LearnIR: Learnable Posterior Sampling for Real-World Image Restoration
Authors: Yihang Bao
Zhen Huang
Shanyan Guan
Songlin Yang
Yanhao Ge
Wei Li
Bukun Huang
Zengmin Xu
Venue: ICLR 2026 Poster (2026)
Keywords: Image restoration
diffusion model
residual
Primary area: generative models

Abstract: Image restoration in real-world conditions is highly challenging due to heterogeneous degradations such as haze, noise, shadows, and blur. Existing diffusion-based methods remain limited: conditional generation struggles to balance fidelity and realism, inversion-based approaches accumulate errors, and posterior sampling requires a known forward operator that is rarely available. We introduce **LearnIR**, a learnable diffusion posterior sampling framework that eliminates this dependency by training a lightweight model to directly predict gradient correction distributions, enabling *Diffusion Posterior Sampling Correction (DPSC)* that maintains consistency with the true image distribution during sampling. In addition, a *Dynamic Resolution Module (DRM)* dynamically adjusts resolution to preserve global structures in early stages and refine fine textures later, while avoiding the need for a pretrained VAE. Experiments on ISTD, O-HAZE, HazyDet, REVIDE, and our newly constructed FaceShadow dataset show that LearnIR achieves state-of-the-art performance in PSNR, SSIM, and LPIPS.

Published as a conference paper at ICLR 2026
LEARNIR: LEARNABLE POSTERIOR SAMPLING FOR REAL- WORLD IMAGE RESTORATION
Yihang Bao
Zhen Huang
Shanyan Guan Songlin Yang²
Yanhao 2e Wei Li
Bukun Huang Zengmin Xu-.4,5.t
School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology.
2 vivo Mobile Communication Co., Ltd
3 Zhejiang Gongshang University
4 Center for Applied Mathematics of Guangxi (GUET)
5 Anview.ai
byh11@mails guee.ggeeeee.. edu.cn xzm@guet. edu. cn
Seaeanghhnnhhaiiy guanshanyan, songlin.yang halege, S.wei..yxhh/evivo.oom hbx10098163.com
ABSTRACT
Image restoration real-world conditions is highly challenging due hetero- gencous degradations such as haze. noise, shadows, and blur. Existing diffusion- based methods remain limited: conditional generation struggles to balance fidelity and realism, inversion-based approaches accumulate errors, and posterior sam- pling requires a known forward operator that is rarely available. We introduce LearnIR, learnable diffusion posterior sampling framework that eliminates this dependency by training a lightweight model to directly predict gradient correc- tion distributions, enabling Diffusion Posterior Sampling Correction (DPSC) that maintains consistency with the true image distribution during sampling. In addi- tion, Dynamic Resolution Module (DRM) dynamically adjusts resolution pre- serve global structures in early stages and refine fine textures later, while avoiding the need for a pretrained VAE. Experiments on ISTD, O-HAZE, HazyDet, REV- IDE, and our newly constructed FaceShadow dataset show that LearnIR achieves state-of-the-arn performance in PSNR, SSIM, and LPIPS.
INTRODUCTION
Real-world imaging environments often introduce a multitude of degradations as haze, noise, shadows, and motion blur-that compromise the visual quality of natural images. Image restoration aims to solve the crucial task of recovering a clean, high-fidelity image from its degraded observa- tion. This is a classic and inherently ill ill-posed inverse problem that is further complicated by the fact that multiple heterogeneous degradation types often appear simultaneously and are intricately intertwined, thereby posing significant and persistent challenge for existing restoration methods.
With the development of deep generative models (Ho al. 2020 Song et al.) 2021). promising direction is to frame image restoration as a conditional image generation problem. By leveraging degraded image as a condition, these models are trained to synthesize a high-quality image while preserving its underlying structure and semantics. Among these, diffusion models have recently shown unprecedented success, thanks to their capacity to learn intricate distribution transforma- tions. When combined with dedicated mechanisms for low-free www-freuuncc structure alignment (e.g., resampling (Choi et al. 2021 Cao et al.] 2025) or frequency-domal projection (Xiao et al.) 2024 Shang et al. )2024) and high-frequency detail synthesis (e.g., dynamic degradation-aware diffu- sion (Wang et al.] 2025b)). diffusion models can achieve superior performance. Nevertheless, fundamental trade-off remains: balancing faithful restoration and plausible generation.
A complementary approach to conditional generation is diffusion-innersionn based restora- Guo et al. 20236). While this
tion (Whang al. 2022 Choi et al. 2021 Wang al. 2025b
"Equal contributions. 'Corresponding author. Project page: github.tuu.c. wtw...cwm//ittihaaaaeeeeeeee leaaniR

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Published as a conference paper at ICLR 2026
paradigm can achieve impressive detail recovery, the process of inverting the degraded image into the latent space inherently accumulates errors, leading to noticeable deviations from the input. More- over, these methods are often inefficient due to the necessary adding and subsequent removal of
noise. In contrast, diffusion-based posterior sampling (Chung et al. [023] Zhao et al. 2024 Zirvi et [024] Rout al., 2023) has shown that combining the generative prior with data consistency constraint can effectively solve ill-posed inverse problems, such as Gaussian deblurring. However, this approach is severely limited in practical and diverse real-world scenarios, since requires precisely known forward measurement operator A (e.g., randomly masking the image proposed in DPS (Chung et al.] 2023)) ) which must also be explicitly reused during inference.
In this work, we introduce LearnIR, novel learnable diffusion posterior sampling framework for efficient and faithful real-world image restoration. Unlike existing approaches that rely on a known forward measurement operator, our method bypasses this requirement. Leveraging the closure prop- erty of the normal distribution, we train a lightweight model to directly predict the distribution of the gradient correction term a key component in diffusion posterior sampling (Chung et al., 2023) thereby establishing a robust mechanism to maintain denoising consistency with the true image dis- tribution. Specifically, LearnIR performs Diffusion Posterior Sampling Correction (DPSC) during inference through a compact pre-trained model that adaptively learns and applies corrections to the diffusion trajectory at each step. By removing the dependency tively steers the generative process toward more accurate reconstructions, akin to inversion-based methods, but without requiring an explicit mapping between clean and degraded images.
forward operator, DPSC effec-
Furthermore, to obtain richer global context and simplify the pipeline, we introduce novel Dynamic Resolution Module (DRM) specifically designed for pixel-space image restoration. The DRM dy- namically adjusts image resolution during training by applying large-scale downscaling in the early sampling stages better preserve global structures, followed by large-scale upscaling in the later stages to promote fine texture generation. This design not only achieves a superior balance between structural integrity and detail fidelity but also removes the need for a pretrained VAF, significantly reducing computational costs and enabling a simplified end-to-end image generation pipeline.
We validate the proposed LearnIR framework on the ISTD (Wang et al. 2018). O-HAZE (Ancuti) ct al. (018),, HazyDet (Ancuti et al. 20188), REVIDE (Zhang et al. 2021) and our newly constructed FaceShadow dataset for the challenging tasks of haze removal and shadow removal. Experimental results clearly demonstrate that LearnlR uniformly outperforms existing methods, including Resfu-
sion (Shi et al., 2024).. ShadowRefiner (Dong et al.] 2024), and ConvIR (Cui et al. [0024). among
others, by significant margin in PSNR (Hore & Ziou (01O) and SSIM (Wang et al. 2004) across all tested datasets. These results validate the effectiveness of our proposed LearnIR framework.
PRELIMINARIES
2.1 LEARNING RESIDUAL DENOISING MODELS
Standard inversion- based diffusion methods often suffer from instability in intermediate states, com- plicating the identification of an optimal sampling starting point. To address this, recent works such as ResFusion (Shi et al. 2024) incorporate a residual term R into the diffusion process, defined as:
R y Fo,
where y represents the degraded image and 2n denotes the clean image. Incorporating this residual into the forward diffusion process modifies the transition equation to:
Et Va, xo + (1 Vā.) R + v1 - ā, E, <~ (0, I).
(I)
Substituting = y 1a--a mg into Eq. equation myields the reformulated forward process:
x; = (2Va, - 1)x0 + (1- (1-va. vo.)y+v1-aae
(2)
A critical challenge in the forward process is that De is unknown during inference. However, Eq. equation 2 reveals that the dependence on To vanishes when the coefficient (2/ā, 1) ap- proaches zero. Based on this observation, a stable sampling timestep T" can be identified via the following minimization (Shi et al. 2024]:
T = arg min Vox
(3)
1=1
2

