trained on 4 NVIDIA RTX 3090 GPUs in
two stages. We employ the Adam W optimizer 47 with Cosine Annealing Restart Cyclic LR
scheduler 46). It is trained on an all-weather dataset [67 651, consistent with prior works 40
67 55
63
95
79 For evaluation, MODEM is tested on established benchmarks including Testl [39 40
Rrop 57 Snow 100K
45 and a real- real-world snow test set 45). Due to the page limit, more
details are given in Appendix A. and A.2
5.1
Comparisons with State-of-the-arts
Quantitative Comparison. Our quantitative evaluation assesses MODEM against both unified mod-
els
40
67
95
55
79
65)
and task-specific methods 669
10,
41
45|
87
43
58 [7
73
66
93
39
29
81.
As reported in Table [ MODEM achieves SOTA performance, with an and notable 1.02dB
average PSNR improvement 0.5dB across benchmarks 39 40
57
45
gain on Outdoor-Rain PSNR, MODEM yields compelling visual results, a point further elaborated in our qualitative com- parisons. Furthermore, comparisons with leading task-specific methods in Tables 2 to 4 confirm MODEM consistently attains SOTA results. These evaluations underscore MODEM capability to effectively estimate and adapt to diverse, spatially heterogeneous weather degradations. Additionally, the comparisons of complexity can be found in Appendix A.3
39
40
While slightly below Histoformer on Rain [57] by 0.05dB
Qualitative comparison. We provide qualitative comparisons across diverse scenarios in Figs. 6 and 8 For image desnowing on Snow 100K
(45) MODEM effectively removes heavy snowflakes struggle to address. For joint deraining and
and visual artifacts that other models 995
55
65
dehazing on nutdoor-Rain (39 40), MODEM excels in restoring richer texture details and produces images with noticeably fewer artifacts. For raindrop removal on the Raindrop [57]. MODEM again

---

Table 5: Comparison of perceptual metries, including referenced (LPIPS.) and non-referenced
(Q-Alignf. MUSIQQ) scores. Best results are bolded; second-bes are underlined.
Method
Snow100K
Outdoor
Raindrop Snow100K
MUSIQ Q-Align LPIPS
Histoformer 65
0.0919
0.0445
0.0778
0.0672
WeatherDiff [55]
0.0982
0.0541
0.0887
0.0615
MODEM (Ours)
0.0880
0.0407
0.0699
0.0650
Histoformer 665
3.7207
3.7598
4.1445
4.0156
3.5449
WeatherDiff [55]
3,4531
3,5293
3.8691
4,0000
3.4512
MODEM (Ours)
3.7324
3.7695
4.1875
4.0664
3.5586
Histoformer 63
64.2526
64.2581
67.7461
68.4852
59.4040
WiatherDiff 55
62.6267
63.1278
67.4814
69.3608
59,4493
MODEM (Ours)
64.2438
64.2853
68,2926
69.7925
59.6042
Table 6: Comparison of different methods on various real-world datasets using the Q-Align metric.
Method
Snow (00K0OKee
RainDrop
NTURain
RESIDE
WeatherStream
WeatherDiff (55)
3.4531
4,0000
3,2031
3.4219
1.9561
Histoformer 65
3.7207
4.0156
3.2266
3.2891
1.9434
MODEM (Ours)
3.7324
4.0664
3.2891
3.3164
1.9863
demonstrates superior detail preservation and artifact reduction. Furthermore, real-world snowy images 455 MODEM achieves superior results as shown in Fig. 6 even without any additional fine-tuning, showcasing excellent generalization and real-world applicability, which be attributed to its profound understanding and adaptive modeling of degradation characteristics. Due to the page limit, more visual comparisons be found in Appendix A.8
5.2 Perceptual Quality and Geal-World Performance
Comparison of perceptual metrics. We report referenced (LPIPS 88
and non-referenced (Q-
Align 72), MUSIQ (33) scores, all computed using the pyiqa library (6. with the same settings
applied for all methods. As shown in Table our method achieves SOTA perceptual quality.
Comparison of real-world datasets. To provide quantitative evidence of our model's performance the challenging real-world scenarios. evaluated model the real-world data from the Snow -0K-Real [45], RainDrop [57], RESIDE (36, NTURain [8] and WcatherStream [84] datasets
using the Q-Align (72). The results presented in Table 6 As the results show, method achieves
state-of-the-aa performance on real-worle datasets when compared to the previous state-of-the-art
method, Histoformer (65), and the diffusion-baste approach, WeatherDiff (55)
5.3 Ablation Studies
We evaluate the impact of the Morton-Ordes scan, DDEM, DAFM and DSAM. Morton-Order facilitates structured spatial feature processing within the SSM, enabling the model to better capture contextual dependencies and preserve local structural coherence. As shown Table configurations incorporating the Morton scan generally yield improved performance, underscoring its benefit in organizing spatial information for sequential modeling. DDEM provides the degradation priors Zo and 7 that guide the DAFM and DSAM. As indicated in Table configurations lacking DDEM exhibit a significant performance drop. DAFM, which utilizes the global degradation prior Zo. plays a crucial role in adaptively modulating features based on the overall estimated weather type and severity. DSAM, guided by the spatially adaptive kernel Z,, allows the MOS2D to selectively focus on and modulate features pertinent to local degradation characteristics or specific image regions. While removing DSAM shows marginal gains on certain snow metries, impairs performance on tasks like raindrop removal, which demands strong local adaptation due to the highly local nature of raindrops, and on mixed rain&haze scenarios where intricate local texture recovery is challenging. Thus, DSAM, guided by the spatially adaptive kernel Z1, is crucial for achieving robust, balanced performance across diverse weather conditions by guiding the network selectively address these local characteristics. The combination of all components employed in full MODEM, consistently

---

(a) Input
(b) WGWSNet
(c) WeatherDiff
(d) Histoformer
(e) Ours
(f) GT
Figure 8: Visual comparisons of MODEM against totte-of-thearte unified methods across diverse adverse weather restoration tasks. Top Row: Image desnowing. Middle Row: Joint deraining and dehazing. Bottom Row: Raindrop removal.
Table Ablation study results across different datasets and factor combinations.
Factors
Snow 100K-S
Snow 100K-L
Outdoor
RainDrop
Morton DDEM DAFM DSAM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
38.03
0.9672
32.33
0.9283
32.89 0.9399
32.69
0.9423
X
N/A
N/A
37.61
0.9650
32.12
0.9249
32.37
0.9224
32.38
0.9390
V
38.15
0.9675
32.59
0.9298
32.77
0.9404
32.72
0.9435
V
X
37.43
0.9643
32.07
0.9240
32.19
0.9308
32.62
0.9387
V
38.08
0.9673 32.52
0.9292
33.10
0.9410
33.01
0.9434
yields the best results. This result is further supported by t-SNE 68 in Fig. 7 Compared to
Histoformer [65], MODEM exhibits significantly improved clustering of features corresponding to different weather types. This indicates that the combined action of the components enables MODEM to learn more discriminative and well-separated feature representations, which directly contributes to enhance restoration capabilities. More ablation studies be found in Appendix A.6
6 Conclusion
In this paper, we introduced the Morton-Order Degradation Estimation Mechanism (MODEM) to address the challenge of restoring images degraded by diverse and spatially heterogeneous adverse weather. MODEM integrates a Dual Degradation Estimation Module (DDEM) for extracting global and local degradation priors. with a Morton-Orde SD-Selective-Scan Module (MOS2D) that employs Morton-coded spatial ordering and selective state-space models for adaptive, context-aware restora- tion. Extensive experiments demonstrate MODEM's state-of- oftte--f-the-art performance across multiple benchmarks and weather types. This superiority is attributed to its effective modeling of complex degradation dynamics via explicit degradation estimation guiding the restoration process, leading to more discriminative feature representations and strong generalization to real-world scenarios.
Acknowledgement
We would like to thank Mingjia Li for the insightful discussions and feedback. This work was partially supported by the National Natural Science Foundation of China under Grant no. 62372251. The computational resources of this work was partially supported by TPU Research Cloud (TRC).
10

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arXiv preprint arXiv:2401.099
[95] Yurui Zhu, Tianyu Wang, Xueyang Fu, Xuanyu Yang, Xin Guo, Jifeng Dai, Yu Qiao, and Xiaowei Hu. Learning weather-general and weather-specific features for image restoration under multiple adverse weather conditions. In CVPR, pages 21747-21758. IEEE, 2023.
