Diffusion Priors for Variational Likelihood Estimation and Image Denoising
Authors: Jun Cheng
Shan Tan
Venue: NeurIPS 2024 spotlight (2024)
Keywords: real-world denoising
image restoration
diffusion models
Primary area: machine_vision

Abstract: Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However, existing diffusion priors-based methods either consider simple noise types or rely on approximate posterior estimation, limiting their effectiveness in addressing structured and signal-dependent noise commonly found in real-world images. In this paper, we build upon diffusion priors and propose adaptive likelihood estimation and MAP inference during the reverse diffusion process to tackle real-world noise. We introduce an independent, non-identically distributed likelihood combined with the noise precision (inverse variance) prior and dynamically infer the precision posterior using variational Bayes during the generation process. Meanwhile, we rectify the estimated noise variance through local Gaussian convolution. The final denoised image is obtained by propagating intermediate MAP solutions that balance the updated likelihood and diffusion prior. Additionally, we explore the local diffusion prior inherent in low-resolution diffusion models, enabling direct handling of high-resolution noisy images. Extensive experiments and analyses on diverse real-world datasets demonstrate the effectiveness of our method. Code is available at https://github.com/HUST-Tan/DiffusionVI.

Diffusion Priors for Variational Likelihood Estimation and Image Denoising
Jun Cheng, Shan Tan'
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology cheng248hust. edu. en, shantan@hust. edu.
Abstract
Real-world noise removal is crucial low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However, existing diffusion priors-based methods either consider simple noise types rely ap- proximate posterior estimation, limiting their effectiveness in addressing structured and signal-dependent noise commonly found in real-world images. In this paper, we build upon diffusion priors and propose adaptive likelihood estimation and MAP inference during the reverse diffusion process tackle real-world noise. We introduce an independent, non-identically distributed likelihood combined with the noise precision (inverse variance) prior and dynamically infer the precision posterior using variational Bayes during the generation process. Meanwhile, we rectify the estimated noise variance through local Gaussian convolution. The fi- nal denoised image is obtained by propagating intermediate MAP solutions that balance the updated likelihood and diffusion prior. Additionally, we explore the local diffusion prior inherent in low-resolution diffusion models, enabling direct handling of high-resolution noisy images. Extensive experiments and analyses on diverse real-world datasets demonstrate the effectiveness of our method. Code is available at /htpp:://// : h/gitttuub com www.woooooo-eeee - TanaTaaanDiifionn
Introduction
Real-world imaging modalities, such as photography and biomedical imaging, frequently encounter complex image noise that is both signal-dependent and spatially correlated (3]. Removing such noise is critical for subsequent image analysis and understanding. Existing deep learning- based image denoising methods rely on either large amounts of paired images for supervised training [50 48
25.25) noisy images for self-supervised training [1 23
However, collecting massive amounts of data is expensive and time-consuming in real-world scenarios. Therefore, designing effective and data-efficient real-world denoising methods is of significant practical importance.
46 33]
Incorporating image priors and the likelihood, and conducting the corresponding posterior inference (e.g., maximum-a-posterioon (MAP) estimation and mean estimation), is classical and data-efficient approach to image restoration 26 18). Nowadays, deep generative models such as VAE, GAN, and Normalizing- fllow have shown the capacity capture and model complex image statistics, surpassing traditional analytical image priors [32]. Recent diffusion models have demonstrated state-of- thehharrt
image generation capabilities [14
37 and have been incorporated into various image restoration
tasks as powerful image priors 19
12 5
"Corresponding Author
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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The essence of applying diffusion priors to address image denoising lies in accurately integrating the degraded image into the generation process of pre-trained diffusion models, underscoring the importance of the likelihood function. Unlike Gaussian white noise, real-world image noise is intricate and challenging to model precisely and analytically [17 21]. Many existing methods based 10,, making them ineffective for real-world noise removal. On the other hand, some approaches targeting complex and non-linear degradations employ hard data-consistency strategies and approximate posterior inference during the generation process 12 45,8), 81. yielding unsatisfactory real-world denoising outcomes due to their coarse likelihood modeling. Although structured and heteroscedastic Gaussian likelihood function can well approximate real-world noise, such a model is computationally expensive due to the large covariance matrix and also impractical due to the unknown noise variance.
on diffusion priors solely account for i.i.d. Gaussian noise [19
To tackle these challenges, this paper integrates variational Bayes and presents adaptive likelihood estimation and MAP inference during the generation process of diffusion priors to handle real-worll noise. We introduce an independent, non-identically distributed (i.ni.d.) likelihood combined with precision prior to model real-world noise. Such a choice allows modeling the spatially variant feature of noise and meanwhile avoids modeling covariance, trading off the accuracy for practical feasibility. Based on variational Bayes, the i.ni.d. precision posterior at each step in the reverse process is subsequently inferred, which adaptively refines the likelihood function and aligns with the real-world noise model. Additionally, estimated noise variance, compensating for the lack of spatial correlation in the i.ni.d. likelihood function. By adaptively updating the likelihood at each reverse diffusion step, the final denoised result is achieved by progressively propagating the intermediate MAP solutions that strike the best balance between the noisy image and diffusion prior.
introduce local Gaussian convolution to rectify the
Furthermore, real-world images exhibit diverse resolutions, often differing from those of pre-trained diffusion models. Existing methods utilize patch-based [12] resize-based [19] operations, which are laborious and may impact low-level details. We observe that diffusion models pre-trained with low- resolution (LR) images tend to yield local diffusion priors effective for image restoration, enabling the direct treatment of nigh-resolution (HR) noisy images. The main contributions of this paper are summarized as follows:
We propose adaptive likelihood estimation and MAP inference based on diffusion priors and variational Bayes to address real-world complex noise.
We explore the local prior exhibited by diffusion models pre-trained with LR images.
Our method outperforms other unsurpervised denoising methods as well as diffusion priors- based methods on diverse real-world image denoising datasets.
2
Related Works
Deep Learning-based Image Denoising. By harnessing modern deep architectures and large-scale paired training datasets, supervised learning-based denoising methods such as VDN (48), Restormer 49 and GRL 2.5 have significantly enhanced in-distribution denoising performance. However, their reliance on extensive paired data poses challenges for real-world applications, prompting the exploration of sulf-super denoising approaches. These include Blind spot (BS)-based methods (e.g., SSDN [22], Noise2Self (3) Nei2Nei [66,, and B2U [4]), resampling-based methods (e.g.. (34) ) and regularization-basee
methods (e.g., Noise2Score 20) and Stein (38)). However, these methods assume spatially independent or analytical noise, which deviates from the structured and complex real-world noise. Recent advancements, such as AP-BSN [23] and LG-BPN (66, have integrated Pixel-shuffle and masked convolution into BS networks to address real-world noise. Other approaches have leveraged disentangled representation learning || [] Nonetheless, these methods often require large quantities of noisy images and lack data efficiency. Several single image-based deep learning methods (e.g.. DIP 42 I. Self2Self (36, ZS ZS- [27, and ScoreDVI (7)) have been proposed, but their performance in real-world denoising scenarios remains suboptimal, underscoring the need for more effective approaches.
Nr2N 29 and R2R
Diffusion Priors for Image Restoration. Diffusion models have exhibited remarkable image generation capabilities [4 40 37 and have been integrated into inverse problems as diffusion priors to address various image restoration tasks in an unsupervised manner [24]. Existing methods based
2

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on diffusion priors can be broadly categorized into two aspects: linear inverse problem-solving based on exact degradation models (e.g., DDRM [9]. DDNM 43 MCGDiff [5], and FPS
(TO). and nonlinear inverse problem-solving based on approximate posterior inference (e.g., DPS g GDP 45 ). In the former, these methods typically assume analytical noise, such as additive [2], and DR2
white Gaussian noise, overlooking real-world noise that is signal-dependent and spatially correlated.
Given the difficulty in precisely modeling and estimating real-world noise, these methods often prove ineffective in handling such noise.
In the latter, hard cata-consistency terms are introduced to replace accurate likelihood modeling, and approximate posterior inference is conducted during the inverse diffusion process to address complex degradations. However, due to the absence of explicit constraints from likelihood functions, these methods heavily rely on proper hyperparameters (e.g., guidance scales in GDP [12], step size in DPS 8 or downsampling factors DR2 45 leading significant reconstruction errors. Diverging from these methods, we refrain from specifying the accurate noise model but introduce the noise precision prior and dynamically estimate posterior using variational Bayes the reverse diffusion process, enabling adaptive estimation of likelihood functions and better posterior inference.
3 Methods
3.1 Preliminary
The Diffusion model is class of generative models used model the distribution ((2)). Its forward process is Markov chain with fixed Gaussian transition and length T, which gradually corrupts the data zo by adding Gaussian noise according a pre-defined variance schedule 7)1, ,
T II (( - (a v 96T-11
nice property of the forward process is that sample I, any step can be obtained from To in closed-form manner:
g(2,(an) = (zxi Siteivvae Va (1- I) + 24 = varzo + vI ā,e
(2)
where a, = 1 71, de IT. Cg N)O.
In the reverse process, the diffusion model progressively recovers data from noise distribution p(zr). which is again Markov chain with learned Gaussian transition:
p(Zur) p(xr)())))))))))
plt) -N(po
t=1
where of is constant relating to т) and can be pre-computed. And no (Jra, 1) is usually parameterized by DNN co(x,,t): t):
1 Vat
3e VI αq
(o( 1)
c0(
3.2 Naive Image Denoising
Consider the image formation process yo = [(x0; n) in the real-world scenario, where n is the raw noise, is the transformation function, y/ E and E RR (N is the total pixel number) are the observed noisy image and original clean image, respectively. Noise Yo generally exhibits signal-dependent and spatially correllly-correltted characteristics, e.g., sRGB noise 23]. due to the Poisson nature photons and compound transformation in f. Suppose there are no non-linear parts in f. the image formation process can be simplified as you = Zo + +n((a)) with corr(n) ng) > 0, where no is the image noise related to the signal Zn; corr(i.j) represents the correlation coefficient between two neighboring elements and j.
Real-world image denoising task is to recover clean and high-quality from noisy yo, which turns into solving the posterior p( (y)) Bayesian statistics. As the pre-trained diffusion model possesses superior image priors, it is natural to inject the observed information yo into its reverse diffusion
3