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Published as a conference paper at ICLR 2026
LEARRING
NOW
CARRINNG
(a)
(b)
(d)
(c)
Figure 1: Real-World Image Restoration with LearnIR. This figure provides visual compari- son of LearnIR's real-world image restoration capabilities. The top row shows the degraded inputs, which include various complex degradations like haze and shadows. From left to right, the images show (a) and (b) de-hazing, (c) facial shadow removal, and (d) and (e) object shadow removal. The bottom row presents the corresponding outputs generated by our LearnIR framework. As clearly ev- idenced by the results, method effectively removes these complex and intertwined degradations while faithfully preserving fine image details and generating visually high-fidelity results.
At this specific timestep T", the forward state TT becomes independent of æp and can be approxi- mated solely using the degraded input y and noise:
V y + vI- -rr Vār y + vI âT
ET
Consequently, the reverse sampling process can be initiated at T", The model is trained to predict the residual-shifted noise, with the objective function reformulated as:
L = -6 (x, e][[]
Tes = e+ (1 V1-var)VT= &i
where
R.
(5)
81
2.2 DIFFUSION POSTERIOR SAMPLING FOR NOISY INVERSE PROBLEMS
Inverse problems are fundamental to numerous scientific and engineering applications (Groetsch & Groetsch 1993), aiming to recover an unknown signal æ Rd from a degraded observation y E Ik via the model:
y A(w) + +n, n ~~ ~~
where A(-) is a forward operator (potentially non-linear or ill-posed). Since the mapping >> y is typically many-to-one, recovering x: requires sampling from the intractable posterior distribution p( y).
Diffusion models have recently emerged robust generative priors for such ill-posed problems. Methods like Diffusion Posterior Sampling (DPS) (Chung et al. 2023) enable conditional sampling by modifying the reverse diffusion score. By applying Bayes' rule, the conditional score function decomposes into:
Va, p(x; b) = Va. logp(z;) + V a, logp(y xx).
Here, the prior score Va, log p(x, is provided by pretrained diffusion model sa t). The second term, the likelihood score Va, log ply wt), enforees data consistency. However, deriving p(y æ;)) analytically is intractable because it requires marginalizing over Tg.
To approximate this term, DPS leverages the expected denoised estimate (x((x)) = E(xo yielding the approximation:
p xx) Emg me) [p(y xu)]
ply Elwoo xx))
(8)
~ p(y to (2)))
3

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Dynamic Resolution Module
Adaplive trainable posterior fine-tuning
D Ot ory,2"
S14)
520
spprppeet
No Cz
Diffusion Posterior Sampling Correction
Foll Poll
Ho Hale..yy1)
Velle
Figure 2: Overview of the LearnIR Framework. The smooth equivalence transformation (Shi
et al. 2024) identifies the optimal sampling step T (blue line) to bypass the unstable intermediate states derived from observation y. The proposed framework consists of key components: 1) The Dynamic Resolution Module (DRM) projects inputs into a time-dependent latent space via
D(,,2") to balance structural coherence and detail recovery; 2) The Diffusion Posterior Sampling Correction (DPSC) acts boug-and-play regularization to analytically eliminate the trajectory inconsistency (structural bias) discussed Appendix A.44
assuming a Gaussian measurement noise model as defined in Eq. equation
p ma) x exp 20 lly A(xo)11
By differentiating the approximated likelihood with respect to æx, we obtain the guidance term:
Vn, log p(y ax)
V n:
A(
σ²
Substituting this back into Eq. equation 7 results in the final conditional score update rule:
V log p( y) = so( t) V V A(to)
with 2
o²
METHODOLOGY
In this section, we present LearnIR, robust framework for residual-based image restoration. As il- lustrated in Fig. 2 our approach integrates two complementary mechanisms: Dynamic Resolution Module (DRM) that constructs resolution-aware latent space to suppress noise and redundancy, and a Diffusion Posterior Sampling Correction (DPSC) that operates within this space to align the diffusion trajectory with the true posterior. The full algorithm detailed Section 3.3
3.1 DRM: DYNAMIC RESOLUTION MODULE
Drawing inspiration from multi-scale generation frameworks such MDM (Gu et al. 2024 and Pixelflow (Chen et al., 2025). we incorporate a Dynamic Resolution Module (DRM) to enable adap- tive processing across spatial scales. By processing high-noise states lower resolutions, DRM effectively captures global context while mitigating artifacts such as texture inconsistency.
Resolution-Aware Latent Mapping. We define a dynamic downsampling operator D(; 8), where the scale factor s is governed by time-dependent schedule st)). Unlike standard diffusion operating in a fixed pixel space, our process evolves in a variable-resolution latent space. Specifically, timestep f, the clean image Dn and the degraded image are mapped to their latent counterparts:
(t)
D(æa, s(1),
2 (1) D(y,
(10)
4

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Consequently, 2( denotes the latent noisy at the specific resolution determined by s(t).
Latent Residual Diffusion. To maintain consistency with the residual learning objective (Sec. 2.1 extend the residual formulation into this dynamic latent space. We define the latent residual R as:
R₂ [ 20
(11)
Substituting this into the forward process, the transition kernel in the latent space becomes:
g(zt 2 ) = N(zs: vār 2 + (1 v R (1-0+)I) ox)
(12)
This ensures that the degradation prior R2 effectively guides the noise injection regardless of the spatial scale.
Coarse-to-Fine Sampling Strategy. The schedule stt) facilitates coarse-to-fin fo- trajectory, as illustrated in Figure 2 During the early high-noise stages (f 2 T/2), the model operates a downsampled resolution (s Sdown) to focus on global structure. In later stages (t < T/2), it transitions to the native scale (s = sup) to refine high-frequency details. We implement this resizing via efficient, non-traine trainable interpolation, allowing LearnIR to leverage pre-trained priors without complex architectural changes.
3.2 DPSC: DIFFUSION POSTERIOR SAMPLING CORRECTION
Motivation. We start from the standard training objective of diffusion models. Typically, the denoising loss is formulated as an & or Eg loss:
dennosse E _0 .e,t ||c -
(13)
where Ep denotes the noise prediction network. While effective, this loss only ensures accurate noise estimation at each timestep, but does not guarantee that the learned reverse posterior pa( = xt) matches the true posterior g zt, = (0) induced by the forward process. This mismatch, which we refer to as inconsistency, tends to accumulate across multiple sampling steps and manifests as artifacts such color shifts.
Consistency Regularization. To address this issue, we introduce a consistency regularization term Luomsistency, which directly minimizes the discrepancy between the forward- prordd-rocess distribution and the pverse-process distribution predicted by the model. The final training objective is given by
Liotal = Ldenoise + >C
(14)
where À is weighting hyperparameter.
Towards Consistency Loss. To construct Leonsistency. we first formally quantify the discrepancy between the forward and reverse processes in the DRM latent space. We achieve this by analyzing the true forward posterior distribution (Definition [ and the model-predicted reverse distribution (Definition 2). Here, 2, denotes the latent state timestep t, whose spatial resolution is implicitly determined by the schedule s(t) (Sec. 3.1;; similarly, (1)) and (0) are the resolution-dependent latents of the clean image and the degraded image, respectively.
Definition 1. In the residual formulation of the forward process in Eq. 12 the variable forward follows Gaussian distribution:
forward 2t-1 ~ N (VoL-120 (1-vaar)) Rz, (1 - 1I)
(15)
(t) where R. = 2n denotes the residual in the DRM latent space.
(1) Definition 2. The preee-predicted reverse distribution pe (Zt-1 Zzs Zi .) in the residual-based
VP-SDE or DDPM is Gaussian distribution:
(
prod N (ort"
1-
6 (2,, 2(0,0) (1 -1-1)( (111 1
(16)
Var(1 σn)
where eT denotes the residual noise predictor.
5