[96] Zhen Zou, Hu Yu, Jie Huang, and Feng Zhao. Freqmamba: Viewing mamba from a frequency perspective for image deraining. In Proceedings of the 32nd ACM international conference on multimedia, pages 1905-1914 2024.
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A Appendix
A.1 Implement Details
MODEM is implemented in PyTorch [56] and trained on 4 NVIDIA RTX 3090 GPUs. The main backbone contains residual groups with [4, 4, 6, 8, 6, 4, 4] MDSLs sequentially, and a final refinement group with 4 MDSLs. Downsampling and upsampling are performed using PixelUnshuffle and PixelShuffle, respectively. The initial channel size is 36. The DDEM employs residual groups with MDSLS each, operating with 96 channels. We train MODEM in two stages. In Stage I, DDEM takes the channel-concatenated degraded image 11.0 and ground-truth IGT input. We use the Adam W optimizer [47] with a learning rate of 3 x 10-4, weight decay of x 10-1 and betas set to (0.9, 0.999). The learning rate is scheduled by a Cosine Annealing Restart Cyclic LR [46] scheduler with periods of [92k, 208k] iterations and restart weights [1. 1J. The minimum learning rates, 7mmnn for these cycles are [3 x 10 1 x 10-6]. Progressive training is adopted with patch sizes [128, 160, 256, 320, 384] and corresponding Per-GPU mini-batch sizes [6, 4, 2, 1, 1] for [92k, 84k, 56k, 36k, 32k] iterations each, totaling 300k iterations. In Stage 2, DDEM processes only Lo. initializing parameters from Stage 1. The same A optimizer settings and Cosine Annealing Restart Cyclic LR scheduler parameters are employed. Progressive training patch sizes [128, 160, 256, 320, 376] with per-GPU mini-batch sizes [8, 2, 1, 1].
A.2 Datasets and Metries
To ensure fair and comprehensive evaluation, MODEM is trained and tested consistent with those utilized in prior works [40] 67 55 65| 95 79]. Our composite training data aggregated from
multiple sources, including 9,000 synthetic images featuring snow degradation from Snow 100K (45) 1,069 real-world images affected by adherent raindrops from the Raindrop [57]. and an additional 9,000 synthetic images from Outdoor-Rain (39] which are degraded by a combination of both fog and
rain streaks. For performance evaluation, we utilize several distinct test sets: the Test 39 40. the designated test split from the RainDrop (57), both the Snow 100K-L and Snow100K, subsets (55,
and a challenging real-world test set from Snow 100K comprising 1,329 images captured under various adverse weather conditions. We report PSNR and SSIM on these test datasets.
A.3 Complexity Analysis
We report the parameters and inference time. The inference time is performed on a single Nvidia RTX 3090, with single 256 256 input image, detailed in Table
Table Comparison of parameters and inference time, along with average PSNR.
Methods
WGWSNet [95]
WeatherDiff (55)
Histoformer (65)
MODEM (Ours)
Time (ms)
24.83
1.67x10
109.07
92.86
Parameters (M)
2.65
82.96
16.62
19.96
Average PSNR
31.54
31.57
33.68
34.18 18
Table 9: Comparison of inference time (ms) for different input sizes and average PSNR.
Input Size
WGWSNet (95)
WeatherDiff (55)
Histoformer 65
MODEM (Ours)
256 x 256
24.83
1.67 x 106
109.07
92.86
512 x 512
110.34
5.37 10
576.15
443.02
1024 x 1024
439.13
x.35x107
3056.29
1946.34
Average PSNR
31.54
31.57
33.68
34.18 18
To be more comprehensive, we evaluate the inference speed on larger resolutions in Table As can be seen, compared to Transformer-based architectures like Histoformer (65), as the number of pixels increases, MODEM's complexity scales in near-linear fashion, demonstrating significantly better scalability. This stands in contrast to the quadratic complexity often associated with Transformers, granting MODEM a distinct computational advantage.
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Table 10: Comparison of parameters and inference time for other Mamba-style methods.
Method
MambalR 20
Mamba [91
MODEM (Ours)
Parameters (M)
15.78
8.93
19.96
Time (ms)
790.61
233.41
92.86
Table 11: Comparison of inference time (ms) between Hilbert scan and Morton sean.
Input Size
256
256
512 512
1024
1024
Hilbert sean (28 Morton scan (Ours)
604.00
10134.91
88288.
92.86
443.02
1946.34
To further contextualize model's performance, compared MODEM with other Mamba-style methods, MambalR [20] and FreqMamba [91]. As shown in Table although MODEM has a larger parameter count compared both MambalR (20) and Freqa 191, it achieves significantly
faster inference time, highlighting the superior efficiency of our architectural design.
For scanning methods, Hilbert scan 28 is another locality-preservinn alternative. with significantly higher computational cost, whereas the Morton-order can be calculated efficiently with simple bitwise operations as shown in our Eq. (6). To be clear, we compared the inference speed of the Morton and Hilbert seans. For the Hilbert scan, we used the official implementation from LC-Mamba (28). The speed (ms) of different resolutions are shown in the Table I1 with all tests performed on a single RTX 3090 GPU. Our method is significantly faster than Hilbert.
However, it comes
A.4 More Visualizations of Features
1.0
RrinDrup
06
04
0.0
Outdour
0.8
04
Snow 100K
06
02
(a) Input Image
(b) Long Range CAha-1
(c) Local CBa
(d) Output MOS2D yk
Figure 9: With respect to sample (a), (b)-(d) visualize the long-range CAhx-1 (c) local CBrrk and (d) output of MOS2D yk. respectively.
A.5 Limitations
While our proposed MODEM demonstrates state-of-the-arr performance across a variety of adverse weather conditions, we acknowledge certain limitations. illustrated Fig, [0 of challenging real-world snow scenarios, MODEM, like other contemporary methods, can encounter difficulties in achieving perfect restoration when faced with images containing extremely large, high-contrast snowflakes. Such scenarios are particularly challenging if these specific visual patterns of snow, differing significantly scale, density, or opacity from typical training examples, are underrepresented or entirely absent in the training data distribution. Nevertheless, empowered by its robust degradation estimation capabilities, MODEM still achieves comparatively better results in these extreme cases, effectively suppressing artifacts and preserving some structural detail. This highlights ongoing
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challenge in achieving perfect generalization to all unseen severe degradations, but also underscores the significant benefit of incorporating explicit and adaptive degradation estimation.
(a) Input
(b) WGWSNet
WeatherDiff (d) Histoformer
(e) Histoformer+
Ours
Figure 10: Visual comparison on challenging real-world snow case from the dataset in 45 illustrating performance under severe degradation unseen during training. We compare MODEM to the prior methods [95 55 65]. where "+" denotes additional training of Histoformer.
A.6 More Ablation Studies
The Morton-order scans an image by processing it in small, contiguous block-like regions, moving from one adjacent block to the next (refer to the scale-space theory). This ensures that pixels that are close in the 2D image stay close in the ID sequence. To further investigate the impact the scanning scheme itself, we offer an ablation study within our MODEM, comparing the Morton scan against others
20
24
As shown in Table [2] our Morton achieves the best performance.
Table 12: Ablation study of diffrent scanning scheme.
Snow 100K-L
know100K-S
Outdoor
Rain
Methods
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
Raster (MambalR (20)
32.33
0.9283
38.03
0.9672
32.89
0,9399
32.69
0,9423
Continuous (Zigzag (74)
32.17
0.9266
37.74
0.9662
32.35
0.9385
32.59
0,9422
OSS (VmambalR [63]
32.14
0.9262
37.39
0.9651
32.61
0,9387
32.11
0,9413
Local (aacalMamba (25
32.23
0.9266
37.75
0.9661
32.60
0.9382
32.53
0.9418
Hilbert (LC-Mamba 28
32.46
0.9287
37.96
0.9671
32.99
0.9414
32.82
0.9433
Morton (Ours)
32.52
0.9292
38.08
0.9673
33.10
0.9410
33.01
0.9434
We conduct an ablation study on the contribution of the loss terms. We have also performed an ablation study on the placement (before/after the average pooling) of the KL divergence loss. The results are presented in the table below. They confirm that each component contributes positively.
