From Noise Estimation to Restoration: A Uniﬁed Diffusion and Bayesian

Risk Approach for Unsupervised Denoising

Reeshad Khan

, Ukash Nakarmi

and John M. Gauch

Department of Electrical Engineering and Computer Science, University of Arkansas, Fayetteville, Arkansas, U.S.A.

{rk010, unakarmi, jgauch}@uark.edu

Keywords:

Diffusion, Stein’s Unbiased Risk Estimator, Bayesian Loss, SURE, PURE, PGURE, MRI Denoising,

Unsupervised Learning.

Abstract:

Deep Neural Networks (DNNs) have revolutionized image denoising, challenging traditional methods such as

Stein’s Unbiased Risk Estimator (SURE) and its extensions (eSURE and PURE), along with Extended Poisson

Unbiased Risk Estimator (ePURE). These traditional approaches often struggle to generalize across different

noise types, especially when noise characteristics are unknown or vary widely, and they are not equipped

to handle mixed noise scenarios effectively. In response, we present a novel unsupervised learning strategy

that leverages an enhanced diffusion model combined with a dynamically trained Deep Convolutional Neural

Network (DnCNN). We introduce adaptive Bayesian loss functions—Bayesian-SURE, Bayesian-PURE, and

a newly developed Bayesian-Poisson-Gaussian Unbiased Risk Estimator (Bayesian-PGURE)—that adjust to

estimated noise levels and types without prior knowledge. This innovative method enables signiﬁcant im-

provements in handling mixed noise conditions and ensures robustness across varied imaging scenarios. Our

comprehensive evaluations on MRI data corrupted by Gaussian, Poisson, and mixed noise demonstrate that

our approach outperforms existing algorithms, achieving superior denoising performance and image ﬁdelity

under diverse, unpredictable conditions. Our contributions advance the state-of-the-art in medical imaging

denoising, establishing a new benchmark for unsupervised learning frameworks in managing complex noise

dynamics.

1 INTRODUCTION

Magnetic Resonance Imaging (MRI) serves as a criti-

cal tool in clinical diagnostics due to its non-ionizing

nature and superior tissue contrast capabilities, offer-

ing safe imaging without radiation exposure (Jalata

et al., 2024). Despite these advantages, MRI scans

are inherently affected by noise introduced during

the acquisition process, which often necessitates ad-

vanced denoising techniques to improve image qual-

ity (Manj

on and Coupe, 2019). While traditional

denoising methods like BM3D (Burger et al., 2012)

have been effective for synthetic noise types such as

Gaussian (Zhang et al., 2017a) and Poisson (Cherry

et al., 2012), the advent of Deep Learning (DL) has

shifted paradigms towards more adaptive, data-driven

approaches.

Deep Neural Networks (DNNs) have demon-

strated a remarkable ability to manage both synthetic

https://orcid.org/0009-0008-9870-022X

https://orcid.org/0000-0002-5351-3956

https://orcid.org/0009-0008-7417-1212

and realistic noise scenarios, outperforming classical

methods under diverse conditions. However, the con-

ventional training of DNN-based denoisers often re-

lies on the availability of pristine, noiseless ground

truth images—a requirement seldom met in practi-

cal scenarios (Zhussip et al., 2019). This challenge

has led to the development of unsupervised learning

techniques such as Deep Image Prior (DIP) (Ulyanov

et al., 2020) and Noise2Noise (Lehtinen et al., 2018a),

which leverage the inherent capabilities of DNNs to

reconstruct high-quality images from noisy data with-

out needing clean examples (Ulyanov et al., 2018),

(Lehtinen et al., 2018b).

Building upon the foundations of Stein’s Unbiased

Risk Estimator (SURE) (Metzler et al., 2020) and its

variants eSURE (Zhussip et al., 2019), Poisson Unbi-

ased Risk Estimator (PURE) (Kim et al., 2022), and

Extended Poisson Unbiased Risk Estimator (ePURE)

(Kim et al., 2022), our work introduces an innovative

unsupervised framework that combines an enhanced

diffusion model (Ho et al., 2020) with a dynamically

trained DnCNN (Zhang et al., 2017b). This approach

Khan, R., Nakarmi, U. and Gauch, J. M.