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The stochasticity of the reverse sampling process defined by Eq. 16 introduces additional sam- pling noise 5 (N,, While the injection of this random noise is essential for generating sample diversity, its accumulation across steps may lead to noticeable discrepancies from the desired pos- terior trajectory, such as color shifts (Appendix (A.4). To mitigate this issue, prior works introduce gradient-based corrections, which briefly review below.
Definition 3. (Denoising Posterior Sampling (Chung al. 2023)). This method approximates
p(zz) 2x) by p Zy 2 =
(8)
-E
zel and further estimates
2, log pl ( zx)
-2
1 V.. -
2/00
A( (z)))
(17)
where A(-) denotes the forward degradation operator in the corresponding space, and the full derivation provided in Appendix(A.10 At each sampling step, the trajectory is corrected as
2t-1 2 - 11 22 log pepp((2) p(2] zt);
(18)
where 2/-1 is the original reverse-diffusio prediction, and is a scaling factor that controls the magnitude of the gradient correction.
Theorem 1. Based Definitions 7 and the DPS gradient in Eq. 17 can be expressed in the DRM latent space as
2. log
ze) x pred forward
21-1
(19)
By comparing Eg. 19 with the update rule in Eq. 18 where z,-1 corresponds to #t-1 and z corresponds to 2 2oorward, we see that the DPS gradient precisely captures the discrepancy between the forward and reverse processes in the DRM latent space. Leveraging the closure property of Gaussian distributions, this discrepancy can be modeled as
prod
pred 21-1
forward
(N(E,, (0) 2)), 0² 0z 20 ,)))
(20)
zt-1
where the closed-form expressions of μa and o² are given in Appendix A.17
Final Consistency Lass. Based on the above derivation, we define the consistency loss as the & distance between the analytic mean μ and the predicted mean βe of the offset:
Connsistnccy
zy (1) .) - (z, 21 (0) t) 22,, pa(ze,
(21)
where is analytically computed via Eq. 51 and já is the corresponding prediction output by the learnable correction network.
3.3 TRAINING AND INFERENCE
Algorithm Overview. Algorithms and 2 summarize the training and sampling procedures of LearnIR in the DRM latent space. During training (Algorithm D. we first determine a truncation step 7" via the smooth equivalence transformation, which locates stable midpoint of the diffusion trajectory. At each iteration, we sample t Uniform( , T')),, and project the clean image 2p and degraded observation y into the resolution-aware latent space via DRM obtain = and (f) Zy Their difference R. = Zy 2 encodes the degradation prior at the current scale. Based on (z(*), R.z,, we construct the forward latent foooward with the residual diffusion process and derive residual noise target ees that absorbs the effect of R.. The network predicts both a residual noise res and correction mean [4g that approximates the analytic mean μ of the discrepancy between the forward and reverse posteriors (cf. Eq. 20p. The overall objective is therefore the sum of denoising loss on e/e and a consistency loss that regresses [4g toward μu, explicitly aligning the learned reverse dynamics with the true forward posterior in the DRM latent space.
At inference time (Algorithm 2). we again compute T" and initialize žy around the latent observa- tion =(T'), For each timestep t T'. -. 1..... 2, DRM provides the latent observation z, upon which we first perform standard ceverse-diffusion update to obtain a provisional state x Then DPSC is applied: the correction network un together with Gaussian perturbation Cz yields an

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Algorithm Training
Algorithm 2 Sampling
Require: Total diffusion steps
T,
degraded
Require:
Total steps T. degraded image 34
image y, ground truth 20
priors {Gi pretrained 6gs Ps
pretranndd
1: repeat
1:
1-ã. &.
2: T" ara min Iiai
#
2: arg min Iva.
3: Sample & Uniform(1, ....., )
3: Sumple N(0.
4: =0
D(mo s(t)), D(v. s(t)) # Sec.
Fr vori 2/ + or
5:
Rg = =/²
#1 Eq.
5: for
6:
a Jar-i 10 (1 ((r n +VI ac-ie
6: Sample = ~ N(0, (0, 1)
7:
= (1- ( / n R2
#i-1
vi-a 10 is. z3" + vT===
#t
8:
4/-1 vin 2: Varliaad ( 2...))))) V/.
8:
V1, log p(x (1)
x, )
po (1) Oz
9:
# timee ((((2..7 2 ,0, 02))
BBg
9:
Z z
Vz, log p(z
jord
10:
Take grudient step on
10:
end for
11:
re|l=" =f" oll" v. 10111=- psl 2/
#5e F3
11:
(+) रiーor 7 (())
12:
untill convergence
(g(#
Input
ShadowFormer
FusionNet
ShadowRefiner
Ours
GT
Figure 3: Visual comparisons on the ISTD datasets. Qualitative comparison of shadow removal results on the ISTD dataset using different restoration methods.
approximation to the DPS gradient in the latent space, which is subtracted from 2/_ to produce the corrected state z that better follows the desired posterior trajectory while respecting degrada- tion constraint. At t
the restored image Do is reconstructed from 21 through the residual-baie -based reverse transform, with an additional correction term from μ4g, In this way, DRM controls the spatial scale for robust structure modeling, while DPSC suppresses trajectory inconsistency and structural bias along the entire sampling path.
EXPERIMENTS
4.1 EXPERIMENT SETUP
We conduct experiments on the same benchmarks, including the ISTD dataset (Wang et al. 2018), several dehazing datasets (O-Haze Ancuti et al. (2018), HazyDet Feng et al. (2024), and RE- VIDE Zhang et al. (202T)). and our newly constructed FaceShadow dataset. The detailed con- struction procedure and implementation details of the FaceShadow dataset are further presented in Appendix A.3.3 Detailed descriptions of the datasets, evaluation protocols, and experimental se- tups-including training hyperparameters and inference strategies-art provided in Appendix (A.5 Since different methods involve distinct model architectures and parameter settings, we adopt their publicly recommended configurations for both training and inference, and perform all evaluations on a single 1100 GPU for consistency.
We build upon the RDDM (Liu et al. 2024) architecture to train the residual diffusion model, and in- troduce an additional branch for posterior refinement. Appendix(A.oe Dopendix/A.6.pproovides provides ablation analysis on how different architectural choices affect residual modeling and posterior adjustment performance.

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Input
ConviR
DeHamer
Ours
GT
Figure 4: Visual comparisons the HazyDet datasets. Visual comparisons of dehazing results
produced by different methods on the HazyDet dataset.
Input
Zhang et al
DiFaReli
Resfusion
Shadow R
Ours
Figure 5: Visual comparisons on 1,000 real-world face shadow images from the FaceShadow test set.
Quantitative comparison of shadow removal methods at a resolution of 256 x 256 on the ISTD dataset. Methods are categorized based the use of shadow masks. "Mask-free" indicates that the model does not use explicit shadow masks during training or inference (Dong et al. 2024). Violet
Table 1:
highlights the best-perfeee best-performing method among mask-free approaches, while blue indicates the best among methods using masks. The best and second-best results are marked bold and underline, respectively.
Methods
Mask-free
PSNR
SSIM t
MAE
LPIPS
Input Image
20.33
0.877
11.35
0.198
DHAN Cun et al. 2020
No
26,86
0.919
6.29
0.105
FusionNet (Fu 2021
No
25.88
0.715
5.88
0.112
ShadowFormer (uo et al.
2023a
No
30.47
0.928
5.34
0.075
Resfusion Shi 2024
No
30.09
0.932
4.79
0.068
DCShadowNNt Jin et al.
2021
Yes
24.02
0.677
5.88
0.125
ShadowRefiner [Dogg al.
2024
Yes
28.75
0.916
5.48
0.080
Refusion [Luo et al. 2023
Yes
25.13
0.871
5.63
0.109
LearnIR (Orr)
Yes
29.57
0.927
5.12
0.072
8