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(or generation) process defined in Eq. B to achieve the conditional inference of Zo:2 given yo. i... p(Zo:r(yo). Due that yo and intermediate I, exhibit large distribution gaps (as they have different noise types and strength) and it is also difficult to directly model p(yo]()) g we hence follow [39 45| and re-corrupt Yo using Eq. 2 each step to obtain yt, which serves as intermediate conditions. Such choice results in the target conditional distribution:
T p(ro.T/u0) - p(xT) II p(re- 11- & p(IT) II 1kooe-i t=1
т
(5)
where y/ = yā + /I - aee, and p(ar vr) = p(rr) as oT and yr are approximated independent
normal distributions.
Structured and heteroscedastic Gaussian likelihood model. The right-hand side of Eq. (5) explicitly involves the prior p(2;-1l04,) and likelihood p( at each step t. The prior ((z;- has been available from the pre-trained diffusion model in Eq. (3), necessitating the modeling of p()t-1/zt-1). As discussed above, in principle we can assume that yo follows the structured and heteroscedastic Gaussian distribution N (w {xx)), where is the non-diagonal covariance matrix with variances related to signal Tu, which allows modeling the signal-dependent and spatially properties of worl-world noise. As a result, we derive that
Mt-1 = V - (zo + Ac2) + v 0z- = It-1 v aa- AA" (ixo),, 62 ~ N(,11)
(6)
which indicates that p(y | detailed derivation in the Appendix A.1
M1 E(x+-1)) with Σ(x,-1) = σz d)-1E(ro). See
As the prior p(z,-1 (2;)) in Eq. 3 and likelihood p(y+- ( in Eq. (6) both have Gaussian forms, the posterior distribution in Eq. ( is theoretically computable. Nevertheless, we note that the above formulation presents several practical challenges. First, specifying an accurate E(ro) for Yo is difficult, which involves the estimation of noise variance and the noise correlation between neighboring pixels. These estimations are hard to achieve based on a single yo and are open research problems [17. In addition, the posterior inference with non- non-diagonal covariance matrix Σ is both memory- demanding and computationally expensive. These challenges prevent the direct application of the structured heteroscedastic Gaussian likelihood.
3.3 Variational Denoising with Adaptive Likelihood Estimation
To deal with these difficulties, we consider p(yo|=,) = AZ diag(do)) which has diagonal precision matrix diag((ón) (i.e., the inverse of the covariance matrix, Φ E TR. Such diagonal
Gaussian likelihood allows modeling the spatially variant feature of real-world noise but ignores the noise correlation at this stage. Based on Eq. (6). popppllla----.-- then becomes:
Φo
- 1 = (1 diag( az-1
Hyperprior for precision Φi. Instead of specifying an accurate do. which is again difficult, we introduce the independent Gamma hyperprior p(@p) = I Gamma(øh: a, B) for do (a and / are scalars), which serves the rough precision prior for noise in yo. Meanwhile, based on Eq. 77) it is straightforward that Φ follows
N II Ganma(@ with 0:-1 = ax B Baa-1
p(01-1)=
Because p():-1) merely provides initial gauss about the noise precision (also variance) each step f, we then expect to find the corresponding precision posterior p(ó--1/2;-1, Vt-1), which is more accurate and allows better likelihood function p(xt-1/2,-11 1). As posterior d,-1 depends on TT-1, we have to simuteniously infer them together, i.e., the following joint distribution:
p(r:-1. 11-1) p(y. 10:-110 ) + p((::))))(((x-1llll
p( (2))
where 7 S the temperature parameter, which typically utilized in variational inference to scale the likelihood function (2).

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Variational inference of precision posterior. As 11- Mt-1) ) in Eq. 9 is a non- trivial distribution, we hence choose a trivial and factorized variational distribution g(2 Φ.-1) ((#=-1)9(()1))) to approximate the true posterior p( dt-1 Lt. Mr--),, under the KI.-divergence distance. Following the mean-field variational Bayes presented in [4) the optimal
can be solved by eycling through π4-1 and Φt-1 and replacing each in turn with revised estimate of
g(x;-1) and g(or-1). Specifically, we derive the following alternate update scheme for finding the optimal g(
Update g(*-1)). Given g( the optimal g" (z)-1) provided by log.9" (x(-) = Es, 1ogp( poo
(10)
which corresponds to
g (xt--))= -
(11)
with mean / and variance 02- as
P-- of E Vt-1 + Mo( f) 06% diag E( +
fo?
(12)
E(ot-1)0 +
where @ denotes element-wise multiplication; E(0:-1) step T is initialized as constant (which is robust different initializations) and then updated as E( = / (see Update 2).
Update g(cr-1). Similar to ())+-1). the optimal ( given 1 is
N
g" (ox-1)
Gamma (i Il
(13)
1=1
with shape á and rate 3 as
2ل_1 = 27 1/-1= BB-1+ (vi ( 22 + +0?_11)
(14)
27
The detailed derivation of Eqs. and
(33) is given in the Appendix A.2
During the updates, â,-1 and B in ( are adptively updated and become signal-dependers verges, we can obtain the approximated posterior distribution g(or-1) and the updated likelihood I
MAP estimation with updated likelihood.
indicated by Eq. (14). Once the cycling con-
p(y--1/7 E Pel-v~le ~g(d,, ( 1 11-1) at step I. As result, by maximizing the condi-
tional distribution Eq. (5) at step I, the optimal x²_1 that balances the image prior and the observed
Ut-1 can be obtained as follows:
27-1 argmax Dogp(y-11 111=1) + logp(x--11a
= argmax E log p(p) 1 11-1) + log 1(
- argmax - -I-----a--1 1) (((rr-1)) (I1-1
140 (2 t))²
(15)
of
o
- + म, (1-1) t), with क. of
1/E(d.-1)
where E(Ø:-1) = / is the expectation of noise precision posterior (and hence 1/E(d:-1) =
8 is the estimated noise variance at step (), and म, E [0, 1] suggests that the optimal x;_ is the convex combination of yt-1 and μN [z( t). Note that, in the second row of Eq. (5). we utilize the following Jensen's 's Incquality
log bog((y-1(m = log Es, 1-9lo 11 21-1) 2 Es, E log log ae
(16)
and employ the lower bound of log ((). (.,1)) Optimizing this lower bound generally produces satisfactory solutions, like in variational inference, VAE, and diffusion models.
Rectification of /((r:1). By considering the diagonal Gaussian likelihood, the noise correlation between neighboring pixels in yo (and y:) is ignored, which affects the estimation of the precision
5