From Noise Estimation to Restoration: A Uniﬁed Diffusion and Bayesian Risk Approach for Unsupervised Denoising.

DOI: 10.5220/0013187300003912

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2025) - Volume 3: VISAPP, pages

547-555

ISBN: 978-989-758-728-3; ISSN: 2184-4321

547

not only addresses the limitations of existing meth-

ods—particularly their struggles with generalization

across unknown or mixed noise types—but also sets

new benchmarks in MRI denoising.

Our method leverages Bayesian-enhanced loss

functions—Bayesian-SURE, Bayesian-PURE, and

Bayesian-Poisson-Gaussian Unbiased Risk Estimator

(Bayesian-PGURE)—which dynamically adapt to the

estimated noise characteristics, thus allowing for ro-

bust denoising performance even when the noise type

and level are not a priori known. This adaptive capa-

bility is crucial for practical applications where noise

properties can signiﬁcantly vary, such as in medical

imaging environments (Kim et al., 2020), (Kim et al.,

2022).

Furthermore, we extend the theoretical under-

standing of unsupervised denoising by drawing con-

nections between our Bayesian-enhanced methods

and the Noise2Noise framework, suggesting that our

Bayesian approaches can be viewed as a generaliza-

tion capable of handling correlated noise scenarios

more effectively (Lehtinen et al., 2018b). The experi-

mental validation of our models on MRI datasets con-

taminated with Gaussian, Poisson, and mixed noise

types demonstrates superior performance over tradi-

tional methods, particularly in scenarios where the

noise characteristics deviate from standard assump-

tions.

Our contributions not only advance the state-of-

the-art in image denoising but also open avenues

for future research into unsupervised learning models

that can seamlessly adapt to varied and dynamically

changing environmental conditions, thereby signiﬁ-

cantly impacting both the theory and application of

machine learning in medical imaging.

2 BACKGROUND

The evolution of image denoising techniques, partic-

ularly for medical applications such as MRI, has re-

quired a deep understanding of both traditional and

advanced methodologies. This section introduces the

foundational concepts and established estimators, set-

ting the stage for the innovative approaches we de-

velop in subsequent sections. The core of our ap-

proach leverages Stein’s Unbiased Risk Estimator

(SURE) and its Monte Carlo variant (MC-SURE),

frameworks that have been extensively validated in

other domains. Our work extends the application of

these established methods to the complex noise char-

acteristics inherent in MRI data, a domain where the

acquisition of noise-free ground truth is notably chal-

lenging.

We review the principles of SURE (Metzler et al.,

2020) and MC-SURE, discussing their theoretical

underpinnings and the rationale behind their effec-

tiveness in scenarios lacking clean data. By adapt-

ing these methods to the realm of medical imaging,

speciﬁcally to MRI, we aim to demonstrate their ro-

bustness and utility in a ﬁeld where accurate image

restoration is critical yet burdened by inherent noise.

This adaptation not only underscores the versatility of

these estimators across various applications but also

sets the stage for detailed examinations of their per-

formance in the subsequent sections of this study.

2.1 Stein’s Unbiased Risk Estimator

(SURE)

In the context of denoising Gaussian-contaminated

signals or images, a typical model involves a linear

equation:

y = x + n (1)

where x ∈ R

represents an unknown signal, y ∈

is the observed noisy measurement, and n ∈ R

denotes i.i.d. Gaussian noise with n ∼ N (0, σ

I),

where I is the identity matrix.

The SURE (Stein’s Unbiased Risk Estimator)

(Metzler et al., 2020) is a widely-used approach to es-

timate the mean squared error (MSE) associated with

an estimator h(y) of x. It is given by the expression:

η(h(y)) =

||y − h(y)||

− σ

2σ

∑

i=1

δh

(y)

δy

(2)

This equation suggests that the random variable

η(h(y)) is an unbiased estimator of the MSE of h(y),

given by:

n∼N (0,σ

)



||x − h(y)||



= E

n∼N (0,σ

)

{η(h(y))}

(3)

Obtaining an analytical solution for the divergence

term in equation (2) is limited to special cases, such as

when the estimator h(y) is a non-local mean or linear

ﬁlter. To utilize (2) in more general cases, an approx-

imate solution for the divergence term is necessary.