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Table 2:
Quantitative comparison of various dehazing methods fixed resolution of 512 512 pixels. For evaluation, three widely used benchmark datasets are employed: O-Haze, HazyDet, and REVIDE. In the results table, the best and second-best scores are highlighted in bold and underline. respectively.
Methods
O-HAZE
Ancuti et aal.222111
2018
HagyDet (Fng et al. 2024
REVIDE
Zhany al. 2021
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
Input Image
13.38
0.520
0.355
15.98
0.553
0.310
16.52
0.601
0.280
FFA-Net QQn et al 1020
22.12
0.770
0.150
23.11
0.726
0.145
22.80
0.735
0.160
GrälDehazeNel
2019
MSBDN Dong a. 2120
24.36
0.749
0.130
24.77
0.712
0.135
24.50
0.720
0.140
DcHamer
25.11
25.39
25.15
ConviR Cur et al. 2029
25.36
0.780
0.108
25.67
0.781
0.102
25.05
0.755
0.105
Resfusion eta 2024
24.25
0.710
0,145
24.13
0.701
0.155
24.00
0.705
0.165
M8-TayloFFormte Ufi 2025
25.43
0.105
24.97
0.755
0.120
25.25
0.775
0,118
LearalR (Ours)
27.70
0.832
0.055
27.32
0.905
0.065
25.43
0.795
0.085
4.2
QUANTITATIVE RESULTS
ISTD Dataset. We compare our approach against DHAN (Cun et al. 2020). FusionNet (Fu et al, ShadowFormer (Guo al. 2023a). Resfusion (Shi al.) 2024). DCShadowNet (Jin al.
202
1021
ShadowRefiner (Dong et al. 2024). and Refusion (Luo et al. (202)). As shown in Tab, our
method outperforms mask-free approaches, with PSNR gain of 0.82 dB, SSIM improvement of 0,011, and MAE reduction of 0.36, while remaining competitive with mask-based models.
FaceShadow Dataset. We benchmark against Zhang al. (2020), DiFaReli (Ponglertnapakor
itt al. 2023), Resfusion (Shi et al., 2024). and ShadowRefiner (Dong et al. 2024). Due to space limitations, some quantitative results are moved to Appendix A.5.4 Tab. 5 shows that our method achieves the best PSNR, SSIM, and LPIPS, with gains of 2.44 dB, 0.073, and 0.013 respectively, highlighting effectiveness under complex facial shadow conditions.
Dehazing Datasets.
We compare against several representative dehazing approaches, including
FFA-Net QQn et al. 2020). GridDehazeNet (Liu et al., 2019). MSBDN (Dong et al. (020), De-
Hamer (Guo et al. 2022). ConvIR (Cui et al.) 2024), and MB- Fayoroorrrrrmmer V2 (Jin et al. 2025))
As shown Tab. 2 our method consistently outperforms these otate-of-the-arr models across all
three widely used benchmarks-O-HlAA
HazyDet, and REVIDE.
Specifically, our approach achieves significant performance gains of +2.27 dB PSNR and +0.04 SSIM on O-HAZE, and +1.65 dB PSNR and +0.1 124 SSIM on HazyDet, demonstrating its robustness in real-world hazy scenes. Furthermore, on the REVIDE dataset, our method also obtains superior restoration quality with clear improvements in PSNR, SSIM, and LPIPS, confirming its effectiveness on challenging real-world hazy images.
4.3 QUALITATIVE COMPARISONS
Fig. 3 and 5 show qualitative comparisons on the ISTD dataset, the Dehazing datasets, and the FaceShadow dataset. Our results are consistently closer the ground truth in both color fidelity and structural detail, removing shadows and haze without introducing artifacts or color shifts. Com- pared with other methods, our pixel-space diffusion formulation better preserves high- gighffreuuncc details and suppresses boundary artifacts, while maintaining realistic textures and color saturation across diverse scenes. For challenging facial images under complex lighting, our approach further demonstrates stronger structure-preserving capabilities. Additional real-world results are provided Appendix A.5.7
4.4 ABLATION STUDY
We conduct ablation experiments on the FaceShadow test dataset. Additional results are included in the appendix A.6 for for
completeness, further validating our method.