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Algorithm Difusion priors-based variational image denoising
Input: Pre-trained diffusion model, noisy observation yo, hyperparameters a, 8, temperature
1: 2T ~ ~N(00, () E(OT) =
2: to. do
3: Compute p t) based on Eq.
44: Compute yr-1 based on Eq.
4: Set p
0, pi-1 = (31, ()
5: while || R1-1l12 2 le do
6:
Update ( (
-, 1) using Eq.
7: Update g( = II Gamma 0 Bt_) using Eq. 14
8: end while
9: Solve optimal Tt-1 using Eq.
or Eq.
end for
11:
return 250
256x256 images sampled from 128x128 diffusion model
512x512 images sampled from 256x236 diffusion model
Figure 1: Unconditional HR images generation from LR diffusion models
posterior and noise variance 1/E(Φt-1). This is apparent as transformations in f (c.g.. demosaicking in the ISP pipeline) will cause the local correlation of noise variance (or precision) while elements in E( are updated independently as shown in Eq. [14). Motivated by the analysis of spatial correlation of real-world noise in [23], introduce local 2D convolution with normalized Gaussian kernel Gl,, s) (1 is kernel size and is the scale) to manually rectify 1/E(Ør-1). That is,
of
1/E(Ør-1) Con((1/((0)-)) G(1, s)), f-11 of + 1/B(or-1)
(17)
By progressively calculating = each step based on Eqs. 15 and
17 the final denoised result
Tp can be obtained. The whole denoising algorithm is presented in Alg.
Local Diffusion Priors
The common practice of sampling images from pre-trained diffusion models to maintain the sam- pling resolution identical to the training resolution, which produces the best generation performance. In image restoration tasks, however, the resolution of the observed noisy image generally mismatches that of the pre-trained diffusion model. Existing approaches typically use patches [12] or resize operations [99 to address this issue, which is cumbersome and may affect local details.
We observe that when a diffusion model trained with the U-Net architecture on low-resolution (LR) images is employed sample high-resolution (HR) images, exhibits local properties. Fig. D shows sampled 512 x 512 and 256 x 256 images from pre-trained 256 x 256 and 128 x 128 diffusion models, respectively, and it is clear that the generated textures mainly focus local areas. As HR
images contain more redundant information, denoising HR images is simpler than denoising their LR
counterparts under the same noise level [4]. When the LR diffusion model is used to generate HR samples, there is only short time window for it to decide the structures of the sampled images [15]. thus the generation tends be local. Similar traditional TV priors and Markov random fields that focus on designing local image statistics, we note that the local property of LR diffusion models is also effective for image denoising. This allows us directly adopt the pre-trained LR diffusion prior to denoise HR noisy images without additional operations.
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Table 1: Selection of and for different test datasets.
Datasets
SIDD
FMDD
CC
PolyU
Datasels
SIDD
FMDD
CC
PolyU
value
0.03
0,025
0.01
0.005
value
1.0
100
4 Experiments
4.1 Experimental settings
Datasets. We consider several real-world denoising datasets to evaluate our method, including SIDD [. PolyU 44), CC (30], and FMDD [SI] SIDD validation, PolyU and CC datasets contain natural sRGB images from smartphones or commercial camera brands, where SIDD consists of 1280 patches with size 3 x 256 x 256, PolyU and CC consist of 100 and natural images with size x 512 512, respectively. FMDD contains 48 fluorescence microscopy images with size 512 x 512.
Implementation Details. We utilize the 256 256 unconditional diffusion model @ provided by 9 as the diffusion prior throughout our main experiments, regardless of the resolution of input noisy images. The total diffusion steps are 1000 by default, i.e., E [1.... 1000]. We choose a 1 and Gaussian kernel size 1 = 9. The hyperparameters 3 and for different datasets are summarized in Table I Different a/3 represent the rough estimation of the prior precision for noises in different datasets, and Gaussian kernel scale controls the range of local spatial correlation. The temperature set to 1/5 for all datasets and will be ablated in the sequel. For SIDD dataset, the sizes of T0.7 are 3 x 256 x 256. For the remaining datasets, they are 3 x 512 512. The denoised results for FMDD are obtained by averaging the channel dimension of xo to get one-channel images. All experiments conducted on Nvidia 2080Ti GPU.
Compared methods. We consider several representative single image-based unsupervised denoising methods, including DIP [2). Self2Self (36), PD-denissig [52], ZS- ZS-N2N [27]. and ScoreDVI [7]. We also compare against AP-BSN (33,, a self-supervised denoising method that can be trained on noisy images of test sets directly. In addition, several diffusion priors-based based image restoration methods, including DDRM [9) GDP [2], and DR2 [45] are chosen to denoise real-world images. For these compared methods, we utilize their official source code and report the corresponding performance. Particularly, these diffusion-
methods employ the same diffusion prior as ours. As DDRM can only handle i.i.d. Gaussian noise and requires the noise std addm. we hence set dddm = a/a, i.e. the prior noise std in our method. GDP introduced the hard data-fidelity term 81|20 - yo yol12. where do is the estimated denoised result at each reverse diffusion step, and & is the guidance scale. We tune different & for different datasets. DR2 first obtained the intermediate -t-1 by adopting a low-pass filter DD and setting -; 4 D (1 2 and then conducted inference from step 7 + 0.257 to т. We set D= 8 (Downsampling factor) and = 100 for DR2. We evaluate the quantitative denoising quality using PSNR and SSIM metrics.
4.2 Main Results
We present quantitative comparisons of different methods in Table and visual comparisons in Figs. 3 (and Figs. 5 in the Appendix AA.4). Overall, our method achieves the best quantitative (on average) and qualitative performance across all compared methods.
First, while Self2Self excels on PolyU and CC datasets, shows poor denoising capacity (both PSNR/SSIM values and visual results) on SIDD and FMDD that contain severe image noise, as shown in Fig. S PD-denoising is generally effective but often introduces small artifacts that hinder visual effects, as seen in Fig. S ZS-N2N struggles with real-world noisy images and typically leaves noticeable noise after denoising due to its reliance on the independent noise assumption. Regarding diffusion bases- methods, GDP and GR2 perform poorly on real-world denoising, introducing artifacts (see Figs 5a and ( and over-smoothing (see Fig. (3). possibly because they adopt hard cata-consistency methods, which significantly deviate from the true likelihood function. As DDRM assumes Gaussian white noise, the denoised images often retain some noise, which cannot entirely removed, as shown in Figs 3 and 5b. ScoreDVI is the most competitive method against ours, but it sometimes blurs images and loses local textures, as indicated by Fig. 2 Unlike these methods, our approach effectively removes severe noise while preserving image details and textures.
7

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Table 2: Quantitative comparisons (PSNR(dB)SSSMM of different methods on diverse real-world
image datasets. The best and second-best PSNR/SSIM results are marked in bold and underlined.
Methods
SIDD Validation
FMDD
PolyU [47
CC [C]
Average
DIP [42
32. 1 11/0. 740
32.90/0.854
37.17/0.912
35.61/0.912
34,45/0.855
Self2Sell 36
29.46/0.590
30.76/0.695
38.33/0,962
37.45/0.948
14,00/0,800
PD-denoising [22]
33.97/0.820
33.01/0.856
37.04/0.940
35.85/0.923
34.97/0.885
ZS-N2N [2
25.58/0.433
31.61/0.767
36.05/0.916
33.58/0.854
31.71/0.743
ScoreDVI 7
34.75/0.855
33.10/0.865
37.77/0.959
37.09/0.945
35.68/0 906
GDP 12
27.65/0.615
27.68/0.698
32.30/0,900 905
31.45/0.916
29.77/0.784
DR2 45
32.02/0. 728
30.52/0.813
34.37/0.925
32.30/0 876
32.30/0.88 836
DDRM 19
33.14 18.14/00.96
32.54/0.837
33.14/0.767
96.04/0.923
33.72/0.83.
Ours
34.76/0.887
33.14/0.860
38.71/0.970
38.01/0.959
36.16/0.919
APBSN 23
36.80/0.874
31.99/0.336
37.03/0.951
34.88/0.925
38.18/0.897
50/0004
21:300
31.5807775
29.0EVO 741
33,0000000
27-40V046011
26, 75/06277
2R 13W7755
Noiay
CDP
DDRM
APBSN
SvonDVI
OLUS
Gl
Figure 2: Visual comparison of different denoising methods in SIDD validation dataset.
PD
DR2
ZSN2N
DDRM
SooeDD
NiaxD800 5 125, 6000 skir 3 nt
APESN
GDF
Ouis
GT
Figure Visual comparison of different denoising methods PolyU. (36.77/0.916), APBSN 677.59/0.944), DR2 (34.53/0.864), Self2Self (39.44/0.961),, 7SN2N (35. 12/0..98,,7) GDP (33.43/0.888), DDRM (33.61/0.773), ScoreDVI (37.76/0.939) Ours (39.01/0.965)
PSNR/SSIM values:
Although APBSN achieves the best PSNR values the SIDD dataset, it frequently introduces noticeable color artifacts (see Figs. 2 and oversmooths images (see Fig. 7). In addition, when applied to FMDD, PolyU, and CC datasets that contain fewer noisy images, its denoising performance significantly degrades and underperforms method. This highlights the advantage of data- efficient approach.
4.3 Ablation and Analyses
Adaptive likelihood estimation (ALE). We analyze 1/B(do) 3 2g. the estimated noise variance, and present quantitative and qualitative results in Fig. Fig. 4a demonstrates that / effectively reflects the noise variance of yo- That is, B ao exhibits larger values in noisier areas of yo and smaller values (black) in less noisy areas. Fig. 4b implies that the average of 3 åo are inversely correlated with PSNR values denoised images, which is reasonable since noisier images are more challenging to denoise and hence have lower PSNR. Conversely, the prior noise variance 8/a 3e-3