2.2 Poisson Unbiased Risk Estimator

(PURE)

The Poisson Unbiased Risk Estimator (PURE) (Kim

et al., 2022) is designed to address denoising scenar-

ios where the noise model is strictly Poissonian, often

relevant in medical imaging and photon-limited imag-

ing environments. The model for PURE (Kim et al.,

2022) is expressed by:

y = x + n

(4)

VISAPP 2025 - 20th International Conference on Computer Vision Theory and Applications

548

where x ∈ R

denotes the true signal, y ∈ R

the observed image, and n

∈ R

represents Pois-

son noise, which is signal-dependent, differing from

Gaussian noise.

The PURE (Kim et al., 2022) estimator for the

mean squared error (MSE) of an estimator h(y) of x,

considering Poisson noise, is given by:

PU RE

(h(y)) =

∑

i=1

(y) − y

log(h

(y))) (5)

This estimator effectively leverages the log-

likelihood of Poisson-distributed data, providing a

robust framework for noise estimation and image

restoration under Poisson noise conditions.

2.3 Poisson Unbiased Risk Estimator

(PURE) and Poisson-Gaussian

Unbiased Risk Estimator (PGURE)

Following the Gaussian noise scenario and inspired

by (Luisier et al., 2011), we extend our approach to

address mixed noise conditions commonly encoun-

tered in medical imaging and other photon-limited

imaging applications. PURE (Kim et al., 2022) and

PGURE provide frameworks to handle purely Pois-

son noise and a combination of Poisson and Gaussian

noise, respectively.

PGURE, in particular, is described by the follow-

ing loss function, adapted for noise levels that are not

known beforehand and may vary spatially or tempo-

rally across the image:

PGURE

(h(y)) =

∑

i=1

(y) − y

log(h

(y)))

−

∑

i=1

δh

(y)

δy

(6)

This formulation incorporates the Bayesian ap-

proach to dynamically estimate both the parameters

of Poisson (λ) and Gaussian (σ

) noise components,

allowing for a more precise and adaptable denoising

process.

2.4 Monte-Carlo SURE (MC-SURE)

MC-SURE is a Monte Carlo method proposed by Ra-

mani et al. (Ramani et al., 2008) to estimate the di-

vergence and, consequently, the SURE loss.

Assume

b ∼ N

0,1

∈ R

is a Gaussian vector which

is independent of n or y. Ramani et al(Ramani et al.,

2008) show that,

∑

i=1

δh

(y)

δy

= lim

ε→0





h(y + ε

b) − h(y)



(7)

Therefore, by applying this eq 7 to the divergence

term in eq 2:

∑

i=1

δh

(y)

δy

≈

εN

(h(y + ε

b) − h(y)) (8)

Here,

is the transpose of

b, and ε is a small

positive value to approximate the limit.

3 METHODS

This section outlines our innovative approach for un-

supervised image denoising, leveraging a diffusion-

based model (Ho et al., 2020) for dynamic noise

estimation combined with Bayesian formulations of

SURE, PURE, and PGURE for training our denoiser.

Our method signiﬁcantly enhances the adaptability

and effectiveness of deep learning denoisers in han-

dling various real-world noise types without the need

for paired clean and noisy images.

3.1 Noise Estimation Using Diffusion

Models

Our approach utilizes a diffusion model (Ho et al.,

2020) as a dynamic noise estimator, which is trained

to predict both the type and level of noise directly

from noisy images. This model operates by gradually

adding noise to a clean image and learning to reverse

this process, thereby predicting the noise characteris-

tics at each step.

For Gaussian noise, the model adds and reverses

noise as follows:

Diffusion: x

t+1

1 − β

ε, ε ∼ N (0, I),

(9)

Reverse: x

t−1

−

, t)

1 − β

, (10)

For Poisson noise, the diffusion equations adapt to

the signal-dependent nature:

Diffusion: x

t+1

1 − β

∼ Poisson(λ), (11)

Reverse: x

t−1

−

, t)

1 − β

(12)

where β

are the variance schedules, ε and ε

rep-

resent Gaussian and Poisson noise, respectively, and

, λ

are the noise levels predicted by the model.