Table 13: Ablation study of the loss function.
Snow 100K-L
Snow 100K-S
Outdoor
RainDrop
Methods
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
w/o Correlation Loss
32.30
0.9278
37.79
0.9668
32.91
0.9403
32.69
0.9427
w/o KL Loss
32.12
0.9249
37.61
0.9650
32.37
0.9224
32.38
0.9390
Replace KL Loss
31.85
0.9237
37.16
0.9638
32.77
0.9389
32.57
0.9387
MODEM
32.52
0.9292
38.08
0.9673
33.10
0.9410
33.01
0.9434
A.7 More Quantitative Comparisons
We retrain three prominent Mamba-style restoration networks 20 63 96 on the all-weather setting.
These experiments were conducted carefully following the settings used by other recent methods like ConvIR [13], FSNet [92]. and Histoformer 665 while also respecting their original training
configurations. The results are presented in Table 14
Our MODEM achieves the best performance.
Table 14: Comparison with Mamba-lin like Methods.
Snow 100K-L
Snow 100K-S
Outdoor
RainDrop
Methods
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
MambalR 20
28.59
0.8729
33.34
0.9330
24.73
0.8808
32.16
0.9393
Famba 96
27.09
0.8624
33.52
0.9331
19.89
0.7519
30.60
0.9198
VmambaIR 633
31.07
0,9168
36.35
0.9605
24.23
0.8558
32.18
0.9392
MODEM
32.52
0.9292
38.08
0.9673
33.10
0.9410
33.01
0.9434
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A.8 More Visual Comparisons
Further visual comparisons are presented in Figs. 11 to 14
Input
Trans Weather
Chen et al.
WGWSNet
WeatherDiff
Histoformer
Histoformer+
MODEM
Input
Trans Weather
Chen et al.
WGWSNet
WiatherDiff
Histoformer
Histoformer+
MODEM
Figure 11: More visual results for desnowing on real-world snowy images 45
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Input
Trans Weather
Chen et al.
WGWSNet
WeatherDiff
Histoformer
MODEM
GT
Input
Trans Weather
Chen et al.
WGWSNet
WeatherDiff
Histoformer
MODEM
GT
Figure 12: More visual results for image desnowing on the Snow 1 100K
45
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Input
Trans Weather
Chen et al.
WGWSNet
PeatherDiff
Histoformer
MODEM
GT
Input
Trans Weather
Chen et al.
WGWSNet
WiatherDiff
Histoformer
MODEM
GT
Figure 13: More visual results for deraining&dehaazing on the Test dataset
39
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Input
Trans Weather
Chen et al.
WGWSNG
WiatherDiff
Histoformer
MODEM
GT
RESERVED
RESERVED
RESERVED
RESERVEU
Input
Trans Weather
Chen et al.
WGWSNet
RESERVED
RESERVED
RESERVED
RESERVED
WeatherDiff
Histoformer
MODEM
GT
Figure 14: More visual results for raindrop removal on the Raindrop dataset
57
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30


Reviews:
[{"review_id": "GuOHMmjQdr", "reviewer": "Reviewer_QaHQ", "summary": "This paper primarily introduces an ordering mechanism based on the Morton-order for images. The proposed Morton-Order 2D Selective Scan Module (MOS2D) combines the Morton ordering with S6 blocks (Selective State Space Model). The paper argues that the proposed ordering scheme better captures the spatial locations of pixels when transforming to the 1D sequence which is fed to the S6 block. The end application is restoring images afflicted by adverse weather such as rain, haze and snow.", "questions": "Other than the questions listed in weaknesses, a few minor questions are:\n\n**Q1.** How is Fig. 7 generated? Are the features taken from the latent or are they priors?\n\n**Q2.** After pixel at (0,0) and (0,1) are scanned, the next is at (1,0) and not (0,2), making a Z curve along this specific path. Have the authors considered combining multiple scan paths?\n\n**Q3.** Citation of the original Morton order paper is missing [1].\n\n[1] Morton, Guy M. \"A computer oriented geodetic data base and a new technique in file sequencing.\" (1966).\n\n**Comments**\n\nOrdering schemes like Morton-order have been explored in the literature in context of point clouds [1] and now even for image restoration [2], the authors should consider citing these works. Although the latter is fairly recent and can be considered contemporary to this work.\n\n[1] Chen, Guangyan, et al. \"Pointgpt: Auto-regressively generative pre-training from point clouds.\" Advances in Neural Information Processing Systems 36 (2023): 29667-29679.\n\n[2] Ouyang, Zongzhi, and Wenhui Li. \"MMamba: Enhancing image deraining with Morton curve-driven locality learning.\" Neurocomputing 638 (2025): 130161.", "limitations": "Yes, the authors discuss the limitations of their work, but no discussion on the societal impact is provided.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n**S1.** The paper is well-written and straight-forward to follow.\n\n**S2.** The proposed method scores strong results on the adverse weather dataset, and performs efficiently (although measured on 256x256 resolution input images).\n\n**Weaknesses**\n\n**W1.** One of the core claims of this work is that the proposed ordering scheme is better at preserving spatial locations when transforming 2D images to 1D sequence. However, there is no comparison with a single Mamba-style restoration network in Tabs. 1-4. There exist many works that explore how well SSMs perform in image restoration problems, many of which the paper already cites in the related work, but does not compare to. This is crucial to understand if indeed the proposed ordering mechanism is better than the prior mechanisms such as OSS in [1], or SS2D in [2], etc.\n\n[1] Shi, Yuan, et al. \"Vmambair: Visual state space model for image restoration.\" IEEE Transactions on Circuits and Systems for Video Technology (2025).\n\n[2] Liu, Yue, et al. \"Vmamba: Visual state space model.\" Advances in neural information processing systems 37 (2024): 103031-103063.\n\n**W2.** Have the authors thought about discontinuities that exist in the scanning order? In Fig. 1, this is visible in (d) when once the first 4 columns and first 4 rows are complete, the next one is col 5, row 1 pixel which is not spatially next to the last pixel that was scanned. Due to this, it is necessary to understand why the proposed scheme is better and why zigzag like scheme [1] or Hilbert curve based scanning [2] is not better?\n\n[1] Hu, Vincent Tao, et al. \"Zigma: A dit-style zigzag mamba diffusion model.\" European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2024.\n\n[2] Jeong, Min Wu, and Chae Eun Rhee. \"LC-Mamba: Local and Continuous Mamba with Shifted Windows for Frame Interpolation.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025.\n\n**W3.** Since the training setup is a 2-stage pipeline, I assume the entire model (along with DDEM) is trained given the loss in eq.11. If so, during stage 2, does the restoration backbone now start from scratch or the stage 1 acts as pretraining for the restoration method? In the latter stage (not starting from scratch), there is an issue with the GT information leaking as priors $Z_{0}$ and $Z_{1}$ into the main restoration network.", "was_revised": true, "final_justification": "My major concerns were regarding comparison with other scanning approaches in Mamba style architectures. The authors provided detailed comparisons with several different Mamba-style methods, motivating that Morton-ordering is computationally efficient and achieves better performance. The new details alleviated my concerns and I have raised the rating to be positive.", "rebuttal": "**Q1: Measured on 256x256 resolution? (S2)**\n\n**A1:** Thank you for your positive feedback. To be more comprehensive, we have now evaluated the inference speed on larger resolutions. The results (in ms), tested on a single RTX 3090 GPU, are shown below:\n\n| Input Size | WGWSNet | WeatherDiff | Histoformer | MODEM   |\n| ---------- | ------- | ----------- | ----------- | ------- |\n| 256*256    | 24.83   | 1.67e6      | 109.07      | 92.86   |\n| 512*512    | 110.34  | 5.37e6      | 576.15      | 443.02  |\n| 1024*1024  | 439.13  | 1.35e7      | 3056.29     | 1946.34 |\n| Avg. PSNR  | 31.54   | 31.57       | 33.68       | 34.18   |\n\nThe average PSNR is calculated across the 4 benchmarks shown in Table 1 of the main paper. We will include this more comprehensive evaluation in the revision.\n\n**Q2: Compare with Mamba-style network? (W1)**\n\n**A2:** Thank you for your question. To our knowledge, MODEM is the first Mamba-style architecture for the unified all-weather task, which is why other Mamba-style methods were not in our initial comparisons.\n\nAs suggested, we further retrained three prominent Mamba-style restoration networks, separately on each of the three tasks within the all-weather setting. As these models were not specifically designed to our target task, we tried our best to retrain them using configurations provided by the authors and following the data usage that is commonly-adopted by the community (e.g. Histoformer and ours). \n\n| Method    | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| --------- | ---------- | ---------- | --------- | --------- |\n| MambaIR   | 28.59      | 33.34      | 24.73     | 32.16     |\n| FreqMamba | 27.09      | 33.52      | 19.89     | 30.60     |\n| VmambaIR  | 31.07      | 36.35      | 24.23     | 32.18     |\n| MODEM     | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\nWith respect to the scanning style, we have already provided a comparison in ablation study. As shown in **Table 5 (row 1)**, replacing our Morton-order scan with a raster scan (as used in MambaIR) leads to a performance drop. This reveals the benefit of Morton-order's locality preservation. Additionally, to further investigate the impact of the scanning scheme itself, we here offer an expanded ablation study **within our** **MODEM****,** comparing the Morton scan against others. As can be seen from the results, our Morton manner achieves the best performance.