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DAY ERASE
0.15
Narey
16
Exl Vs
PSNR
A
15
0.00
200
400
600
300
1030
1250
Image
(a) Visual results of Ba/âu
(b) PSNR average Bu/āa.
Figure The estimated noise variance 1/E(0o) = 8 /ā on SIDD dataset
Table 3: Ablation adaptive likelihood estimation and local Gaussian convolution
with ALE X
with Gaussian Conv
SIDD
FMDD
PolyU
CC
X
32.12/0.741
27.07/0.530
35.40/0.895
33.10/0.830
34.63/0.870
13.11/0.865
38.70/0.969
37.82/0.956
34.76/0.887
33.14/0.860
38.71/0.970
38.01/0.959
indicated by the black plot in Fig. 4b are constant for all noisy images. These analyses suggest that the ALE captures the signal-dependent features of real-world noise effectively.
In addition, skip the variational inference process and directly use the prior precision p(o,-1) to derive -; resulting in -;ー - + (1 Tz- (o 1), क = o (af a + 3). The corresponding denoising result (i.e., without ALE) is reported in the second row of Table 3 and is
largely behind the denoising result of using ALE, further verifying the effectiveness ALE.
Rectification in Eq. (17). By introducing the local Gaussian convolution operation, explicitly refine the estimated noise variance 1/E(@r-1). As shown the fourth row of Table using
T/E(ØL-1) consistently improves the quantitative performance.
Table 4: Ablation of temperature CC dataset
Table 5: Ablation of 33 and CC dataset
> value
1/2
1/1
3 value
Sc-3
To-2
1.30-2
PSNR/SSIM
37.7400.55
37.73/1955
37.90009557
PSNR/SSIM
38,090.957
38.01.0.959
37.47/0.953
value
1/5
1/10
1/20
value
1,0
1.2
PSNRUSSIM
38.0100.599
800
35.3510.913
PSNR/SSIM
37.86009977
38.01AU.939
38. 10009599
Table 6: Denoising performance of using diffusion priors pre-trained with other image resolutions
Res.: Train + Test
SIDD
Res.: Train - Test
CC
PolyU
FMDD
128 256
34.80/0.836
256 512
38.01/0.959
38.71/0.970
33.14/0.860
256 + 256
34.76/0.887
512 > 512
37,01/0.950
38.33/0.966
33.02/0.859
Temperature y. When y S the effect of diffusion priors p(x;-1/xx) is reduced within the variational inference during the reverse diffusion process. As shown in Table 4 decreasing gradually improves the quantitative denoising performance, peaking at 1/5. Further reducing ? degrades PSNR/SSIM as insufficient diffusion priors are involved in variational Bayes.
3 in prior precision and kernel scale Regarding 3, it roughly represents the noise level of noisy image y (given a = 1) and we choose according to the empirical variance of the textureless area of y for one test set. kernel scale is set by considering the spatial correlation of noise present in real-world images. We ablate these two parameters in Table 5 which indicates that they are relatively robust moderate changes.
Local diffusion priors. We consider diffusion models pre-trained with other image resolutions as diffusion priors, including the 128 x 128 version and 512 x 512 version | The corresponding denoising performance is reported in Table and implementation details are provided in the Appendix A.3.1 Regarding SIDD, we observe that matching the resolution of diffusion priors and test images (both 256 x 256) achieves the best performance. Such a result is reversed for the remaining datasets,
"https//openaiipubiic.bb wtwp://wwb....iiiioowweeedttttto 2021/512x512 diffusion.pt

---

Table 7: The quantitative performance on removing other non Gaussinn synthetic noises
CBSD68 (2
Poissom (A 30)
Bernoulii (p = 0.2)
KodaK [13]
Puissom (A 30)
Bermoulii (p = 0.2)
ZS-NIN
27.5510.78 781
20.200 200.228
ZS-N2N
28.09007550
19.98/0.200
Ours
29.24H0.833
26.11/0.784
Ours
30.56/0.839
27.17/0.799
where the 256 256 diffusion prior for HR images is more effective than its 512 x 512 counterpart. This is likely because training HR diffusion models (e.g., 2 512) is more challenging, resulting in inferior generation performance (e.g., FII) compared to L.R diffusion models 9 Consequently, the local prior inherent in medium-resolution diffusion models is superior for restoring HR images.
4.4 Application to other non-Gaussian noises
Although our method is designed to handle real-world noise, it can also address other non- non- Gaussian noises, including Poisson noise and multiplicative Bernoulli noise. As these synthetic noises are spatially independent, we do not utilize Eq. (17) in our method. We report the denoising performance in Table 7 with ZS-N2N [16] selected for comparison. Experimental details and visual results are given in the Appendix A.3.2 and A.5 Our method achieves better quantitative metrics than ZSS-N2N on Poisson denoising and also preserves more local details and textures (see Fig. (). While ZS-N2N shows better SSIM than ours on Bernoulli denoising. it causes intensity shifts (see Fig. 9 and thus has poorer PSNR.
4.5 Application to image demosaicing
In addition denoising, our method is readily available for image restoration with pixel-wise degradation, e.g., image demosaicing, To adapt our method to this task, we define the forward process yo M @ no. where M is the degradation operator, and denotes element- wise multiplication. For demosaicing, M is the binary mask with O values indicating missing pixels of you We can incorporate
M into p( 1 1:-1) in Eq. (15). which results #t-1 Ma2+1/EB 13' Table 8 we
Maf
compare our method against DDRM on image demosaicing (CFA pattern: RGGB), and our method shows better results.
Table 8: Results of image demosaicing
Table 9: Results of different sampling steps
Dataset
Ser14
CBSD68
Step
1000
500
250
DDRM
24.68/0.714
24.52/0.705
SIDD
34.76/08887
33.5400.838
29.89.0.25
Ours
26.02N0.75
25.43/0.332
CC
38.01/09599
17.18419447
22.72/0716
Limitation. Our method builds on the DDPM sampling with total of 1000 diffusion steps. Denoising a single noisy image with a resolution 256 x 256 on an Nvidia 2080Ti GPU takes approximately 230 seconds, which is inefficient. In comparison, ZS-N2N takes about 16 seconds, despite its inferior denoising performance. Naively reducing diffusion steps in our method leads to apparent performance decreases, as indicated in Table 9 Our next move is to incorporate advanced accelerated sampling strategies into our method to reduce inference time while maintaining performance.
5 Conclusion
In this paper, we built upon diffusion priors and variational Bayes and proposed adaptive likelihood estimation and MAP inference during the reverse diffusion process, to handle real-world image noise that is structured and signal-dependent. The employed i.ni.d. likelihood function, combined with the precision prior and variational Bayes, allowed for the dynamical update of i.ni.d. noise precision posterior in each step of the generation process. This strategy adaptively refined the likelihood function and enabled the better MAP inference. Our method achieved excellent denoising performance on diverse real-world image denoising datasets and was also effective for removing other non-Gaussian synthetic noises.
Acknowledgment
This work was supported in part by the National Natural Science Foundation of China (NNSFC), under Grant Nos. 61672253, 62071197, and 62471192.
10

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A Appendix
A.1 Derivation of Eq.
6
As analyzed in Section 3.2 in principle can model the likelihood function of real-world noisy images as p(yo (2)) = N (zo. E(xo)), where a non-diagonal covariance matrix and its variance is related to its mean zo (or signal). In order to incorporate Yo into the inverse diffusion process and shorten its gap to 2t-1. we can construct 9t-1 based Eq. (2) to obtain yt-1 - a 180
vI - -i-ar-ee 122 For yo. can be sampled from the multi-variate Gaussian p(yo (zn) N (zaa) i.e. = To + Ae, where AA E(ro), and A is obtained by Cholesky decomposition. Finally,
we obtain
Wt-1 180-180 + V1 ât- vār-i Ac2) + / dz-16
(18)
= V + / - an-1 + vā--1Arz = 21-1 + vāl-1Ac2
A.2 Derivations of Eqs. 11 and 13
Regarding Eq. 1O), we have
Edg logplyt dr-1
N
(8i-1 - x
(+/-1- 1u))2
Eab
Σ
+ const
27
201
km1
N
(vi-1
1)2
(x))
11:)
B(ol_1)
+ const
2n
20
(19)
(wh-1
=x(1))²(((( 10
j06 + (xr²
-1,)8
const
2707
(E(oi_1)o} + +z)(t/1)²
pb)) +
+ const
2
where 14 = (1 l). We observe that Eq. (19) has the summation and quadratic form of at and hence ((x+-1) is identified as a diagonal Gaussian distribution. By completing the square, we can obtain
((=1-1)=NC =N( ((( 3 1/-1 147 E(or-1)0 +
?a? E(Øi-1)0 + +7
diag(
(20)
Similarly, given g(x+-1), the optimal g ( is provided by
log g" (Φt-1) Ex,-, log Io Φr 1ag
(21)
which corresponds
Eng
log p(y:((y 1 [21-1 21-1 1
(Vi-1
x{_1)²
=Ear
log 0i
Vi -01---1))log
logg 1o) 11.10%111 const
-
27
27
N
(vi-1 B(x{_1))2 + of
log di_1
Hi + (az-1 10g -3-100/-1 + const
2n
(22)
From Eq.
12 we identify each ((6)_1) ) is independent gamma distribution and hence g(dr-1) is
1
B (V/_1 )) (02-1)
g ('( II Gamma (0) (0/11:0011 01-1 +
(23)
27'
27
14