From Noise Estimation to Restoration: A Uniﬁed Diffusion and Bayesian Risk Approach for Unsupervised Denoising

549

Noise Type and Level Prediction

Within the framework of the diffusion model (Ho

et al., 2020), the noise type (e.g., Gaussian, Poisson)

and its corresponding level (parameters such as σ for

Gaussian or λ for Poisson) are predicted by an auxil-

iary neural network module:

σ,

λ = f

, t) (13)

where f

represents the neural network trained to

predict noise parameters based on the diffused image

and timestep t. This prediction enables tailoring

the denoising process to the speciﬁc characteristics of

the noise, enhancing the effectiveness of subsequent

denoising steps.

3.2 Bayesian SURE, PURE, and

PGURE

Utilizing the estimated noise parameters, we com-

pute the Bayesian versions of the SURE, PURE, and

PGURE losses for training our denoising network.

These losses adapt to the estimated noise levels and

types, providing a ﬂexible framework for training un-

der varying noise conditions.

Custom Bayesian Loss Formulations

To address the variations in noise type and intensity,

we introduce custom Bayesian loss functions that dy-

namically adjust based on the estimated noise charac-

teristics:

Bayesian SURE (BSURE) is designed for Gaus-

sian noise environments and is formulated as:

BSURE

= MSE(y, ˆy) − σ

+ 2σ

· div(ˆy, y)

where MSE is the mean squared error, σ is the esti-

mated noise level, ˆy is the denoised image, y is the

noisy image, and div represents the divergence esti-

mated via a Monte Carlo approach.

Bayesian PURE (BPURE) applies to Poisson

noise conditions:

BPURE

= ˆy − y log(ˆy) + λ − y log(λ)

where λ is the estimated Poisson noise level.

Bayesian PGURE (BPGURE) is used for mixed

noise scenarios, combining the features of BSURE

and BPURE.

These loss functions are weighted dynamically

based on the predicted noise type, ensuring optimal

denoising performance across different imaging con-

ditions. This approach not only enhances the gener-

alizability of the model but also tailors the denoising

process to effectively handle the speciﬁc noise char-

acteristics present in medical imaging, where noise

types can vary signiﬁcantly.

3.3 Modiﬁed Bayesian SURE

(Bayesian-SURE)

Our research introduces a Bayesian adaptation of

the SURE (Metzler et al., 2020) framework, termed

Bayesian-SURE, which incorporates a prior distribu-

tion on the noise level, allowing for a dynamic estima-

tion process that is more robust in practical settings

where the noise level might not be known a priori.

This approach utilizes a Bayesian inference method

to estimate the noise variance σ

dynamically:

Bayesian-SURE

(h(y)) =

||y − h(y)||

−

∑

i=1

δh

(y)

δy

(14)

Here,

represents the estimated noise variance

derived from the Bayesian posterior, enhancing the

ﬂexibility and adaptability of the SURE method to

varying noise conditions.

3.4 Enhanced Monte-Carlo SURE

(MC-SURE)

In our project, we propose a modiﬁed Monte Carlo

SURE estimator to enhance the accuracy and reduce

the variance of the divergence estimation, crucial for

effective denoising performance. The traditional MC-

SURE, as described by Ramani et al. (Ramani et al.,

2008), relies on a single Gaussian perturbation vec-

tor

b to estimate the divergence term crucial for the

SURE loss calculation.

Our enhancement involves averaging multiple in-

dependent estimations of the gradient, each derived

from a distinct Gaussian vector. This modiﬁcation is

inspired by the Central Limit Theorem, which sug-

gests that averaging a set of independent estimates re-

duces variance, leading to a more robust and stable

estimator. The modiﬁed equation is as follows:

∑

i=1

δh

(y)

δy

≈

MεN

∑

j=1

(h(y + ε

)− h(y)) (15)

where M is the number of independent Gaussian vec-

tors

, each sampled anew for the estimation. This

approach mitigates the noise in the gradient estima-

tion by averaging over multiple perturbations, thus

leading to a more accurate and reliable estimate of the

divergence.

This modiﬁcation not only enhances the reliabil-

ity of the SURE loss estimate but also stabilizes the

optimization process in iterative denoising methods,

potentially resulting in higher quality reconstructions

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550

and improved generalization across different noise

conditions.