\n\n| Method               | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| -------------------- | ---------- | ---------- | --------- | --------- |\n| Raster (e.g.MambaIR, Vmamba) | 32.33      | 38.03      | 32.89     | 32.69     |\n| Continuous (zigzag)  | 32.17      | 37.74      | 32.35     | 32.59     |\n| OSS (VmambaIR)       | 32.14      | 37.39      | 32.61     | 32.11     |\n| Local (LocalMamba)   | 32.23      | 37.75      | 32.60     | 32.53     |\n| Hilbert (LC-Mamba)   | 32.46      | 37.96      | 32.99     | 32.82     |\n| Morton (Ours)        | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\nWe will include this additional comparison in the revision for completeness. \n\n**Q3: Discontinuities of Morton-order scan? Combine multiple scan paths? (W2 & Q2)**\n\n**A3:** Thank you for this question. Since any sequential 2D scan will inevitably suffer from internal discontinuities, the key is to find a scanning method that is better suited for the image restoration task. As prior research has demonstrated [1, 2], for images, **immediately surrounding pixels are** **typically** **far more informative than pixels in the next row or column**. The Morton-order scans an image by processing it in small, contiguous block-like regions, moving from one adjacent block to the next **(refer to the scale-space theory)**. This ensures that **pixels that are close in the 2D image stay close in the 1D sequence,** unlike a raster or zigzag scan (continuous scan in Fig. 1b), which scans line-by-line and creates large gaps between long-distance pixels.\n\n[1] Regional Attention for Shadow Removal, ACM MM 2024\n\n[2] A Comparative Study of Image Restoration Networks for General Backbone Network Design, ECCV 2024\n\nWhile LocalMamba (Fig. 1c) also attempts to solve this issue, it is limited to applying a raster scan within pre-defined local windows and then using another raster scan to connect them, which still does not ensure pixel-level proximity across the image, although mitigated to some extent. As for Hilbert curve, it is another locality-preserving alternative. However, it comes with a significantly higher computational cost, whereas the **Morton-order can be calculated efficiently with simple bitwise operations as shown in our Eq. 6**. To be clear, we compared the inference speed of the Morton and Hilbert scans. For the Hilbert scan, we used the official implementation from LC-Mamba. The speed (ms) of different resolutions are shown in the table below, with all tests performed on a single RTX 3090 GPU. Our method is significantly faster than Hilbert.\n\n| Input Size   | 256*256   | 512*512    | 1024*1024   |\n| ------------ | --------- | ---------- | ----------- |\n| Hilbert scan | 604       | 10134.91   | 88288.46    |\n| Morton scan  | **92.86** | **443.02** | **1946.34** |\n\n**To better validate these arguments, we have conducted a new ablation study of scan patterns, with the results shown in Answer 2.** \n\n**We only need a single scan.** This evidence confirms that a **single** Morton-order scan is both effective and efficient. Therefore, for architectural simplicity, we prioritize a superior single-pass approach rather than compensating for a weaker scan with multiple paths. We will clarify this in more detail in the revision.\n\n**Q4:** **GT** **leaking? (W3)**\n\n**A4:** Thank you for this question. The parameters for the Stage 2 model are initialized from the weights trained in Stage 1 as mentioned in Appendix A.1. First, and most importantly, **at no point during training was our model ever exposed to any images from the test sets, while** **at inference,** **our** **trained** **model** **merely** **takes** **the degraded image** **as input**. This is how supervised deep learning works, and comparison fairness is guaranteed in this work. \n\nWe tried to capture the point from the reviewer on this question. There might be some confusion about our two-stage training. Thus, to make it clear, we here emphasize the pipeline of the two-stage strategy:\n\nIn Stage 1, the input to the DDEM consists of both the GT and the degraded images from the training set, while the main backbone only receives the degraded image. The DDEM ultimately outputs only a single degradation vector. By providing the DDEM with both the degraded image and GT from the training set, the DDEM is explicitly trained to **understand the difference between the degraded image and GT**, and thereby learn to extract the degradation representation required for the main restoration backbone, which serves as the ideal supervisory target for Stage 2.\n\nIn Stage 2, the inputs to both the DDEM and the main backbone **consist of only the degraded image, without any GT**. The Stage 2 model inherits its parameters from Stage 1, and **the DDEM in this stage receives only the degraded image as input**. Simultaneously, there is a frozen DDEM receiving both the GT and the degraded image. **The degradation information from this frozen DDEM is then used to supervise the trainable DDEM via the KL** **divergence** **loss, as shown in Eq. 13.** **So, the paired GT-degraded images from the** **training set** **are used to better train the degradation estimation module, but this is entirely separate from GT leakage during inference.**\n\nFurthermore, **our** **MODEM** **demonstrates excellent generalization capabilities benefiting from our two-stage degradation estimation strategy.** As shown in Figure 6, MODEM achieves superior results on real-world images. **This is a dataset** **that** **was not explicitly trained or finetuned on and for which no GT was ever available**. To quantify this, we computed non-reference metrics (Q-Align, MUSIQ), and our method achieves the best results, as shown below. This strong real-world performance is compelling evidence of a robust, generalizable representation, not overfitting via information leakage.\n\n| Method      | Q-Align$\\uparrow$ | MUSIQ$\\uparrow$ |\n| ----------- | ------------------- | ----------------- |\n| MODEM       | **3.5586**          | **59.6042**       |\n| Histoformer | 3.5449              | 59.4040           |\n| WeatherDiff | 3.4512              | 59.4493           |\n\n**Q5: Explanation of Figure 7? (Q1)**\n\n**A5:** Thank you for this question. **Since Histoformer does not have a dedicated prior design, extracting features from the latent space is the only comparable approach.** So the features used to generate the t-SNE plot in Figure 7 were extracted from the latent. The relative position of feature extraction within our network was kept consistent with that of Histoformer. We will add a precise description of this process to the revision of the paper for clarity.\n\n**Q6: Reference? (Q3 & Comments)**\n\n**A6:** Thank you for providing the reference to the Morton paper[1] and its application in the 3D vision domain[2]. We will certainly cite these works in our revision to better contextualize our approach and strengthen the discussion. Regarding MMamba[3], as you noted, this work was published after our submission deadline. Although the scanning mechanisms are similar, our work's primary focus lie in the **modeling and perception of degradation estimation**, a concept not central to MMamba. We will be happy to cite it in the revision.\n\n[1] A computer oriented geodetic data base and a new technique in file sequencing.\n\n[2] Pointgpt: Auto-regressively generative pre-training from point clouds.\n\n[3] MMamba: Enhancing image deraining with Morton curve-driven locality learning."}, {"review_id": "nHmk1IIYFW", "reviewer": "Reviewer_sL85", "summary": "The authors propose MODEM, SSM-based image restoration model for adverse weather removal.\nBeside general scanning methods, they utilize Morton scanning to better preserve spatial locality and capture contextual information.\nTo maximize the effect of Morton scanning, they introduce MOS2D module and training strategies.\nWith those contributions, their model achieves a significant margin over previous models.", "questions": "1. Please include more comprehensive ablation studies to validate the effectiveness of DSAM in various settings, such as presenting results when only DDEM and DAFM are used. Additionally, ablations on the loss terms should be conducted. Specifically, it is important to report the model’s performance when knowledge distillation (KD) is removed (i.e., after stage 1), and also to show how well the model performs when trained without ground truth supervision.