---

A.3 Additional implementation details
A.3.1 Applying class-conditional diffusion models as diffusion priors
We note that [9] only provides the 256 256 unconditional diffusion model eg (Z t) trained on ImageNet, and the remaining diffusion models are class-conditional i.e., co(Te, t) with the class label c. There are two ways to utilize these class-conditional diffusion priors for image denoising. Regarding each noisy image, we first sample a class label from randānt(O, 1000) and input it to (T C, combined with I; and I. One way is then ignoring the guidance from pre-trained classifier during the generation process and directly computing pa pafaz,, L) based ep (2 () and Eq. (4) The other way is further updating jso (Ztz, 1) to po( 1) + 9.0r my log Pe (c/ar)) where py (cl2)) the classifier and Is is the guidance scale. Basically, found these ways resulted in similar denoising performance, and Table 6 used the first way.
A.3.2 Experiments on denoising non-Gaussian synthetic noises
Synthesis of noisy images. Regarding Bernoulli noise, we obtain the noisy image by yo ( M, M torch. march.bemmulliftocc..nee. ((keee_) p 0.2; Regarding Poisson noise, we obtain the noisy image by yo torch. forch.poisson(> 2o)/A, X, À 30.
Hyperparameters. For our method, we set 8 1e-2 and 3 S for Bernoulli noise and Poisson noise removal, respectively. The remaining hyperparameters are identical to those of our main experiments.
A.4
Visual comparisons of denoising results real-world datasets
30.391730
J., 2806614
SL.8V03910
21 15A
OUBLE
OUBLE
OUBLE
OUBLE
OUBLE
OUBLE
WORD
WORD
WORD
WORD
WORD
WORD
NOIS
PD deniin
GDP
SSA
OXES
31 TITSA
OUBLE
OUBLE
OUBLE
OUBLE
OUBLE
OUBLE
WORD
WORD
WORD
WORD
WORD
WORD
W
DIP
Saraser
DORM
APISN
SoIeDVI
GI
Denoising result of 34 14.png
23.552
19.770 207
NasSv
PD-denoleing
GDP
ZSN2N
OueS
26.06, 7D/0.55
21.7000467
32.01/0.115
29.20/7/33
DIP
Self2Self
DDRM
AISSN
SardOV
GT
(b) Denoising result of 10. (0_..nng
Figure 5: Visual comparison of different denoising methods in SIDD validation dataset.
A.5 Visual comparisons of denoising results on synthetic noises
15

---

NOES
ZSNZN
DDRM
ScoceDV
GT
Figure 6: Visual comparison of different denoising methods in PolyU,
Nois
2SN2N
DDRM
ScorDD
Confocal FISH
APDSN
Sar2sen
GDF
O12
GT
Figure 7: Visual comparison of different denoising methods in FMDD.
kodim07
NOS
Jeifenfal
rijenjal
ceijenfal
Brifenfal
Noisy
ZSN2N
Ours
Figure 8: Visual comparison of denoising results on Poisson denoising (A 30)
kodim24
126007
Noisy
ZSN2N
Ours
GT
Figure 9; Visual comparison of denoising results Bernoulli denoising (p 0.2)
16