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Table 3: Ablation study results under different model configurations.
Configurations
PSNR t
SSIM
LPIPS $
w/o DPSC
24.12
0.899
0.072
w/o DRM
27.25
0.925
0.063
w/o DRM & DPSC
22.86
0.865
0.103
Full Model
28.52
0.965
0.058
w/o DPSC DRM
Input
w/o DPSC
w/o DRM
Full Model
GT
Figure 6: Ablation Studies. Visual comparisons the FaceShadow dataset under different setups.
4.4.1 MODULE-WID WISE ABLATION STUDY
Dynamic Resolution Module (DRM). To evaluate the contribution of the proposed dynamic res- olution module, we first remove it and examine its impact on overall performance. As reported in Tab. removing this module results in performance degradation, including notable drop of 5.66 dB in PSNR, 0.10 in SSIM, and a 0.045 increase in LPIPS. Visual results in Fig, @ooofiim that omit- ting this component yields inferior reconstructions compared the full model. Nevertheless, this module allows multi-scale image resizing during training, significantly accelerating convergence. These findings emphasize the importance of MSD in achieving high-quality image restoration.
Diffusion Posterior Sampling Correction (DPSC), From the results in Tab. we observe that removing the DPS module significantly hurts 0.066 in SSIM, and an increase of 0.045 in LPIPS. Visual comparisons in Fig- c further highlight the degradation. Specifically, in the second and third columns of the first row, models without DPS introduce prominent artifacts, suggesting that dynamic offset alone is insufficient. Moreover, using only the diffusion model without DPS leads to residual artifacts that persist in the final result. Our full model yields the cleanest and most faithful reconstructions. These results underscore the critical role of the proposed DPS module in enhancing both visual and perceptual quality.
cottmaance-cuusinng a drop of 5.66 dB in PSNR,
CONCLUSION
In this paper, we propose prructure-preserviin consistency offset module designed to enhance the quality of image restoration. Specifically, we first provide a theoretical reformulation of the posterior distribution involved
denoising process during training. This addresses the issue of distribu- tional shift at inference when no explicit reverse process is available. By fitting the inferred poste- rior distribution during sampling, our approach effectively approximates the real image distribution, thereby improving structural consistency and visual fidelity of the restored outputs. Additionally, we introduce a dynamic resolution module that adaptively adjusts image resolution during training, enabling the model capture distributional characteristics in the pixel space from multiple scales. This mechanism not only accelerates training but also enhances structural representation and fine- various image restoration
grained detail preservation in the outputs. Extensive experiments tasks demonstrate that our proposed consistency-driver offset mechanism significantly outperforms existing methods in terms of both structural consistency and perceptual quality.
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6 REPRODUCIBILITY STATEMENT
We are committed to the reproducibility of our theoretical and empirical results. All theoretical claims made in this paper are accompanied by detailed derivations and proofs, which can found in Appendix AA.1 We clearly state all assumptions required for our theorems in Section 2 and Our proposed algorithm is formally described with comprehensive pseudocode in Algorithm | and of the main paper. Furthermore, complete description of the experimental setup, including all model hyperparameters, data processing procedures, and evaluation protocols, is available in Ap- pendix AA.3 We believe this provides sufficient information for independent re-implementation of our work.
ACKNOWLEDGEMENTS
This work was supported in part by the Guangxi Natural Science Foundation (2024GXNS- FAA010493), the Guangxi Key Research and Development Program (JB2504240003), the Shang- hai Municipal Commission of Economy and Informatization (2024-ZZL-GGZN-00000 the Na- tional Natural Science Foundation of China (52262047, 61862015), and the Science and Technology Project of Guangxi (AD23023002, AD21220114).
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A APPENDIX
A.1 RELATED WORK IN IMAGE RESTORATION
Previous image restoration methods can be broadly categorized into two paradigms: inversion-based methods and conditional diffusion-based methods.
Inversion-based Methods. Several works (Delbracio & Milantar 2023 Li et al. 2025 Wu et al,, 2024) enhance diffusion- image restoration by embedding inversion mechanisms into the gen- erative process, effectively bridging the gap between degraded observations and diffusion priors. To improve alignment between intermediate latents and measurements, recent methods (Shi et al.) Liu et al. 2024 Shang et al.) 2024) incorporate residual priors, which mitigate error accu- mulation and boost reconstruction quality. Moreover, efficient inversion-based solvers (Zirvi et al.) 2024 Wang et al. 2025a) have been proposed to enable real-time adaptation in blind restoration. For instance, (Chihaoui et al. (2024) optimizes the initial noise input while preserving the sampling trajectory, and accelerates inversion via large time-step skipping. Similarly, Wu et al. (2024) enforce measurement consistency at each step and leverage oignal-guided initialization for improved quality with negligible computational overhead.
2024
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Conditional diffusion-based Methods. Conditional diffusion models have significantly advanced image restoration by incorporating degradation-awe awaree priors, offering more controllable and accu- rate generation than their unconditional counterparts. Early works such [Meng al. 2022 and (Saharia et al. 2022) adopt supervised conditional frameworks, where degraded images are intro- duced either direct inputs
intermediate guidance during sampling. Building this idea, Plug-and-Play approaches, including (Kawar et al.) (022). (Zhu et al., (023). and (Chung et al. 2023), decouple training and inference by guiding pretrained unconditional priors with degraded observations, without altering the backbone network. To further improve efficiency and generaliza- tion, unified conditional modeling frameworks have emerged. For example, (Zhang et al. 2023), (Mei et al. 2024), and (Rajagopalan et al., 2025) incorporate encoded degradation features into diffusion process, with GenDeg further synthesizing diverse corruptions to enhance robustness against unknown degradations. In addition, several task-specific architectures have been developed to target distinct degradation types: Yue et al. (2025) jointly models atmospheric scattering and degradation masks for accurate dehazing. Luo al. (2023) employs dual-domain Transformer to address both low-light and blur conditions, and Ye et al. (0244) enhances figh-freuuecc details via learned texture priors.
A.2 USE OF LARGE LANGUAGE MODELS (LLMS)
In the preparation of this manuscript, Large Language Models (LLMs) were utilized as an auxil- iary tool for language refinement and stylistic improvement. Specifically, these models assisted in enhancing clarity, grammar, coherence, and conciseness across various sections of the paper. This application of LLMs was strictly limited editorial support-such rephrasing sentences, iden- tifying grammatical errors, and suggesting more academic phrasing and did not involve content generation, conceptual development, or the formulation of scientific arguments. The authors main- tained full intellectual control over the scientific content and conclusions presented herein.
A.3 PROOF FOLLOWING RESFUSION
For Eq. 15 Resfusion (Shi et al. 2024) introduces the residual term and identifies an optimal sampling step 7" that minimizes information loss. This step corresponds to the point where v is closest to :
T T' arg min 1=1
1 2
0:
(22)
At this step, ær can be approximately represented in two equivalent forms:
2T 2 (1- (L-V D* + vI QT
Var (3 vI aT
(23)
Here, ~~ (0, I) denotes standard Gaussian noise, and y is the input to the model. These ap- proximations suggest that at the specific step 7", the intermediate variable 2T preserves both the structural content of y and stochastic perturbations, making it a high-fidelity intermediate represen- tation.
A.4 STRUCTURAL BIAS IN RESIDUAL-GUIDEL DIFFUSION MODELS
In essidual-guided diffusion models, the forward process is reformulated as:
3 Va # + (1 vaz) R + v1 04 6,
(24)
where zy is the ground truth, R = 2. Eo is the degradation residual, and e ~ N/ Z) is Gaussian
noise.
The model jointly predicts residual and noise components,
(xr, 1) + Ro (a !),
9
leading to the total training loss:
Lisal Emp.e.t (21, t) ccl2 + Al| (ax,,)) R|
(25)
Since R and generally correlated (Cov ( E) * 0), their estimation interferes with each other.
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Proposition 1 (Mutual Estimation Interference). Let æ, AR Be with A 11 Vaa. B vI au and assume R, are correlated. Then no estimator 0 can simultaneously minimize
E|| Rozz)) - R + ((]léa(x:)) - =
without interference from cross terms induced by Cov R, E) #
Implication. Noise and residual jointly determine the perturbation direction of their estima- tions inherently compete. Reducing error in one component necessarily increases error in the other, leading to fundamental trade-off.
A.5 EXPERIMENTAL DETAILS AND DATASETS
A.5.1 EXPERIMENTAL DETAILS
We use the peak signal-to-noise ratio (PSNR), structural similarity (SSIM, (Wang al. 2004 ) learned perceptual image patch similarity (LPIPS, (Zhang et al. 2018)), and mean absolute error (MAE) as quantitative metries. The batch size, image resolution, and training epochs for each task are summarized in Tab. 4
Table 4: Experimental settings for our LearnIR during the training stage
Shadow Removal
Haze Removal
Super-Resohue Resolution
Tasks
ISTD
FaceSw
O-HAZE
HazyDet
REVIDE
DIV2K
Batch size
32
16
16
16
16
16
Image/patch size
256
512
512
512
512
1024
Sampling steps
5
5
5
5
5
Learning rale
le-4
le-4
le-4
le-4
le-4
lc-4
Training epochs
5k
5k
5k
5k
5k
5k
A.5.2 TRAINING DETAILS
We adopt two-stage training strategy for LearnIR. In Stage 1, we train LearnIR at fixed input resolution, with the Dynamic Resolution Module (DRM) disabled, so that the model first focuses on learning the gradient correction term for Diffusion Posterior Sampling Correction (DPSC). In Stage 2, we fine-tune the same model with DRM enabled under dynamic resolutions using smaller learning rate, allowing LearnIR quickly adapt various image resolutions while preserving the DPSC behavior learned in Stage 1.
A.5.3 DATASETS
ISTD Dataset. The ISTD (Wang et al. 2018) is a widely used benchmark for shadow removal. consists of triplets of shadow images, corresponding shadow masks, and ground-trute truth shadow-fres images. The dataset includes 1,330 triplets for training and 540 triplets for quantitative evaluation.
In real-world applications, shadow images typically lack corresponding annotated masks, and man- ually creating high-quality masks is expensive and hard to scale. Our proposed consistency offset mechanism effectively leverage information from pretrained data to enable high-quality shadow removal without requiring shadow masks during inference.
Dehazing datasets. O-Haze (Ancuti et al., 2018) is the first outdoor haze dataset consisting of 45 pairs of hazy and corresponding haze-free images, collected across diverse outdoor scenes. The hazy images are captured under real atmospheric conditions using professional haze machines, en- suring photorealistic haze simulation. Importantly, both hazy and clear images are taken under identical illumination settings in controlled environments. HazyDet (Feng et al.) 2024) a large- scale dataset containing over 383,000 real-world instances, constructed from synthetic hazy images generated using the Atmospheric Scattering Model (ASM). The hazy variants are derived from clear- weather UAV images, making the dataset suitable for evaluating real-world dehazing performance. REVIDE (Zhang et al,, 2021) is a worl-world video dehazing dataset constructed from diverse out- door scenes with naturally captured haze conditions. It provides paired hazy and haze-free video
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Figure Synthetic Face Shadow Dataset Samples from our synthesized FaceShadow dataset, which includes diverse identities and scene conditions with realistic facial shadows.
sequences, enabling frame-level supervision for evaluating dehazing performance under dynamic illumination, motion, and atmospheric variations. The dataset contains high-quality annotations and consistent temporal correspondence, making a valuable benchmark for assessing both image- and video-level dehazing robustness.
FaceShadow Dataset. In real-world scenarios, facial images are often affected by various lighting conditions, particularly shadows. These interferences not only degrade the accuracy of computer vision tasks such as face recognition and expression analysis but also impose greater challenges on the generalization ability of related models. However, existing public face datasets contain extremely limited paired data with explicit shadow and shadow-free correspondences, making difficult to obtain accurate one-to-one real-world samples. Therefore, to better study and advance the task of face shadow removal, it essential to construct large-scale, high-quality, and paired synthetic face shadow dataset. To this end, we build upon the face shadow synthesis method proposed by (Zhang et al. 2020) to construct a novel dataset FaceShadow which contains 30,000 image pairs. Each pair consists of shadowed facial image and its corresponding shadow-free version. The dataset features rich diversity across different ages, genders, and scene conditions, as illustrated in Fig. 7 The 30,000 synthetic pairs are split into 29,000 pairs for training and 1,000 pairs for quantitative evaluation on the validation set. Furthermore, to thoroughly evaluate the generalization of our proposed method in real-world applications, introduce an additional 1,000 pairs of real face shadow images collected from the Internet to serve as the test set for fine-tuning and real-world application testing.
DIV2K Dataset Evaluation. The DIV2K (Agustsson & Timofte 2017) (Diverse 2K resolution images for image super-resolution) critical benchmark in the SR field. consisting of 1000 high- resolution (2K) diverse images, commonly used for training and comprehensive testing of modern SR models. Due its size and image complexity, performance on DIV2K is often considered the definitive measure of a model's robustness and generalization ability.
A.5.4 ADDITIONAL EXPERIMENTAL RESULTS
For completeness, provide additional quantitative comparisons in terms of PSNR, SSIM, and MAE on the FaceShadow datasets. These detailed results are presented Tabs. 5 due to space limitations in the main text.
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Quantitative comparison of face shadow removal methods under 512 512 resolution. Two datasets are used for evaluation: the synthetic FaceShadow dataset and real-world test set. The best and second-best results are highlighted in bold and underline, respectively.
Table 5:
Synthetic Dataset
Real Dataset
Methods
PSNR t
SSIM
LPIPS
PSNR 1
SSIM
Input Image
16.28
0.823
0.159
17.12
0.825
Zhang et al. (hhang et al. 2020
25.18
0.876
0.062
24.32
0.865
DiFaReli (Pongiertnanakoil
et al. 2023
26.43
0.897
0.073
25.48
0.872
Resfusion Shi al. 2024
24.45
0.876
0.072
26.22
0.886
LearnIR (Ours)
28.87
0.970
0.049
27.93
0.921
Figure 8: Real face shadow data Samples of real-world facial images with shadows, collected from the Internet. These images feature diverse identities and scene conditions, demonstrating realistic and challenging shadow patterns.
A.5.5 LIMITATIONS
Despite LearnIR's strong performance, it faces certain limitations. As shown in Fig. our model struggles to handle shadow regions with strong color casts (e.g., yellow or red-tinted shadows), often leading to residual artifacts that degrade visual quality. This highlights challenge in generalization under complex lighting conditions and points to a promising future direction toward improving the robustness and adaptability of the proposed method in diverse real-world scenarios. Furthermore, the restoration quality is limited by its reliance accurately learned gradient correction aligned with the true posterior.
A.5.6 EVALUATION ON FACESHADOW DATASET
For completeness, quantitative comparisons in terms of PSNR, SSIM, and MAE on the FaceShadow datasets are presented Table 5 due to space limitations the main text.
A.5.7 EXTENDED EVALUATION ON ADDITIONAL TEST DATA
Real-World Results. To evaluate the robustness of our face shadow removal model, we addition- ally collected a set of real-world facial images with shadows from the Internet. As illustrated in Fig. [ our model effectively removes facial shadows, demonstrating its practical applicability and generalization ability real-world conditions. However, as shown in Fig. | some challenging cases still remain.
A.6 ADDITIONAL ABLATION STUDIES
A.6.1 EFFECT OF DIFFUSION BACKBONES
As shown in Table 6 we compare three different diffusion backbones integrated with the same LeamlR (U-Net) module to evaluate their effectiveness in the residual prediction task. The results demonstrate that RDDM achieves the highest performance, with PSNR 28.87 and an SSIM of 0.970, significantly outperforming DDIM and DiT-B/8. This suggests that the residual-based design
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Input
Output
GT
Figure 9: (Failure Cases) When shadow regions exhibit strong color tints (e.g., yellow or green filters), the model's shadow removal ability degrades significantly, resulting in noticeable residual artifacts that compromise visual quality.
Table 6: Quantitative comparison of different diffusion models with LearnIR (U-Net).
Model
PSNR
SSIM
DiT-B/8 + LearnlR (U-Net)
23.23
0.858
DDIM LeariR (U-Net)
26.11
0.887
RDDM + LearnIR (U-Net)
28.87
0.970
of RDDM facilitates more accurate noise estimation and better alignment with the target distribution. In contrast, DiT-B/8, which leverages transformer-basse structure, shows relatively lower perfor- mance, likely due to its weaker spatial inductive bias in pixel-level generation tasks. These findings validate the choice of RDDM more suitable backbone for residual-basee diffusion frameworks.
A.6.2 ABLATION STUDY THE VAE AND DYNAMIC RESOLUTION MODULES
We conduct experiments on the FaceShadow dataset to evaluate the contributions of the Dynamic Resolution Module (DRM) and different image encoding strategies. Specifically, fully fine- tune the 8x downsampling VAE from Stable Diffusion on all 30,000 face images. Our experiments demonstrate the clear advantages of the proposed Dynamic Resolution Module (DRM), which, com- bined with the DPSC backbone, forms our LearnIR approach. LearnIR significantly surpasses both the VAE baseline and the fixed-resolution setting terms of performance and efficiency during the inference process, as detailed in Table 7
Table 7: Impact of different image encoding strategies model performance and efficiency. For the VAE variants, the reported PSNR and SSIM are shown as fine-tuned / frozen. "DPSC + VAE" denotes the 8x downsampling VAE from Stable Diffusion fully fine-tuned all 30,000 ShceSwadow images, while "freeze VAE" refers to the same VAE with parameters kept frozen during training.
Variant
PSNRT
SSIM
Params (M)
Inference Time (s)
DRM (LearnIR)
28.78
0.970
139
0.276
VAE(ft) VAE(fr)
26.63 / 26.85
0.901 0.951
475
0.532
Fixed-Size
27.12
0.956
139
1.253
19