\n\n2. Visualization results under diverse real-world weather conditions should be provided. Datasets such as RESIDE, NTURain, and RainDS offer a range of real-world adverse weather images that can be used to demonstrate the model’s effectiveness in practical scenarios.\n\n3. Please provide a more detailed explanation of \"HistoFormer+\".\n\n4. Please show the results under different weather conditions in Fig. 3. (rain/snow)\n\n5. The authors should also demonstrate the performance of MODEM on other adverse weather datasets, such as WeatherStream dataset, to validate its generalizability.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 1, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\n1. Although the number of parameters slightly increases, it achieves faster inference speed and better performance compared to the existing state-of-the-art.\n2. MODEM achieves substantial performance improvement on the Allweather dataset.\n3. A structure well-suited for adverse weather removal by separating and processing long-range and localized information based on SSM.\n\nWeaknesses\n1. The explanation of the architecture is not clear. The relationship between Fig. 4 and Fig. 5 is not clearly articulated in conjunction with the text.\n2. The ablation analysis is insufficient. To convincingly demonstrate the effectiveness of the proposed module, a more detailed ablation study is necessary. This should also be extended to the loss terms.\n3. Lack of visualizations for real world scenarios. (e.g. fog, rain)", "was_revised": true, "final_justification": "By reading the rebuttal, the concerns raised in the initial review have been resolved. The connection between the proposed model and the corresponding figures has also become clearer. In addition, the authors provided sufficient experiments and analysis regarding the loss-related question, which confirmed that the proposed approach is well-structured. Therefore, I believe the paper now presents sufficient evidence to support the proposed model, and I am increasing my score to Borderline Accept.", "rebuttal": "**Q1: The explanation of the architecture? & The relationship between Fig. 4 and Fig. 5? (W1)**\n\n**A1:** Thank you for this question. As we described in the caption of Fig. 5, the relationship between Fig.4 and Fig. 5 is that **Figure 5 provides a detailed, \"zoomed-in\" illustration of the internal workings of the MOS2D** module (Fig. 4d), which is the central component of the MDSL block shown in Figure 4(c).\n\n**Figure 4 illustrates the overall framework**, as described at the beginning of Section 4. It shows that the input degraded image is processed by two parallel streams: the Main Restoration Backbone (Fig. 4a), which is composed of multiple MDSL blocks (Fig. 4c), and the Dual Degradation Estimation Module (DDEM) (Fig. 4b). The DDEM's sole purpose is to analyze input degradation and produce two \"guidance\" signals (Eq. 4): a global degradation descriptor ($Z_0$) and a spatially adaptive degradation kernel ($Z_1$). These two priors are then fed into the MDSL blocks (Eq. 5) of the main backbone to guide the restoration.\n\n**Figure 5 then details precisely how this guidance (**$Z_0$ **and** $Z_1$**) is used within each MOS2D module inside an MDSL block.** It shows the internal mechanisms where the feature map entering the MOS2D module is first modulated by the global prior $Z_0$ through the Degradation-Adaptive Feature Modulation (DAFM) (Eq. 7). Subsequently, the adaptive kernel $Z_1$ is used by the Degradation-Selective Attention Modulation (DSAM) (Eq. 8) to further refine the features, making the process sensitive to local degradation patterns. Finally, these modulated features are used to dynamically generate the parameters ($\\Delta, B, C$) for the core S6 block (Eq. 9, Eq. 10).\n\nWe will clarify this architectural relationship more explicitly in the revision.\n\n**Q2: The ablation analysis? (W2 & Q1)**\n\n**A2:** Thanks for this question. Actually, most of the required ablations had been included in the submission. We provided ablation experiments in the **third and fourth rows of Table 5** where DDEM and DAFM exist alone, and where DDEM and DSAM exist alone, respectively. **The 4th row of Table 5 shows the performance when only DDEM and DSAM are used (w/o DAFM), while the 3rd row shows the performance when only DDEM and DAFM are used (w/o DSAM).** These experiments, when compared to the full model, demonstrate that both DAFM and DSAM contribute positively to the final performance, and their combination yields the best results.\n\nThe second row of Table 5 is, in fact, the experiment where the KD Loss is removed. Our KD process, driven by the KL divergence loss, is the sole mechanism used in Stage 2 to train the practical DDEM module. **Removing this KD loss means the DDEM in stage 2 has no supervisory signal and cannot learn to estimate the degradation priors.** Consequently, both DAFM and DSAM become non-functional. This scenario, which reduces our model to a standard Mamba-style backbone without our degradation-aware guidance, is precisely what is evaluated in the second row (\"Morton ✓, DDEM ✗, DAFM N/A, DSAM N/A\"). The significant performance drop observed in this setting powerfully underscores the critical importance of KD loss for our framework's success. We will clarify this in the revision.\n\nAs for the correlation ablation suggested by the reviewer, we conducted an ablation study on the contribution of  the Pearson correlation loss. We have also performed an ablation study on the placement (before the average pooling) of the KL divergence loss. The results are presented in the table below. They confirm that each component contributes positively and that our original design. We will include these new findings in the revised version.\n\n| Setup                | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| -------------------- | ---------- | ---------- | --------- | --------- |\n| w/o Correlation Loss | 32.30      | 37.79      | 32.91     | 32.69     |\n| w/o KL Loss          | 32.12      | 37.61      | 32.37     | 32.38     |\n| Replace KL Loss      | 31.85      | 37.16      | 32.77     | 32.57     |\n| MODEM                | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\n**Q3: More visualization results under diverse real-world weather conditions? (W3 & Q2 & Q5)**\n\n**A3:** Thank you for this valuable suggestion. We have provided qualitative results for real-world snow removal in **Figure 6** of the main paper, as well as for real-world raindrop removal in **Table 1, Figure 8, and Figure 13**. **Due to the rules of the rebuttal process, we are unable to upload new qualitative visualizations at this stage.** To provide quantitative evidence of our model's performance on these challenging real-world scenarios, we have conducted a new set of evaluations using the non-reference image quality assessment (IQA) metric **Q-Align**. This metric is well-suited for assessing perceptual quality without needing a ground truth image. To ensure a fair and reproducible comparison, all scores were computed using the `pyiqa` library with the same default settings applied for all methods. We evaluated our model on the real-world snow dataset as well as the real-world data from the **Snow100K-Real, RainDrop, RESIDE, NTURain and WeatherStream** datasets. The results are presented in the table below.\n\n| Method      | Snow100K-Real | RainDrop   | NTURain    | RESIDE     | WeatherStream |\n| ----------- | ------------- | ---------- | ---------- | ---------- | ------------- |\n| WeatherDiff | 3.4531        | 4.0000     | 3.2031     | **3.4219** | *1.9561*      |\n| Histoformer | *3.7207*      | *4.0156*   | *3.2266*   | 3.2891     | 1.9434        |\n| MODEM       | **3.7324**    | **4.0664** | **3.2891** | *3.3164*   | **1.9863**    |\n\nAs the results show, our method achieves state-of-the-art performance on real-world datasets when compared to the previous state-of-the-art method, Histoformer, and the diffusion-based approach, WeatherDiff. We will incorporate both these new **quantitative IQA results** and the promised **qualitative visual results** into the revised version of the paper.\n\n**Q4: A more detailed explanation of \"HistoFormer+\"? (Q3)**\n\n**A4:** Thank you for this question. \"Histoformer+\" refers to results from a specific pre-trained weight file, `net_g_real.pth`, provided in the official Histoformer repository, while \"Histoformer\" refers to the official version reported in their paper. We would like to state clearly that **all test results and model weights reported in our paper are taken directly from official papers or repositories.**\n\nThe network architecture is identical to the one in their paper. However, **the authors did not provide training details for this specific** **checkpoint**. We will clarify this naming convention in the revision paper to ensure full transparency.\n\n**Q5: The results under different weather conditions in Fig. 3? (Q4)**\n\n**A5:** Thank you for this suggestion. **Due to the rules of the rebuttal process, we are unable to upload new images at this stage.