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Reviews:
[{"review_id": "isYPvVOZSz", "reviewer": "Reviewer_UCEq", "summary": "The paper proposes a method to tackle real world noise using an adaptive likelihood estimation . For this the authors develop a technique to dynamically infer the precision posterior using variational bayes. The authors perform comprehensive evaluation on real world denoising datasets to show the effectiveness of the method.", "questions": "1. Can the authors provide an intuition of utilizing a gamma hyperprior over a gaussian prior like in [1,2]. \n[1] Diffusion Posterior Sampling for General Noisy Inverse Problems\n[2] Manifold Preserving Guided Diffusion\n\n2. Is the method generalizable to other linear inverse problems than denoising [1,2] and DDRM, are all generic methods providing a general formulation to all linear inverse problems.\n\n3. Could the authors provide an analysis of the variation of performance with different number of sampling steps.", "limitations": "Yes, The authors have presented the limitations in a separate section.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 4, "contribution": 2, "strengths": "1. The authors propose an method that could adaptively estimate the posterior distribution and make efficient use of off the shelf methods for real world denoising\n2. The authors find that local priors from diffusion models pre-trained with LR image are more effective in real world denoising tasks.\n3. The paper is well written and easy to follow. Derivations seems to be accurate.", "weaknesses": "1. The authors have utilized a gamma based hyperprior without reasoning the design choice or comparing with other possible prior distribution. In order to show the need for a gamma prior, further experimental analysis are required\n2. The methods seems to be applicable only for real world denoising limiting its practical utility.\n3. Analysis with key diffusion based restoration methods like [1,2] are missing\n    [1] Diffusion Posterior Sampling for General Noisy Inverse Problems\n    [2] Manifold Preserving Guided Diffusion\n4. [2] achieves good results with just 50 steps of sampling.Could the authors provide an analysis of the variation of performance with different number of sampling steps.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your recognition of our work. As there are some overlaps between Questions and Weaknesses, we will consolidate and answer them together.\n\nQ1: The authors have utilized a gamma based hyperprior without reasoning the design choice or comparing with other possible prior distribution. In order to show the need for a gamma prior, further experimental analysis are required\n\nReply: In our paper, we utilized the *i.ni.d.* Gaussian distribution to model real-world noise. And we were dedicated to dynamically estimating the noise precision $\\phi_{t-1}$ at step $t$ by introducing the precision prior and conducting posterior inference. The reason we chose gamma prior for $\\phi_{t-1}$ is that gamma distribution is the conjugate prior for the Gaussian likelihood function with unknown precision, and the corresponding precision posterior also follows a gamma. Such property is commonly used in variational Bayes and allows us to derive the closed-form expression for the precision posterior, see Eqs. (13, 14). As indicated by Table 3 in the main paper, without the prior modeling and variational Bayes, the denoising performance significantly degraded, highlighting the significance of introducing the gamma prior. Other informative priors are also feasible in principle, but there may be no closed-form posterior and the problem becomes intractable.\n\nWe also experimented with a non-informative prior, Jeffery Prior. Particularly, Jeffery Prior for the precision of Gaussian results in closed-form posterior. If we choose $p(\\phi_{t-1})\\propto \\frac{1}{\\phi_{t-1}}$, then the precision posterior $g(\\phi_{t-1})$ is a gamma distribution with shape $\\hat{\\alpha} _ {t-1}=\\frac{1}{2 \\gamma}$, and rate $\\hat{\\beta} _ {t-1}=\\frac{(y_ {t-1} -\\hat{\\mu} _ {t-1} )^2 + \\hat{\\sigma}^2 _ {t-1}}{2 \\gamma}$. Hence, we do not need to specify any extra parameters for $p(\\phi_ {t-1})$ (i.e., $\\alpha$ and $\\beta$, refer to Eq. (14)). However, we found that such prior results in pure zero images and is useless, indicating the importance of utilizing informative priors, e.g., gamma. \n\nQ2: The methods seems to be applicable only for real world denoising limiting its practical utility. Is the method generalizable to other linear inverse problems than denoising [1,2] and DDRM, are all generic methods providing a general formulation to all linear inverse problems.\n\nReply: The primary objective of this paper is to introduce diffusion priors for real-world image denoising, which is significant in photography, microscopy, and CT imaging. In addition to real-world denoising, Section 4.4 of the main paper also verified the effectiveness of our method on synthetic noise removal, including Poisson and Bernoulli noise. Moreover, our method is readily available for image restoration with pixel-wise degradation, including image demosaicing and inpainting. \n\nTo adapt our method to these tasks, we define the forward process $y_0 = M \\odot x_0$, where M is the degradation operator, and $\\odot$ denotes element-wise multiplication. For image inpainting and demosaicing, $M$ is the binary mask with 0 values indicating missing pixels of $y_0$. We can incorporate $M$ into $p(y_{t-1}|x_{t-1},\\phi_{t-1})$ in Eq. (15), which results in $\\hat{\\pi}_ {t-1 }=\\frac{M\\sigma^2_t}{M\\sigma^2_t+1/\\text{E}(\\phi_ {t-1} )}$. We provide visual results of inpainting and demosaicing in Figure 1 of the 6958_rebuttal.pdf. In the following table, we also compare our method against DDRM on image demosaicing, and our method shows better results.\n\n|Demosaicing (CFA:RGGB)|Set14|CBSD68|\n|-|-|-|\n|DDRM|24.68/0.714|24.52/0.705|\n|Ours|**26.02/0.756**|**25.43/0.732**|\n\nWhen $M$ is not the pixel-wise degradation, our method needs more effort to adapt to.\n\nQ3: Analysis with key diffusion based restoration methods like [1,2] are missing.\n\nReply: DPS [1] approximates the gradient of likelihood $\\nabla_ {x_t} \\log p_t(y_0|x_t)$ at step $t$ to $\\nabla_ {x_t} \\log p(y_0|\\hat{x}_ 0)$, which acts as a hard data-consistency term that relates $y_0$ to $x_t$ in the generation process. If the forward model $p(y_0|x_0)$ is given, $x_t$ can be guided by $-s\\nabla_{x_t}\\log p(y_0|\\hat{x}_0)$ with $s$ as the guidance level. MPGD [2] further proposed to first guide $\\hat{x}_0$ based on $p(y_0|x_0)$, and then incorporated the modified $\\hat{x}_0$ into the DDIM sampling. Although they perform well in general noisy inverse problems, they still rely on accurate noise models and are only verified on synthetic noise removal. The following experiment shows that DPS underperforms our method in real-world noise removal.\n\n|Datsets|SDDD Val|CC|PolyU|\n|-|-|-|-|\n|DPS|34.46/0.881|34.48/0.904|36.26/0.940|\n|Ours|**34.76/0.887**|**38.01/0.959** |**38.71/0.970**|\n\nQ4: Can the authors provide an intuition of utilizing a gamma hyperprior over a gaussian prior like in [1,2]\n\nReply: The intuitive interpretation of our method is hijacking the unconditional $x_{t-1}$ at each step and forcing it to approach $y_{t-1}$. The modified $x^*_{t-1}$ is the convex combination of the mean of $x_{t-1}$ and $y_{t-1}$, with the coefficient $\\hat{\\pi}_ {t-1}$ defined by the relative magnitude between $\\sigma^2_{t}$ and the inverse of gamma posterior $g(\\phi_{t-1})$. We provide a visual illustration of our method in Figure 2 of the 6958_rebuttal.pdf.\n\nQ5: [2] achieves good results with just 50 steps of sampling.Could the authors provide an analysis of the variation of performance with different number of sampling steps.\n\nReply: We ablate different sampling steps in the following:\n\n| Steps| $T=1000$|$T=500$|$T=250$|\n| -| - | - | - |\n| SIDD Val| **34.76/0.887**|33.54/0.838| 23.89/0.825|\n| CC| **38.01/0.959**|37.18/0.947|22.72/0.716|\n\nIt is observed that $T=500$ degrades the performance, which is acceptable though. When $T=250$, the denoising fails.  As pointed out in the limitation Section, our method relies on DDPM and requires large sampling steps for good performance. Speeding up the inference is our key direction in the future.", "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": "FavyAxa3ut", "reviewer": "Reviewer_eDuR", "summary": "Overall, this paper presents a novel method in real-world image denoising by proposing a sophisticated method that combines adaptive likelihood estimation, MAP inference, and variational Bayes within the diffusion model framework.", "questions": "1.\tWhat is the NFE for DDRM used in this paper? What is the inference time for DDRM and your method respectively?\n2.\tIn Algorithm 1, the threshold is set to 1e-6. Is performance sensitive to different values?", "limitations": "Authors discussed the limitation in the paper.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tUtilizing variational Bayes to dynamically infer the precision posterior is innovative and provides a more accurate modeling of real-world noise.\n2.\tBy exploring local priors in low-resolution diffusion models, the method can directly handle high-resolution noisy images without extensive patch-based or resize-based operations.\n3.\tThe proposed method's effectiveness is demonstrated through extensive experiments on diverse real-world datasets, showcasing superior performance compared to other unsupervised denoising methods.", "weaknesses": "1.\tThe method relies on hyperparameters (e.g., prior precision, temperature parameter, kernel scale etc.), which might require careful tuning for optimal performance for different datasets. Authors criticize previous methods for being dependent on hyperparameters but do not overcome such limitation in this paper.\n2.\tThe contribution of local Gaussian convolution might be overclaimed. As shown in  Table 3, the performance improvements brought by rectification are pretty limited, which look like experimental variations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your recognition of our work.\n\nQ1: The method relies on hyperparameters (e.g., prior precision, temperature parameter, kernel scale etc.), which might require careful tuning for optimal performance for different datasets. Authors criticize previous methods for being dependent on hyperparameters but do not overcome such limitation in this paper.