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Published as a conference paper at ICLR 2026
Table Inference-time computational cost for LearnIR components. We report the parameters, MACs, inference time, and GPU memory for the RDDM backbone, the DPSC gradient correction module, and the DRM dynamic-resolution interpolation. Notably, DRM uses non-learnable bilinear interpolation, resulting in MACs and memory so small that they are marked as "_" in the table.
Module
Params
MACS (G) x Steps L
Inference Time (8)
GPU Memory (GB)
RDDM
516.5M
1730.7 x 8653.5
0,217 5 1.085
9.8 GB
DRM
8.23 x 10 x = 4.15 10
DPSC
139.4M
233.6 1168.0
0,106 0.531
Full Model (LearnIR)
655.9M
1964.3 9821.5
0.323 1.616
12.2 GB
As shown in Table 7 integrating the Dynamic Resolution Module (DRM) with the DPSC backbone (LearnIR) yields clear benefits in both reconstruction quality and inference efficiency: LearnIR achieves 28.78 dB PSNR and 0.970 SSIM while reducing inference time to 0.276 s.
Notably, observe that fully fine-tuning the 8x Stable Diffusion VAE on the 30,000 FaceShadow images does not improve the DPSC baseline in our setting. Specifically, the DPSC + VAE (fully fine-tuned) variant attains 26.63 dB / 0.901 SSIM, whereas the DPSC VAE (frozen) counterpart achieves 26.85 dB 0.951 SSIM. This indicates that full eestuuninn-iithhoe additional regulariza- tion or careful hyperparameter tuning- can perturb the pretrained latent space and hurt reconstruc- tion quality (particularly SSIM).
Despite this, LearnR (DPSC + DRM) still outperforms both VAE variants and the fixed-resolution baseline, demonstrating that the DRM effectively compensates for encoding-leve differences and yields the best trade-off between quality and efficiency.
Table & provides overview of the inference-time computational costs for the components of the LeamlR method, including the RDDM backbone, the DPSC gradient correction module, and the DRM dynamic-resolution interpolation. Notably, the DRM uses non-learnable bilinear interpola- tion, resulting such minimal MACs and memory requirements that they are marked as "_" in the table. This table aids in understanding the resource consumption of each module during inference and the overall resource requirements of the LearnIR model.
A.7 FORWARD PROCESS OF THE SDE
We introduce the variable transformation in Eq. 26
2. -. + R xz
R
(26)
Taking the differential both sides of Eq. 26 yields:
dx; = dă.
(27)
Substituting Eq. 27 into the forward process of SDE gives:
3(1) 2 x + R) dl + v 3(1) dw
dā
(28)
Reverting back the original variable via wt xz R. the forward SDE with residual can be expressed as:
3(1) (x R)) dt / 3(t) dw
dx
(29)
We can rewrite Eq. 29 into a general form:
dx fx(xz) di ge dwy.
(30)
20