** We alternatively describe these results and promise to include them in the revision.\n\nWe have performed these visualizations internally for other weather conditions. They were not all placed in the submission due to space constraints. **We can observe that the feature maps for $CAh_{k-1}$ and $CBx_k$ always exhibit a clear and consistent separation between long-range and local information, regardless of the weather type.**\n\nAs described in our analysis in Section 3, **the** $CAh_{k-1}$ **term consistently focuses on the broader, more diffuse degradation context (like widespread haze or dense, distributed snowflakes), while the** $CBx_k$ **term focuses on fine-grained local details, including both sharp artifacts and underlying image textures.** We will add these new visual examples of different weather conditions to the revision of the paper to provide a more thorough demonstration. Thank you again for helping us improve the paper."}, {"review_id": "uGatYFj8QD", "reviewer": "Reviewer_6wM5", "summary": "This paper proposes the Morton-Order Degradation Estimation Mechanism (MODEM) for adverse weather removal. MODEM integrates a Dual Degradation Estimation Module (DDEM) for extracting global and local degradation priors, with a Morton-Order 2D-Selective-Scan Module (MOS2D) that employs Morton-coded spatial ordering and selective state-space models for adaptive, context-aware restoration. Extensive experiments demonstrate MODEM’s state-of-the-art performance across multiple benchmarks and weather types.", "questions": "See the Weaknesses", "limitations": "yes.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths.\n\n1, This paper is well-written and easy to follow. Moreover, this paper has clear structure and is easy to understand.\n\n2, Morton-Order Degradation Estimation Mechanism seems to be interesting, which integrates Morton-coded spatial ordering with selective state space modeling to effectively capture spatially heterogeneous weather degradation dynamics.\n\nWeaknesses.\nI find that this paper exists some major concerns.\n\n1, Figure 2 and Figure 2 may be inappropriate. First of all, in Figure 2, the clear image is not equal to the sum of these three component. Putting it in the paper may confuse readers. Moreover, I do not find the significant meaning for putting the Figure 3 in current position. It may be meaningful but not major. The authors should consider to replace these two figures with more convincing demonstration.\n\n2, I also find that in Tables 2-4,  the authors compare with latest method which is published in 2022. The authors should compare with recent state-of-the-art approaches. Comparing with outdate methods is not acceptable.\n\n3, I observe that, in Table 5, the full model is not better than the model without DSAM in the datasets of Snow100K-S and Snow100K-L. The authors should give an in-depth analysis and explanations.\n\n4, The authors do not give the analysis about the two-stage training mechanism. How about only training the first stage without using GT within the same training epoch? Where does the correlation loss derive from? Why not the authors analyze this? Why the authors computing the KL loss at the position of $\\tilde{Z}$? Why not compute the vectors at the position of the feature of Figure 4(b), i.e., the feature before the operation of avg pool.\n\n5, The authors also should compare the results of different scanning manners including, (a) Raster Scanning (b) Continuous Scanning (c) Local Scanning, which is illustrated in Figure 1.", "was_revised": true, "final_justification": "Thanks for your rebuttal. I think that this paper does not have significant novelty for the following reasons:\n\n1, Morton mechanism is not a novel idea. The authors attempt to combine the mamba and Morton.\n\n2, For other modules, such as degradation estimation, are also not new. Various works have been explored. The novelty is incremental.\n\n3, The compared methods in Tables 2,3,4 are out of date, which is not acceptable, although the authors add new experiments during the rebuttal.\n\nI thus maintain my score.", "rebuttal": "**Q1: Figure 2 and Figure 3? (W1)**\n\n**A1:** Thank you for this insightful feedback. The intent of Figure 2 is to provide an intuitive, visual analogy for the terms in Eq. 3 when considering the residual term $Dx_k$. The output $y_k$ in the diagram is meant to represent the output of the S6 block at step $k$. **We used a clean image to visually suggest that this output is a feature representation closely related to the restored clean image.** Due to the constraints of the rebuttal process, we are unable to upload a revised figure at this time, but we will provide a more rigorous illustration in the revision of the paper.\n\nThe Figure 3 provided empirical evidence of our model's behavior by visualizing the intermediate feature maps. Specifically, it shows the feature distributions for the key terms within the MOS2D's S6 block. As analyzed in Section 3, we hypothesized that the $CAh_{k-1}$ term would focus more on long-range degradation information (in the case of Figure 3, the raindrops), while the $CBx_k$ term would focus more on local information, including local image content like fine textures. The visualizations in Figure 3 confirm that our trained model indeed learns the information in this manner. We will add examples from the other tasks in the revision for a more comprehensive demonstration.\n\n**Q2: More comparisons? (W2)**\n\n**A2:** Thank you for this suggestion. We would like to clarify that the all-weather setting is primarily designed for unified models. Consequently, many excellent recent restoration methods have not been evaluated in these benchmarks, which is why they were not originally included.\n\nTo address your concern, we have now benchmarked our method against the recent SOTA approaches, including ConvIR, AST, CODE, FSNet, and the Mamba-based models like MambaIR, VMambaIR, and FreqMamba.\n\nSince ConvIR and FSNet do not address the RainDrop (raindrop removal) or Outdoor (joint rain-haze) benchmarks, we compared them on the overlapping desnowing task. To ensure a rigorous comparison, we evaluated on both the Snow100K-L/S benchmarks from the all-weather setting and the Snow100K-2000 benchmark from the ConvIR and FSNet, as shown below.\n\n| Method | Snow100K-L | Snow100K-S | Snow100K-2000 |\n| ------ | ---------- | ---------- | ------------- |\n| ConvIR | 32.11      | 37.98      | 33.92         |\n| FSNet  | 31.62      | 37.42      | 33.76         |\n| MODEM  | **32.52**  | **38.08**  | **35.76**     |\n\nFor AST, there is an overlap in the RainDrop removal task. We have therefore tested AST on the RainDrop benchmark, and the results are shown in the table below.\n\n| Method | RainDrop  |\n| ------ | --------- |\n| AST    | 30.57     |\n| MODEM  | **33.01** |\n\nFor methods without task overlap (CODE, MambaIR, VMambaIR, FreqMamba), we retrained them on each of the tasks, carefully following the settings used by other recent methods like ConvIR, FSNet, and Histoformer, while respecting their original training configurations. The results are shown in the table below.\n\n| Method    | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| --------- | ---------- | ---------- | --------- | --------- |\n| MambaIR   | 28.59      | 33.34      | 24.73     | 32.16     |\n| FreqMamba | 27.09      | 33.52      | 19.89     | 30.60     |\n| VmambaIR  | 31.07      | 36.35      | 24.23     | 32.18     |\n| CODE      | 30.46      | 36.29      | 26.65     | 32.64     |\n| MODEM     | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\nWe will fully integrate these more comprehensive comparisons into Tables 2-4 in the revision of the paper.\n\n**Q3: Analysis of ablation study? (W3)**\n\n**A3:** Thank you for prompting a deeper discussion on this interesting result. Firstly, the all-weather training data is imbalanced, with fewer images for raindrop removal and deraining/dehazing than for desnowing. The DSAM empowers the model to handle the **fine-grained, localized artifacts** characteristic of these under-represented tasks. Without DSAM's guidance, the network would naturally over-specialize on the more prevalent snow degradation.\n\nAs we analyzed in Section 5.2 for Table 5, this trade-off is evident in the results. Removing DSAM (row 3) results in a marginal performance increase on the snow datasets (+0.07dB on both Snow100K-S/L). However, this comes at a significant cost to the other tasks: performance drops by 0.33dB on the Outdoor dataset and by 0.29dB on the RainDrop dataset. This clearly shows that **DSAM provides the crucial modulation capability for the model to adapt to fine-grained, local artifacts**, preventing it from over-specializing on more globally uniform degradations. We will clarify this point in the revision.