\n\nReply: Our method does rely on some hyperparameters, but they are relatively robust for different choices. We ablate different $\\beta$, temperature $\\gamma$, and kernel scale $s$ on CC dataset, and report the corresponding performance in the following Tables:\n\n| $\\beta$($\\gamma=5,s=1$) | 5e-3 | 1e-2 | 1.5e-2 |\n| :--- |  :---: | :---: | :---:  |\n| PSNR/SSIM |38.03/0.957| 38.01/0.959 | 37.47/0.953|\n\n| $\\gamma$($\\beta=0.01,s=1$) | 1/4 | 1/5 | 1/10 |\n| :--- | :---: | :---: | :---: |\n| PSNR/SSIM| 37.90/0.957| 38.01/0.959| 37.80/0.953|\n\n| $s$($\\gamma=5,\\beta=0.01$)| 0.8 | 1.0 | 1.2 |\n| :--- | :---: | :---: | :---: |\n| PSNR/SSIM| 37.876/0.957| 38.01/0.959|38.10/0.959|\n\n\nIt can be observed that the denoising performance resulting from different hyperparameters does not change significantly, indicating that they are quite insensitive to moderate changes. In addition, regarding compared methods like GDP and DR2, we carefully tuned their hyperparameters, but they still perform poorly in real-world denoising. In the modified version, we will highlight their inability to handle real-world noise rather than the reliance on hyperparameters.\n\nQ2: The contribution of local Gaussian convolution might be overclaimed. As shown in Table 3, the performance improvements brought by rectification are pretty limited, which look like experimental variations.\n\nReply: We agree that the local Gaussian convolution introduced in Eq. (17) is a small technical improvement rather than one of the main contributions of our paper. Therefore, we did not include it into our main contributions, see lines 59-63 of the main paper. But we believe that the local Gaussian convolution is indeed helpful as it consistently enhances the denoising performance of all test datasets as shown in Table 3 regardless of the minor improvement on FMDD and PolyU datasets.  \n\nQ3: What is the NFE for DDRM used in this paper? What is the inference time for DDRM and your method respectively?\n\nReply: We used the DDIM sampling and 20 NFEs for DDRM, following its default setting. The inference time of DDRM for images with resolution $256\\times 256$ is about 4s while our method costs about 230s. As discussed in the limitation section of the main paper, our method relies on the DDPM and large sampling steps for good performance. Speeding up the inference is our next research point.\n\nQ4: In Algorithm 1, the threshold is set to 1e-6. Is performance sensitive to different values?\n\nReply: The denoising performance is insensitive to different thresholds as the alternate optimization in lines 5-8 of Algorithm 1 is guaranteed to converge, as indicated by [1]. In the following table, we ablate different thresholds on CC dataset, and results indicate that the threshold is robust.\n\n| Threshold      | 1e-5 | 1e-6 | 1e-7 | 1e-8 |\n| ----------- | ----------- | ----------- | ----------- | ----------- |\n| PSNR/SSIM     | 38.00/0.958 | 38.01/0.959       | 38.01/0.959      | 38.01/0.959 |\n  \n[1] Bishop C M, Nasrabadi N M. Pattern recognition and machine learning[M]. New York: springer, 2006.", "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": "d21WzGcVCy", "reviewer": "Reviewer_tZQC", "summary": "This work considers the problem of using adapt diffusion models for solving real-world image denoising problem, that is, the noise is not assumed to be i.i.d Gaussian. The authors statistically model the real-world noise as independent, non-identically distribution noise, and then incorporate the adaptive MAP inference into the reverse process of the diffusion model.", "questions": "1. Why is an i.ni.d noise model used to characterize the real-world noise?\n2. Why do we want to adaptively update the parameters in reverse diffusion? Please provide some high-level explanation.\n3. Please justify the accuracy of the approximation used in Eq. 15.\n4. In Fig.3, self2self shows the best numerical performance. Please discuss the result.", "limitations": "The authors have discussed the limitations.\n\n--------------------- After Rebuttal --------------------\nThe responses have addressed my questions. I have raised my score to 5.", "rating": 5, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "N/A", "weaknesses": "1. The paper does not well motivate their choice of i.ni.d noise model. It is not clear why such an i.ni.d noise model can properly characterize the statistics of the real-world noise considered in the paper.\n2. The paper is not well-written, lacking proper motivation and explanation of the design of the proposed method.\n3. The approximation adopted in Eq.15 may lead to incorrect $x^\\ast$. For example, when the function is non-convex, maximizing its Jenson low bounder produce an estimate that is far away from $x^\\ast$.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your review of our paper. As there are some overlaps between Questions and Weaknesses, we will consolidate and answer them together.\n\nQ1: The paper does not well motivate their choice of i.ni.d noise model. It is not clear why such an i.ni.d noise model can properly characterize the statistics of the real-world noise considered in the paper. Why is an i.ni.d noise model used to characterize the real-world noise?\n\nReply: As analyzed in Section 3.2 of the main paper, the real-world image noise is spatially correlated and signal-dependent. A structured and heteroscedastic Gaussian likelihood function can theoretically model real-world noise, but it is computationally expensive due to the large covariance matrix and also impractical due to the unknown noise variance. The reason we chose *i.ni.d.* Gaussian likelihood function $p(y_0|x_0, \\phi_0)=\\mathcal{N}(y_0;x_0, \\phi_0^{-1})$ to model real-world noise is that it allows us to model the spatially variant feature (*ni* in *i.**ni**.d*. means not identical) of real-world noise and meanwhile frees the modeling of covariance (*i* in **i**.ni.d. means independent), as already explained in lines 147-149 of Section 3.3. Such a choice trades off the modeling precision for practical feasibility. Based on this *i.ni.d.* Gaussian model, we can dynamically estimate the noise precision posterior during the inverse diffusion process and then obtain an optimal $x^{*}_{t-1}$ that balances the prior and measurement. As shown in Figure 4 of the main paper, the estimated variance of *i.ni.d.* noise model well matches the noise level of noisy images and is *signal-dependent*, implying that the estimated *i.ni.d.* model is suitable for real-world noise.\n\nAnother feasible choice is the *i.i.d.* Gaussian likelihood combined with our adaptive likelihood estimation (ALE) for the precision **scalar** (not the **vector** in *i.ni.d.* model). This model assumes the same noise variance across the spatial locations of real-world images. We compare this variant against our method and show the result in the following Table:\n\n|Datasets|CC|FMDD|\n|-|-|-|\n|*i.ni.d.*+ALE (ours)| **38.01/0.959**| **33.14/0.860**|\n|*i.i.d.*+ALE| 33.66/0.856|27.29/0.549|\n\nIt is observed that adopting *i.ni.d.* noise model is necessary for real-world denoising and significantly outperforms the *i.i.d.* noise model\n\nQ2: The paper is not well-written, lacking proper motivation and explanation of the design of the proposed method.\n\nReply: As replied to Q1, we would like to argue that the motivation of introducing the *i.ni.d.* Gaussian likelihood for real-world noise has been explained in Section 3.2 and Section 3.3 of the main paper, please see lines 137-144 and lines 146-149. This *i.ni.d.* noise model has also been checked in Figure 4(a) of Section 4.3, where the non-identical variances successfully capture the spatially varying noise level in noisy images.  Nevertheless, we noticed that such motivation was not mentioned in the Introduction section, which may confuse readers and impede the readability. We will modify our introduction in the revised version to include this motivation.\n\nQ3: Why do we want to adaptively update the parameters in reverse diffusion? Please provide some high-level explanation.\n\nReply: The reason we estimate the precision $\\phi_{t-1}$ during the inverse diffusion process is that specifying the accurate noise precision for each spatial location of $y_{t-1}, t=[0,\\cdots T]$ is difficult and impractical, as indicated by lines 94-96, 150-152 of the main paper. Therefore, we assigned $\\phi_{t-1}$ a prior and adaptively infer its posterior using variational Bayes. The updated precision successfully captures the spatially varying noise of noisy images, see Figure 4(a) in Section 4.3. Without the prior modeling and adaptive likelihood estimation, the denoising performance significantly degraded, as indicated in Table 3 of the main paper.\n\nQ4: The approximation adopted in Eq.15 may lead to incorrect x∗. For example, when the function is non-convex, maximizing its Jenson low bounder produce an estimate that is far away from x∗. Please justify the accuracy of the approximation used in Eq. 15.\n\nReply: We argue that as $\\log(\\cdot)$ is a concave function and $\\log p(y_{t-1}|x_{t-1})$ in Eq. (15) equals to $\\log E_{g(\\phi_t)}p(y_{t-1}|x_{t-1}, \\phi_{t-1})$, applying Jensen's inequality **guarantees** to find its lower bound $E_{g(\\phi_{t-1})}\\log p(y_{t-1}|x_{t-1}, \\phi_{t-1})$. Optimizing the lower bound generally produces satisfactory solutions, like in variational inference, VAE, and diffusion models. \n\nWe can empirically check the approximation accuracy in Eq. (15) by approximating $p(y_{t-1}|x_{t-1})$ via Monte-Carlo integration $\\frac{1}{M}\\sum_{s=1}^Mp(y_{t-1}|x_{t-1}, \\phi^s_{t-1}), \\phi^s_{t-1} \\sim g(\\phi_{t-1})$. Then the solution $\\bar{\\pi}_ {t-1}y_ {t-1} + (1-\\bar{\\pi}_ {t-1}\\mu_\\theta(x_t, t))$ with $\\bar{\\pi}_ {t-1} = \\frac{\\sigma_{t}^2}{\\sigma_{t}^2 + \\frac{1}{M}\\sum_{s=1}^M (\\phi^s_ {t-1})^{-1}}$ approaches to the optimal $x^\\dagger_{t-1}$, which can be considered as the ground-truth MAP estimate. \n\nWe compare the denoising performance of using $x^\\dagger_{t-1}$ against using $x^*_{t-1}$ in Eq. (15) in the following Table, which shows that the two methods perform similarly and hence indicates the approximation error is small.\n\n|Method|Using $x^\\dagger_{t-1}$ (GT)| Using $x^*_{t-1}$ (in Eq. (15))|\n|-|-|-|\n|SIDD  Val|34.78/0.888|34.76/0.887|\n|CC|38.01/0.958| 38.01/0.959\n\nQ5: In Fig.3, self2self shows the best numerical performance. Please discuss the result.\n\nReply: We note that Self2Self only performs well on real-world images with relatively light noise, e.g., PolyU and CC datasets, as shown in Table 3. And self2self happened to achieve the largest PSNR for that image of PolyU in Figure 3. However, its numerical performance on the whole PolyU underperforms ours. Moreover, Self2Self fails to handle heavy noise, as shown in Table 3 and Figure 5 of the paper.", "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": "ssJezMAEG7", "reviewer": "Reviewer_sawX", "summary": "The authors propose a way to use diffusion priors for real-world image denoising where the noise statistics are complex and signal-dependent. They use variational inference to estimate the joint posterior of the noise precision and image throughout diffusion time. The result is a MAP estimate of the denoised image that takes into account signal dependence and spatial correlation of the observed noise. The authors also propose to use a low-resolution diffusion model to denoise high-resolution images. In experiments, the authors compare to single image-based denoising methods, a self-supervised denoising method, and diffusion-based methods. They show improved quantitative and qualitative performance against the baselines.", "questions": "* How difficult would it be to adapt this method to provide posterior samples?", "limitations": "I appreciate the authors providing a limitations section. There are probably more limitations of the method that could be discussed, such as not addressing posterior sampling.