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Published as a conference paper at ICLR 2026
where fi(x) - (x R) and gr VB(t). This represents the standard form of forward stochastic differential equation.
To facilitate the derivation of the reverse process, interpret the continuous differential process in Eq. as the limit of its discrete approximation as At 0:
E4+AI = 2z + f((21) At Atc, e~ ((0,)
(31)
A.8 REVERSE PROCESS OF THE SDE
We reformulate the discrete approximation in Eq. 31
conditional probability:
p(1++ xi) N (Ii+iii De fo(x)) oe It
2t (t.
exp
(32)
2g At
Eq. 32 describes conditional probability distribution of the forward stochastic differential equa- tion (SDE). Based on this, use Bayes' rule to derive the conditional probability distribution of the reverse SDE, p(z; x(+Dt)::
p(x; x++1i) & p(2c+Ae xe) p(a))
p(x)+1()
x xx,) exp (log p(x.) - logp((x+4s)
| 24 (x. + log p(x;) - log p(
x exp
(33)
2g At
As shown in Eq. 33 when At is sufficiently small, the conditional probability p(æ++d1 xx) be- comes significantly non-zero only when is close to Tt+At, and vice versa. Therefore, we can approximate the reverse process by considering only the local behavior where æt and I+tdr are sufficiently close, for which a Taylor expansion is applicable.
á at
log poge( logp(x.) (I++S! xx) Va. logp(z:)) + At
log logp(a.))
(34)
It is important to emphasize that the term de p(x:) cannot be neglected. This is because the probability density function p(x;) describes the likelihood of the random variable taking the value æ at time i, which inherently depends both the temporal variable i and the spatial variable The quantity p())+Ar), contrast, corresponds to probability density at time At. Thus, when performing Taylor expansion of p(x;), the partial derivative with respect to time must be explicitly considered. Substituting Eq. Eq.344iin into Eq. 333 yields:
Bi+ - E. [fe(x,) V.a, logn( All +O(AB)
p(æ,
x44 exp
(35)
2g Al
As At + 0, the higher-order term O(At) becomes negligible and can be omitted.
11tttr Ft [f(( V.. æ. log p(gp(x;)) At lel
p(a, (14 x exp
2
[ - Zitat + (f++
22: Vnuae log (ogp(z Atl
exp
2g, A.
(36)
21

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Published as a conference paper at ICLR 2026
Therefore, in the limit as At 0, the conditional distribution p(æ, a++ai) approximates Gaussian with mean
Tc At (f++)(())+))) - git [ogp( At
and covariance of At ALL. We can thus rewrite this as Eq. 37
F:+ (a++ - Ri+1 V mi log logp(ar+ar) At It
(37)
We can further rewrite Eq. 37 in differential form to obtain the reverse-time SDE:
dæ [fe(ar) V. log dt + dw
(38)
reverse-time SDE: (x R) and 9t BBt), we arrive at the final expression for the
Substituting fi(
((C)
B(t)
2 (x R) B(t)V logp((zz) dt + BB(t) dw
dæ
(39)
A.9 DERIVATION OF THE OBJECTIVE FUNCTION IN SCORE MATCHING MODELS
We start from the reverse-tin time stochastic differential equation (SDE), as shown Eq. 39 and dis- cretize it to perform iterative generation, leading to the following form:
2t Zt+ [(++)( Si+ Vay, logp(æ:+4r) - - V.A. N~,
(40)
which forms the basis of the generative process in diffusion models.
The main challenge lies in obtaining the term V Pr(),, i.e., the gradient of the marginal distri- bution at time t. To this end, we utilize the analytical form of p(x; zo) to estimate p(x,) indirectly, leading to the following identity:
Vn, log p(x:) = Bxt-~((a) (an, log p(æ; ao) w(xo)),
(41)
where w(wu) is weight proportional to p(æ, xt).
To avoid the computational cost of taking expectations over all training samples æp, we introduce neural network (x,, t) to approximate the above gradient. Accordingly, define the following least-squares loss:
(( E.g.m. mo) [1),) t) Vz, log xx)
(42)
Minimizing this loss ensures that the network output converges the true reverse-time gradient of the diffusion process, enabling effective modeling of the generative path.
A. DETAILED DERIVATION OF SOLVING INVERSE PROBLEMS IN DIFFUSION MODELS
In the reverse-time process stochastic differential equations (SDEs), we can introduce an inverse problem of the following form:
B(t) [z, R) dt - 3(t) Va. (x; y) dt / (B(t) dw..
dx;
(43)
where R denotes the residual term and w, is standard Wiener process.
According Bayes' rule, the posterior distribution can be obtained by combining the prior p(æ) and the observation likelihood p(y x):
p(æ y) p(y x)) p(x)
(44)
ply)
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Published as a conference paper at ICLR 2026
which allows for inference of the unknown variable conditioned on the observation y. Based on this, the gradient term in Eq. 43 can be rewritten as:
n. log (at y) Va px + Va, log m4).
(45)
Substituting Eq. 45
into Eq. 43 yields:
8(t)
(x. R. dt B(t) (Vo, logpe( + Vx, logpi(y az)) dt
dæ.
2
(46)
+ B(t) dwr.
This decomposition explicitly separates the prior score Ve, lo from the data-consisteney score Vz. log xt), which the basis of diffusion posterior sampling.
A.11 DETAILED DERIVATION DIFFUSION POSTERIOR SAMPLING CORRECTION
We begin by writing the forward update in the residual-guider diffusion process
forward a 20 + ( R. + /1 a,-1 E,
(47)
where R. 2/ 0 and E ~ I),
On the other hand, the reverse prediction from the residual model is
1 az
Üt (it-1)( () - ass
pred
2t Vo((1 āt)
68
res (zt:
(1)
.))
+
6,
(48)
V Voi
which corresponds to the parameterization in Definition 2
To compare these two formulations, we express 2 forward process (cf. [2. and substitute it into Eq. 47 an explicit expression of the offset
(t) with the standard reparameterizztioo of the
After straightforward algebra, we obtain
forward
1
0
2,
21
2t
a2
Va
(1
v/l-11)
211
at
c/ (2,, 211)
(49)
Var(l - ae)
+ ã (1 an)
(2/a.-1 1)(1 - ax)
V ā.-1
e.
av. (ic)
Since E Gaussian and all the other terms are deterministic functions of (z,, (1) 1). the offset follows Gaussian distribution
pred
2
forward
*N
(50)
where the mean and variance are given by
ul 200, Var
1
2 11
-1-
vā (1)
2
(21, x00,)) .t,
Vā:
V Var(1 -ar)
(51)
(z), 2)) (1100)))00
2
((--or-)(( oz)
(2 01-
- 1) ar)
(52)
āi
v a. kc)
This shows that the offset between forward and predicted updates can be modeled as Gaussian correction term, which forms the basis of our diffusion posterior sampling correction.
23