\n\n**Q4: Two-stage training mechanism? (W4)**\n\n**A4:** Thank you for these insightful questions. The primary purpose of our two-stage training is to effectively solve the difficult problem of degradation estimation. **In Stage 1,** we train the DDEM to learn an ideal degradation representation by leveraging the paired GT-degraded images from the training set. Specifically, the DDEM module receives both images as input and is trained to understand their difference, ultimately outputting a single, compact degradation vector. This vector establishes the **perfect degradation prior** that will serve as the supervisory target for Stage 2.\n\n**In Stage 2,** we use this learned degradation prior to supervise the training of our DDEM module via KL divergence, as shown in Eq. 13. Specifically, a **frozen copy of the Stage 1 DDEM** is used to generate the target degradation priors from the paired training images. The practical DDEM, which receives only the degraded image as input, is then trained to match the output of this frozen module. This two-stage training process ensures the MODEM can robustly estimate degradation.\n\nAs shown in our ablation (Table 5, row 2), removing the degradation estimation link severely degrades performance, proving the superiority of our two-stage approach.\n\n**Q5: Compute the** **KL** **loss before the avg pool? (W4)**\n\n**A5:** As we analyzed in our introduction, learning a discriminative degradation representation directly from feature maps is notoriously difficult **because scene content and degradation are deeply entangled**. This is precisely why methods without explicit degradation estimation often struggle on multi-degradation tasks.\n\nOur solution, as described in the introduction, is to disentangle this problem by learning: (i) a global degradation representation that encapsulates high-level weather characteristics, and (ii) a set of spatially adaptive kernels that encode local degradation structures and variations. The effectiveness of these components is demonstrated in the 2nd-5th rows of our ablation study in Table 5.\n\nThe vector $\\tilde{Z}$ is a compact, global descriptor designed to capture the high-level degradation distribution of the entire image. By computing the KL divergence loss on $\\tilde{Z}$, the model is guided to learn a disentangled, conceptual summary of the degradation, avoiding the challenges of a direct feature-map-level replication where content and degradation are deeply mixed. This encourages better generalization by focusing the learning on high-level degradation characteristics, which is validated by our model's strong performance on real-world images (Fig. 6) without any fine-tuning. \n\nAdditionally, to further address your concern, we have conducted an experiment applying the KL loss at the feature-map level before average pooling, shown in the table below.\n\n| Setup           | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| --------------- | ---------- | ---------- | --------- | --------- |\n| w/o KL Loss     | 32.12      | 37.61      | 32.37     | 32.38     |\n| Replace KL Loss | 31.85      | 37.16      | 32.77     | 32.57     |\n| MODEM           | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\n**Q6: Correlation loss? (W4)**\n\n**A6:** We adopted correlation loss following its implementation in Histoformer. Its purpose is to better preserve patch-level linear correlations. We will add the citation to the revision of the paper.\n\n**Q7: Compare the different scanning manners? (W5)**\n\n**A7:** Thank you for this suggestion. We had already provided an initial comparison in our ablation study. Our ablation study **(Table 5, row 1)** shows that replacing our Morton scan with a Raster scan (used in MambaIR) degrades performance.\n\nTo more comprehensively address your concern, we have now conducted an expanded ablation study to include all the scanning methods illustrated in Figure 1, as well as other relevant methods from recent works. We maintained the same MODEM architecture and only replaced the scanning mechanism, with each variant trained under the same settings. The results are presented in the table below:\n\n| Method               | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| -------------------- | ---------- | ---------- | --------- | --------- |\n| Raster (e.g.MambaIR) | 32.33      | 38.03      | 32.89     | 32.69     |\n| Continuous (zigzag)  | 32.17      | 37.74      | 32.35     | 32.59     |\n| OSS (VmambaIR)       | 32.14      | 37.39      | 32.61     | 32.11     |\n| Local (LocalMamba)   | 32.23      | 37.75      | 32.60     | 32.53     |\n| Hilbert (LC-Mamba)   | 32.46      | 37.96      | 32.99     | 32.82     |\n| Morton (Ours)        | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\nThe results confirm that the Morton-order scan consistently performs best, providing strong evidence that its superior 2D locality preservation. We will incorporate this detailed ablation study into the revision."}, {"review_id": "OcyOWek92k", "reviewer": "Reviewer_2iWh", "summary": "This paper introduces a Morton-Order Degradation Estimation Mechanism for adverse weather image restoration. A Morton-Order 2D-Selective-Scan Module is developed to capture long-range dependencies while preserving local structural coherence. Meanwhile, a Dual Degradation Estimation Module is proposed to disentangles degradations. The idea of employing SSM is recently popular in this field, and the newly designed model sounds interesting.", "questions": "1) The authors are encouraged to include comparisons with more recent models in Tables 2–4, especially works from 2023–2024 such as ConvIR[3], AST[4], CODE[5], and FSNet[6], which are highly relevant in this context.\n\n2) In Tab.1, a comparison with the diffusion-based method in terms of PSNR/SSIM is not enough, more perceptual metric is supposed to be provided, such as LPIPS.\n\n3) Complexity Analysis is conducted, while no SSM-based methods are included, such as MambaIR[1], FreqMamba[2].\n\n4) Effective Receptive Field (ERF) visualization of MODEM and competitors (e.g., MambaIR[1]) would help in understanding their long-range modeling ability.\n\n5) Quantitative results (such as non-reference metric, NIQE) or a user study on challenging real-world scenes should be conducted.\n\n6) The ablation study could be extended to explore the contribution of different loss components\n\n[3] Revitalizing Convolutional Network for Image Restoration. TPAMI24.\n\n[4] Adapt or perish: Adaptive sparse transformer with attentive feature refinement for image restoration. CVPR24.\n\n[5] Comprehensive and delicate: An efficient transformer for image restoration. CVPR23.\n\n[6] Image Restoration via Frequency Selection. TPAMI24.", "limitations": "Limitation of the method is not discussed.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Pros:\n\n1) Using Morton Scanning instead of standard Scanning ways brings new insight to this community.\n\n2) The proposed MODEM performs favorably against the considered methods.\n\nCons:\n\n1) Differences between MODEM and existing SSM-based methods (e.g., MambaIR[1], FreqMamba[2]) are supposed to be further analyzed.\n\n2) The space/time complexity of the proposed algorithm is not studied.\n\n[1] Mambair: A simple baseline for image restoration with state-space model. ECCV24.\n\n[2] Freqmamba: Viewing mamba from a frequency perspective for image deraining. ACM MM24.", "was_revised": true, "final_justification": "After reading the comments from other reviewers and the replies made by authors, I would like to maintain my score. While this paper needs more details to help understand, which is expected to be addressed in the coming version, the idea of this paper itself is appreciated.", "rebuttal": "**Q1: Differences between** **MODEM** **and existing SSM-based methods? (Cons1)**\n\n**A1:** Thank you for this suggestion. The key difference is our **explicit degradation estimation**. While methods like MambaIR and FreqMamba are \"blind\" backbones, MODEM features a **Dual Degradation Estimation Module (DDEM)**. The DDEM extracts a **global degradation descriptor** and **spatially adaptive kernels (Eq. 4)**. These degradation priors then dynamically modulate our MOS2D modules via the proposed **DAFM (Eq. 7)** and **DSAM (Eq. 8)** mechanisms, which in turn enables a degradation-aware selective scan process by dynamically modulating the SSM **(Eq. 9, Eq. 10)**.\n\nTo address this concern, we have retrained three prominent Mamba-style restoration networks on the all-weather setting. These experiments were conducted carefully following the settings used by other recent methods like ConvIR, FSNet, and Histoformer, while also respecting their original training configurations. The results are presented in the table below.\n\n| Method    | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| --------- | ---------- | ---------- | --------- | --------- |\n| MambaIR   | 28.59      | 33.34      | *24.73*   | 32.16     |\n| FreqMamba | 27.09      | 33.52      | 19.89     | 30.60     |\n| VmambaIR  | *31.07*    | *36.35*    | 24.23     | *32.18*   |\n| MODEM     | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\nFurthermore, Unlike the simple raster scan used in MambaIR, our MOS2D uses the **locality-preserving Morton scan**. This is specifically designed to enable more structured and effective modeling of the spatially heterogeneous nature of weather degradation. Our ablation in Table 5 already showed its advantage over a raster scan. To further validate this, we conducted an expanded ablation study comparing Morton-order against other scanning patterns.