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* The proposed method is sound and addresses a difficult problem.\n* Plenty of baselines are provided, and experiments show convincing quantitative and qualitative performance. Plus a good number of ablation studies is provided.\n* The proposed method works for other non-Gaussian synthetic noise as well as real-world camera noise.", "weaknesses": "* The proposed method only provides MAP estimates (not posterior samples).\n* Nit: Eq. 6 should be explained more clearly in the text. For example, A should be explicitly defined. And why is the same $\\epsilon$ used twice? Shouldn’t it be $y_{t-1}=\\sqrt{\\bar{\\alpha}_{t-1}}(x_0+A\\epsilon_1)+\\sqrt{1-\\bar{\\alpha}_{t-1}}\\epsilon_2$ for $\\epsilon_1,\\epsilon_2$ independently drawn (since the measured noise is different from the synthetic noise added in the diffusion process)?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your recognition of our work. As some questions overlap with the weaknesses, we will integrate and answer them together.\n\nQ1: The proposed method only provides MAP estimates (not posterior samples). How difficult would it be to adapt this method to provide posterior samples?\n\nReply: Employing MAP inference is more straightforward for our method and also reduces the sampling randomness. In order to obtain posterior samples, we have to sample $x_{t-1}$ from $p(x_{t-1}|y_{t-1},x_t)$ rather than derive its MAP solution as done in Eq. (15). For our method, it is not very difficult to achieve that. First, we can approximate $p(y_{t-1}|x_{t-1})$ by  Monte-Carlo integration, resulting in \n$$p(y_{t-1}|x_{t-1})= E_{g(\\phi_{t-1})}p(y_{t-1}|x_{t-1}, \\phi_{t-1}) \\approx \\frac{1}{M}\\sum_{s=1}^Mp(y_{t-1}|x_{t-1}, \\phi^s_{t-1}) \\approx \\mathcal{N}(y_{t-1};x_{t-1}, \\frac{1}{M}\\sum_{s=1}^M (\\phi^s_{t-1})^{-1})$$\nwhere we utilize uni-Gaussian to approximate the mixture Gaussian regarding the last term; $\\phi^s_{t-1} \\sim g(\\phi_{t-1})$; $M$ is the number of Mente-Carlo samples and should be as large as possible.\n\nThen, as both $p(y_{t-1}|x_{t-1})$ and $p(x_{t-1}|x_t)$ follow Gaussian distributions, $p(x_{t-1}|y_{t-1},x_t)$ is also the Gaussian distribution, from which we can sample $x_{t-1}$  and the final $x_0$.\n\nWe provide some posterior samples of the denoising result in Figure 3 of the 6958_rebuttal.pdf for your reference. We would like to discuss this posterior sampling variant in the revised paper.\n\nQ2: Nit: Eq. 6 should be explained more clearly in the text. For example, A should be explicitly defined. And why is the same ϵ used twice? Shouldn’t it be $y_ {t-1} =\\sqrt{\\bar{\\alpha}_ {t-1}}(x_0+A\\epsilon_1)+\\sqrt{1-\\bar{\\alpha}_ {t-1}}\\epsilon_2$ for $\\epsilon_1$,$\\epsilon_2$ independently drawn (since the measured noise is different from the synthetic noise added in the diffusion process)?\n\nReply: First, we are grateful for pointing out the mistake in Eq. (6), and it should be \n\n$$y_ {t-1}=\\sqrt{\\bar{\\alpha}_ {t-1}}(x_0+A\\epsilon_1)+\\sqrt{1-\\bar{\\alpha}_ {t-1}}\\epsilon_2=x_ {t-1}+\\sqrt{\\bar{\\alpha}_ {t-1}}A\\epsilon_1, \\epsilon_1 \\sim \\mathcal{N}(0, I), \\epsilon_2 \\sim \\mathcal{N}(0, I)$$\n\nIn the following, we will give a detailed derivation and explanation of this equation. As analyzed in Section 3.2, in principle we can model the likelihood function of real-world noisy images as $p(y_0|x_0)=\\mathcal{N}(x_0, \\Sigma(x_0))$, where $\\Sigma$ is a non-diagonal covariance matrix and its variance is related to its mean $x_0$ (or signal). In order to incorporate $y_0$ into the inverse diffusion process and shorten its gap to $x_{t-1}$, we can construct $y_{t-1}$ based Eq. (2) to obtain $y_ {t-1} = \\sqrt{\\bar{\\alpha}_ {t-1}}y_0 + \\sqrt{1-\\bar{\\alpha}_ {t-1}}\\epsilon_2$. For $y_0$, it can be sampled from the multi-variate Gaussian $p(y_0|x_0)=\\mathcal{N}(x_0, \\Sigma(x_0))$, i.e., $y_0=x_0+A\\epsilon_1$, where $AA^T=\\Sigma(x_0)$, and $A$ is obtained by Cholesky decomposition. Finally, we obtain \n$$y_ {t-1} = \\sqrt{\\bar{\\alpha}_ {t-1}}y_0 + \\sqrt{1-\\bar{\\alpha}_ {t-1}}\\epsilon_2 = \\sqrt{\\bar{\\alpha}_ {t-1}} (x_0+A\\epsilon_1) + \\sqrt{1-\\bar{\\alpha}_ {t-1}}\\epsilon_2 = \\sqrt{\\bar{\\alpha}_ {t-1}} x_0 + \\sqrt{1-\\bar{\\alpha}_ {t-1}}\\epsilon_2 + \\sqrt{\\bar{\\alpha}_ {t-1}} A\\epsilon_1 = x_ {t-1} + \\sqrt{\\bar{\\alpha}_ {t-1}} A\\epsilon_1 $$\n\nWe will add the above explanation of Eq. (6) in the revised paper.", "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": "DjyrpUfEqH", "reviewer": "Reviewer_Wzuv", "summary": "This paper proposed a diffusion-based image denoising method. The method leverages the MAP framework with proposed adaptive likelihood estimation method and a pre-trained diffusion prior. Experiments on four real-world datasets validate the advantages of the proposed method.", "questions": "The proposed algorithm involves numerous hyperparameters. How are these selected, and is the algorithm robust to variations in hyperparameter settings?", "limitations": "The authors have acknowledged the limitations of their work.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well-written and easy to understand.\n2. The integration of a reverse diffusion process with adaptive likelihood estimation is novel.\n3. The denoising performance of the proposed method outperforms that of other single-image denoising methods. The experimental results are substantial.", "weaknesses": "1. The title of the paper does not accurately reflect its contributions. The use of diffusion priors to address inverse problems is widely studied, as the author has noted, and this paper builds upon the framework presented in [1]. The significant contribution of this paper appears to be the proposed alternative updating scheme for estimating the likelihood term. However, the title is too generic and does not capture this contribution.\n2. The denoising computational cost is high, and the running time for the reverse diffusion process is lengthy.\n3. In Algorithm 1: Difusion -> Diffusion.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your recognition of our work.\n\nQ1: The title of the paper does not accurately reflect its contributions. The use of diffusion priors to address inverse problems is widely studied, as the author has noted, and this paper builds upon the framework presented in [1]. The significant contribution of this paper appears to be the proposed alternative updating scheme for estimating the likelihood term. However, the title is too generic and does not capture this contribution.\n\nReply: Thanks for your suggestion, and we would like to modify our title to the following one in the revised version if allowed:\n\"Diffusion priors for variational likelihood estimation and image denoising\". \n\nQ2: The denoising computational cost is high, and the running time for the reverse diffusion process is lengthy.\n\nReply: As pointed out in the limitation of the main paper, our method relies on DDPM and large sampling steps for good denoising performance. We tried several other sampling steps and report the performance in the following Table:\n\n|Steps     | $T=1000$ |  $T=500$  | $T=250$  |\n| ----------- | ----------- | ----------- | ----------- |\n| SIDD Val      | 34.76/0.887  | 33.54/0.838  | 23.89/0.825   |\n| CC      | 38.01/0.959     | 37.18/0.947   | 22.72/0.716  |\n\nIt can be observed that $T=500$ degrades the performance, which is acceptable though. In the case of $T=250$, the denoising completely fails. As a result, speeding up the inference is our key direction in the future.\n\nQ3: In Algorithm 1: Difusion -> Diffusion\n\nReply: Thanks for your careful review, and we will correct it in the revised version. \n\nQ4: The proposed algorithm involves numerous hyperparameters. How are these selected, and is the algorithm robust to variations in hyperparameter settings?\n\nReply: Our method involves three hyperparameters: $\\beta$ in the noise prior precision, temperature $\\gamma$ and kernel scale $s$. Regarding $\\beta$ value, it roughly represents the noise level of noisy image $y$ (given $\\alpha=1$) and we can choose $\\beta$ according to the empirical variance of the textureless area of $y$ for one testset. kernel scale $s$ is set by considering the spatial correlation of noise present in real-world images. Temperature $\\gamma$ is an empirical parameter that scales the likelihood function in Bayes' theorem and is generally set to values smaller than 1. We ablate these three parameters in the following tables regarding the CC dataset, which indicate that they are relatively robust to moderate changes.\n\n| $\\beta$($\\gamma=5,s=1$) | 5e-3 | 1e-2 | 1.5e-2 |\n| :--- |  :---: | :---: | :---:  |\n| PSNR/SSIM |38.03/0.957| 38.01/0.959 | 37.47/0.953|\n\n| $\\gamma$($\\beta=0.01,s=1$) | 1/4 | 1/5 | 1/10 |\n| :--- | :---: | :---: | :---: |\n| PSNR/SSIM| 37.90/0.957| 38.01/0.959| 37.80/0.953|\n\n| $s$($\\gamma=5,\\beta=0.01$)| 0.8 | 1.0 | 1.2 |\n| :--- | :---: | :---: | :---: |\n| PSNR/SSIM| 37.876/0.957| 38.01/0.959|38.10/0.959|", "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:
We thank all reviewers for their review of our paper. The response to each reviewer has been posted separately in the following. The 6958_rebuttal.pdf contains figures related to responses to Reviewers  UCEq and sawX.

Meta-review: This paper presents a novel method for real-world image denoising using diffusion priors combined with adaptive likelihood estimation and Maximum A Posteriori (MAP) inference. The method effectively integrates variational Bayes to dynamically infer the precision posterior, leading to a more accurate modeling of real-world noise (Reviewers eDuR, sawX, and Wzuv). The paper is well-written, with clear derivations and thorough experimental evaluation across multiple real-world datasets, showcasing superior performance compared to other unsupervised denoising methods (Reviewers UCEq, sawX, Wzuv).

After a careful consideration of the reviewers' comments, AC recommends accepting this paper. Despite some concerns regarding the justification of certain design choices and the computational cost, the paper presents a good contribution to the field of image denoising. The combination of diffusion priors with adaptive likelihood estimation is both novel and effective, addressing a critical problem in real-world imaging.
Decision: Accept (spotlight)