Reviews:
[{"review_id": "OtHLixn4yB", "reviewer": "Reviewer_Y9b8", "summary": "This paper proposes LearnIR, a diffusion-based framework for real-world image restoration that eliminates the need for a known degradation forward operator—a long-standing bottleneck in diffusion posterior sampling (DPS) methods. The key innovation lies in Diffusion Posterior Sampling Correction (DPSC), which introduces a learnable model to predict the gradient correction distribution that replaces the explicit operator used in DPS. This approach allows posterior refinement without requiring analytical knowledge of the forward degradation process. In addition, the authors introduce a Dynamic Resolution Module (DRM) that adaptively adjusts image resolution during training to balance global structure preservation and fine detail generation while avoiding dependence on a pretrained VAE.\n\nThe method achieves state-of-the-art results on multiple benchmarks, including ISTD, O-HAZE, HazyDet, and a new FaceShadow dataset introduced by the authors. Quantitatively, LearnIR surpasses recent methods such as ResFusion, ShadowRefiner, and ConvIR in both PSNR and SSIM while maintaining efficiency and generalization to complex real-world degradations", "questions": "See weakness.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 4, "strengths": "1. The proposed method bypasses the requirement for a known degradation operator in previous works, enabling the application of DPS-related methods in blind restoration tasks. I think this is an important contribution to the research field.\n2. The method outperforms recent state-of-the-art methods with a large margin, including ISTD, O-HAZE, HazyDet, and a new FaceShadow dataset.", "weaknesses": "In summary, this is a very sound and impressive work, but with poor presentation. I'm happy to increase my rating based on the writing. \n\nMy main concern lies in the presentation and organization of the paper. While the technical contributions appear sound and potentially impactful, the paper is dense with mathematical formulations, and several notations are either inconsistent or insufficiently explained. These issues make the paper difficult to follow, especially for readers who are not deeply familiar with the DPS-related research line.\n\n1. In Section 3.1, the notation $z_t$ is introduced abruptly without prior explanation. Its definition only appears later in Section 3.2, which disrupts the logical flow and makes it challenging for readers to grasp the progression of ideas. Similarly, the notation $\\hat{x}_)$ in Eq. (4) also lacks explanation. I suggest re-checking the presentation so that all key notations are properly introduced before use and accompanied by clear definitions.\n\n2. Theorem 1 claims that Eq. (3) can be expressed as Eq. (16). However, these two equations seem unrelated or at least not directly derivable from one another as currently written. The authors should carefully verify this connection and, if necessary, correct or clarify the statement and its derivation.\n\n3. In step 4 of Algorithm 1, the operator $𝐷^s$ takes $x_0$, $y_0$, and $x^{s-1}$ as inputs, while in other steps (e.g., step 5), it appears to only take $y$ as input. This inconsistency is confusing and suggests either a typographical error or an incomplete explanation of $D^s$'s input structure. A clearer, self-consistent description of the algorithmic steps is required.\n\nOverall, this is a technically solid and promising piece of work with interesting ideas. However, the presentation quality needs significant improvement. The current version suffers from poor organization and inconsistent notation, which hinders readability and comprehension. I would be happy to raise my rating if the authors substantially improve the clarity, consistency, and accessibility of the writing in the revision.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "bdED5d5nHx", "reviewer": "Reviewer_ZY1D", "summary": "The paper proposes LearnIR, which uses a diffusion posterior sampling correction approach to enable robust real-world image restoration. The proposed approach overcomes the limitation of methods such as DPS which require the explicit modeling of the forward degradation operator. Additionally, LearnIR uses a dynamic resolution module instead of a VAE which allows faster restoration with better performance.", "questions": "1. The proposed DRM module is compared with the frozen SD VAE in Sec. A6.2. However, was the SD VAE frozen and paired with the RDDM model for this experiment? The experiment which needs to be performed would be using the RDDM model with the SD VAE being fine-tuned, as the DRM is trained in LearnIR.\n2. In Sec. A6.1, was the DRM also trained with the DiT and DDIM backbones?\n3. For the comparisons, were all methods trained on the same datasets as LearnIR?\n4. While the authors show results on real-world data, the datasets were used for training LearnIR. To further validate generalization, can the authors provide experiments on other real-world haze datasets (such as [1])?\n5. The core approach involves learning to predict score of $p(y|x_t)$. However, this is intractable for real-world degradations and is approximated for learning (Line 144). Could this be considered a limitation of the method and be included as part of limitations?\n6. Experiments comparing computation complexities of VAEs and DRM need to be added to substantiate claims in Line 93.\n\n[1] Zhang, Xinyi, et al. \"Learning to restore hazy video: A new real-world dataset and a new method.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2021.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 4, "contribution": 3, "strengths": "1. The paper is well written and easy to follow.\n2. The proposed DPSC method is well designed, intuitive and effective.\n3. LearnIR achieves state-of-the-art performance on real-world datasets.", "weaknesses": "1. Lack of ablations regarding the effectiveness of the DRM module (see questions).\n2. Limited testing on out-of-domain real datasets to substantiate generalization claim (see questions).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "AzUHHv5HnO", "reviewer": "Reviewer_KzEc", "summary": "This paper proposes the LearnIR framework to address heterogeneous degradations in real-world image restoration, featuring a novel learnable diffusion posterior sampling mechanism. The method trains a lightweight model to directly predict the distribution of gradient correction terms, enabling diffusion posterior sampling correction without requiring a known forward operator. A dynamic resolution module dynamically adjusts image resolution during training, applying large-scale downscaling in early stages to preserve global structures and upscaling later to refine textures. Extensive experiments on multiple real-world datasets demonstrate significant improvements in PSNR and SSIM metrics, particularly in challenging facial shadow removal tasks.", "questions": "● Detailed illustrations need to be added for Sec. 3.3.\n● The authors are highly recommended to provide image results in supplementary material.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "● The learnable posterior sampling correction mechanism eliminates the dependency on a known forward operator, addressing a key limitation of diffusion models in real-world degradation scenarios.\n● The DRM effectively balances multi-scale feature extraction and computational efficiency while avoiding the need for a pretrained VAE.\n● Extensive validation on multiple real-world datasets, including a newly constructed FaceShadow dataset, provides convincing results.", "weaknesses": "● The proposed method introduces training complexity. Joint training of DPSC and DRM modules requires careful hyperparameter tuning. Also, dynamic resolution switching may introduce training instability, with convergence issues insufficiently addressed.\n● The major limitation of diffusion-based posterior sampling method is the scalability to real-world scenarios. However, most current experiments are conducted on synthetic degradation datasets, with the only real-world datasets available being limited to the facial domain. The authors are consider to extend the proposed method to more challenging scenarios such as real-world image super-resolution task and compare with the advanced methods.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hrTxCQDHfK", "reviewer": "Reviewer_m8gP", "summary": "The authors study diffusion-based image restoration, proposing a posterior sampling correction method. They also propose a dynamic resolution module that downsamples/upsamples the input during training, both improving the results and accelerating the training.\n\nThe proposed method is evaluated on the task of haze removal and shadow removal, across four different datasets.", "questions": "Questions/suggestions:\n- In the abstract and introduction you write \"our new FaceShadow dataset\" and \"our newly constructed FaceShadow dataset\", but then in Section 4.1 you write \"three standard datasets: ISTD, [...] and FaceShadow (Zhang et al., 2020)\"?\n- In Table 1 and 2, why results only in terms of PSNR and SSIM? Why not also LPIPS and/or FID?\n- In Section 4.2, ISTD results, it's not clear to me what it means for a method to be mask-free? Also, in the Table 1 caption, should violet and blue be swapped?\n- Line 238, \"Based on Definitions 1 and 2, Eq. 3 can be expressed\": Should this be Eq. 4?\n- Could be interesting to evaluate methods also in terms of computational cost during training / at test-time, at least to see the effect of the proposed DRM?\n- Which dataset are the images in Figure 5 from?\n- Line 260, \"As illustrated in Figure 2, the model...\": This is not illustrated in a lot of detail in Figure 2 though? Perhaps consider tweaking.\n\n\n\n\n\n\nMinor things:\n- I think Section 2 could be tweaked to improve the overall flow a bit.\n- Figure 4 caption: \"(Visual comparisons on the HazyDet datasets)\" --> \"Visual comparisons on the HazyDet datasets\"?\n- Line 96, \"Experimental results clearly and consistently demonstrate that LearnIR consistently outperform\":  \"consistently\" twice, perhaps reformulate.\n- Line 146, \"To obtain an form of the\": typo.\n- Figure 2 caption, \"The blue line in Eq. 3 denotes timestep T', computed using the\": I don't quite understand what you mean, what blue line?\n- Figure 3, \"ShadowForme\" --> \"ShadowFormer\"?\n- Figure 4, \"Dehamer\" --> \"DeHamer\"?\n- Line 322, \"Hazy\" --> \"HazyDet\"?\n- O-Haze is not mentioned at the beginning of Section 4.1? \n- Line 371, \"We benchmark against Zhang et al. (Zhang et al., 2020)\" --> \"We benchmark against (Zhang et al., 2020)\", perhaps?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper is quite well written, few typos or similar issues.\n- The two introduced components, DPSC and DRM, make sense overall and both seem to improve the performance (Table 3, Figure 6).\n- The proposed method seems to perform well overall compared to recent baselines.", "weaknesses": "- The proposed method could be presented/introduced better in Section 3. In particular, 3.1 would benefit from more commentary instead of just stacking definitions/theorems, the flow could be improved. The algorithms in 3.3 would also benefit from added descriptions/explanations.\n- The experimental evaluation could be more extensive/convincing. Only two different tasks. Results are compared with baselines mostly just in terms of PSNR and SSIM, lacking perceptual metrics. \n- The technical contribution/novelty seems somewhat limited, at least based on my understanding of the proposed approach.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)