\n\n| Method               | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| -------------------- | ---------- | ---------- | --------- | --------- |\n| Raster (e.g.MambaIR) | 32.33      | 38.03      | 32.89     | 32.69     |\n| Continuous (zigzag)  | 32.17      | 37.74      | 32.35     | 32.59     |\n| OSS (VmambaIR)       | 32.14      | 37.39      | 32.61     | 32.11     |\n| Local (LocalMamba)   | 32.23      | 37.75      | 32.60     | 32.53     |\n| Hilbert (LC-Mamba)   | *32.46*    | *37.96*    | *32.99*   | *32.82*   |\n| Morton (Ours)        | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\nWe will include these ablation and comparison experiments in the revision.\n\n**Q2: Complexity Analysis? (Cons2 & Q3)**\n\n**A2:** Thank you for this suggestion. In Appendix A.3, we initially provided a complexity analysis comparing our model to the previous SOTA methods in the unified all-weather setting. We did not include MambaIR and FreqMamba as their papers use different benchmarks than our all-weather evaluation.\n\nTo address your concern, we have now conducted a direct complexity comparison with MambaIR and FreqMamba under identical settings (256x256 input, single RTX 3090).\n\n| Method         | MambaIR | FreqMamba | Histoformer | MODEM |\n| -------------- | ------- | --------- | ----------- | ----- |\n| Parameters (M) | 15.78   | 8.93      | 16.62       | 19.96 |\n| Time (ms)      | 790.61  | 233.41    | 109.07      | 92.86 |\n\nThe results show MODEM has a superior balance of performance and efficiency, achieving significantly faster inference than other SSM-based methods. This will be added to the revision.\n\n**Q3: More comparisons? (Q1)**\n\n**A3:** Thank you for suggesting these highly relevant and recent models for comparison. Due to the time constraints of the rebuttal period, we have focused on conducting new experiments on the tasks where our benchmarks overlap with these newer methods. It is important to note that in the all-weather setting, the \"RainDrop\" benchmark is for raindrop removal, and the \"Outdoor\" benchmark is for joint rain and haze removal. Since ConvIR and FSNet do not address the tasks of our RainDrop or Outdoor benchmarks, we have compared our method against them on the Snow100K dataset. To ensure a rigorous comparison, we evaluated on both the Snow100K-L/S from the all-weather setting and the Snow100K-2000 used in the ConvIR and FSNet papers. The comparative results are presented in the table below.\n\n| Method | Snow100K-L | Snow100K-S | Snow100K-2000 |\n| ------ | ---------- | ---------- | ------------- |\n| ConvIR | *32.11*    | *37.98*    | *33.92*       |\n| FSNet  | 31.62      | 37.42      | 33.76         |\n| MODEM  | **32.52**  | **38.08**  | **35.76**     |\n\nFor AST, there is an overlap in the RainDrop removal task. We have therefore tested AST on our RainDrop benchmark, and the results are shown in the table below.\n\n| Method | AST   | MODEM     |\n| ------ | ----- | --------- |\n| PSNR   | 30.57 | **33.01** |\n\nThere were no directly overlapping tasks with CODE. Therefore, we have retrained CODE separately on each of the three tasks within the all-weather dataset, carefully following the settings used by other recent methods like ConvIR, FSNet, and Histoformer, while respecting CODE's original training configuration. The results of this comparison are shown in the table below.\n\n| Method | Snow100K-L | Snow100K-S | Snow100K-2000 | Outdoor   | Raindrop  |\n| ------ | ---------- | ---------- | ------------- | --------- | --------- |\n| CODE   | 30.46      | 36.29      | 33.90         | 26.65     | 32.64     |\n| MODEM  | **32.52**  | **38.08**  | **35.76**     | **33.10** | **33.01** |\n\nWe have made our best effort to present these new and relevant comparisons given the limited time. We commit to conducting a more exhaustive comparison for the revision.\n\n**Q4: More perceptual metric? (Q2 & Q5)**\n\n**A4:** Thank you for this insightful suggestion. We have added new perceptual metrics. We now report referenced (LPIPS) and non-referenced (Q-Align, MUSIQ) scores, all computed using the `pyiqa` library, with the same settings applied for all methods. As shown in the table below, our method achieves SOTA perceptual quality.\n\nQ-Align, higher is better.\n\n| Method      | Snow100K-L | Snow100K-S | Outdoor    | Raindrop   | Snow100K-Real |\n| ----------- | ---------- | ---------- | ---------- | ---------- | ------------- |\n| MODEM       | **3.7324** | **3.7695** | **4.1875** | **4.0664** | **3.5586**    |\n| Histoformer | *3.7207*   | *3.7598*   | *4.1445*   | *4.0156*   | *3.5449*      |\n| WeatherDiff | 3.4531     | 3.5293     | 3.8691     | 4.0000     | 3.4512        |\n\nMUSIQ, higher is better.\n\n| Method      | Snow100K-L  | Snow100K-S  | Outdoor     | Raindrop    | Snow100K-Real |\n| ----------- | ----------- | ----------- | ----------- | ----------- | ------------- |\n| MODEM       | *64.2438*   | **64.2853** | **68.2926** | **69.7925** | **59.6042**   |\n| Histoformer | **64.2526** | *64.2581*   | *67.7461*   | 68.4852     | 59.4040       |\n| WeatherDiff | 62.6267     | 63.1278     | 67.4814     | *69.3608*   | *59.4493*     |\n\nLPIPS, lower is better.\n\n| Method      | Snow100K-L | Snow100K-S | Outdoor    | Raindrop   |\n| ----------- | ---------- | ---------- | ---------- | ---------- |\n| MODEM       | **0.0880** | **0.0407** | **0.0699** | *0.0650*   |\n| Histoformer | *0.0919*   | *0.0445*   | *0.0778*   | 0.0672     |\n| WeatherDiff | 0.0982     | 0.0541     | 0.0887     | **0.0615** |\n\n**Q5: Effective** **Receptive Field** **(ERF) visualization? (Q4)**\n\n**A5:** Thank you for this suggestion. Due to the rules of the rebuttal process, we are unable to upload new ERF visualizations at this stage. We have calculated the size of the ERF for our model and key competitors on a 256x256 input image. We measured the ERF at different contribution thresholds (1%, 5%, 10%, and 15%). The results are presented in the table below:\n\n| Threshold   | 1%        | 5%       | 10%      | 15%      |\n| ----------- | --------- | -------- | -------- | -------- |\n| MODEM       | 243 x 200 | 129 x 67 | 117 x 57 | 116 x 57 |\n| Histoformer | 168 x 250 | 33 x 26  | 7 x 6    | 2 x 1    |\n| MambaIR     | 171 x 232 | 50 x 125 | 13 x 21  | 10 x 18  |\n\nThese results confirm MODEM's larger effective receptive field and superior long-range modeling compared to competitors. We will include the full ERF visualizations in the final camera-ready version of the paper.\n\n**Q6: Ablation study of different loss components? (Q6)**\n\n**A6:** Thank you for your suggestion. The importance of the KL loss was already shown in our Table 5 ablation (row 2). The results show the critical supervisory role of the KL divergence for the degradation estimation process. To further analyze our loss function, we now provide new ablations on the correlation loss and the KL loss placement (before the avg. pool), as shown in the table below:\n\n| Setup                | Snow100K-L | Snow100K-S | Outdoor   | Raindrop  |\n| -------------------- | ---------- | ---------- | --------- | --------- |\n| w/o Correlation Loss | 32.30      | 37.79      | 32.91     | 32.69     |\n| w/o KL Loss          | 32.12      | 37.61      | 32.37     | 32.38     |\n| Replace KL Loss      | 31.85      | 37.16      | 32.77     | 32.57     |\n| MODEM                | **32.52**  | **38.08**  | **33.10** | **33.01** |\n\nThese results confirm that each loss component contributes positively to the final performance. We will incorporate this more detailed ablation study into the revision.\n\n**Q7: Limitations?**\n\n**A7:** We analyze our model's limitations, including failure cases, in Appendix A.4 (Figure 8). As we discuss there, MODEM, like other contemporary methods, can struggle with images containing extremely large, high-contrast snowflakes. Nevertheless, as the visual results show, our method still achieves comparatively better results in these challenging cases. We will reference this analysis in the main text."}]

Author rebuttal:

Meta-review: This paper proposes an effective MODEM for image restoration. It explores morton-coded spatial ordering with selective state-space models to model both local and non-local information. 

This paper received reviews with mixed ratings. The major concerns include limited novelty and insufficient comparisons with recent SOTA methods. 

Based on the provide rebuttal and discussions with reviewers, the authors solve the concerns of reviewers, especially for comparisons with suggested methods by reviewers. 

Based on the rebuttal and recommendations of reviewers, the paper can be accepted. The authors are suggested to revise the paper according to comments accordingly.
Decision: Accept (poster)