3.5 Modiﬁed Bayesian PURE

(Bayesian-PURE)

To enhance the PURE framework, we introduce a

Bayesian adaptation, termed Bayesian-PURE, which

incorporates Bayesian principles to dynamically esti-

mate the parameters of the Poisson distribution, par-

ticularly the rate parameter λ. This modiﬁcation al-

lows for adapting to varying noise levels across dif-

ferent image regions, enhancing the estimator’s ﬂexi-

bility and accuracy in practical imaging scenarios.

The Bayesian-PURE is formulated as follows:

Bayesian-PURE

(h(y)) =

∑

i=1

(y) − y

log(h

(y)))

∑

i=1

(λ

− y

log(λ

))

(16)

Here, λ

represents the estimated Poisson rate for

each pixel, derived from a Bayesian posterior that ac-

counts for the observed data. This approach not only

improves the adaptability of the estimator to differ-

ent noise conditions but also enhances the accuracy

of denoising in environments where noise character-

istics may not be uniform or are unknown a priori.

3.6 Optimization of Deep Denoisers via

Enhanced SURE-Derived Losses

The integration of Stein’s Unbiased Risk Estimator

(SURE) and its variants, including Poisson Unbiased

Risk Estimator (PURE) and Poisson-Gaussian Unbi-

ased Risk Estimator (PGURE), has signiﬁcantly ad-

vanced the unsupervised optimization of deep neural

network (DNN)-based denoisers. Our work extends

these methodologies by incorporating Bayesian prin-

ciples, which dynamically adjust to the noise charac-

teristics estimated from the data, thereby eliminating

the need for pristine ground truth images—a common

limitation in supervised learning paradigms.

We have developed modiﬁed Bayesian SURE,

PURE, and PGURE frameworks, which employ a

Bayesian approach to dynamically estimate noise pa-

rameters and apply these estimations to optimize the

training process of DNNs. These modiﬁcations al-

low for adaptive loss functions that are tailored to the

estimated type and level of noise, enhancing the ﬂexi-

bility and effectiveness of the denoising process. The

Bayesian-enhanced loss functions are deﬁned as fol-

lows:

Bayesian

(y)) =

∑

j=1

(

∥y

( j)

− h

( j)

)∥

−

(

( j)

)



( j)

+ ε

( j)

) − h

( j)

)



)

. (17)

where M denotes the batch size, y

( j)

represents the

j-th noisy image in the batch,

is the dynamically

estimated noise variance for the j-th image, and

( j)

is an auxiliary Gaussian perturbation vector indepen-

dent of the noise inherent in y. This reformulation not

only accounts for the direct error and the noise vari-

ance adjustment but also incorporates a Monte Carlo

estimation of the divergence term, providing a robust

and adaptive framework for the MSE, which is typi-

cally inaccessible in unsupervised settings.

Our experiments demonstrate that this approach

not only streamlines the training process by remov-

ing the necessity for clean data but also signiﬁcantly

enhances the neural network’s ability to generalize

from noisy inputs. By effectively learning to de-

noise through a self-supervised learning framework,

our models achieve superior performance across var-

ious noise conditions, demonstrating robustness and

adaptability in real-world denoising tasks.

4 EXPERIMENTS AND RESULTS

In this section, we evaluate our proposed Bayesian-

enhanced diffusion model (Ho et al., 2020) and

DnCNN (Zhang et al., 2017b) framework on a chal-

lenging MRI dataset and compare its performance to

existing denoising methods. We ﬁrst describe the

dataset and preprocessing steps, followed by prelim-

inary experiments with traditional methods. We then

present the results of our Bayesian approach under

various noise conditions and provide a detailed anal-

ysis of its performance.

4.1 Dataset and Preprocessing

We use fully-sampled 3T knee MRI scans from 22

subjects (11 males and 11 females) as described in

(Anonymous, 2013). Each subject’s volume is seg-

mented into 320×320×256 matrices and sliced into

320×256 axial planes. MRI acquisition was per-

formed using a 3T whole-body scanner, and raw k-

space data were preserved for authenticity.

From these volumes, we generated both axial and

coronal view PNG images for training and evalua-

tion. We used 1000 axial and 1000 coronal images for

training, with 100 images per view for testing. This

From Noise Estimation to Restoration: A Uniﬁed Diffusion and Bayesian Risk Approach for Unsupervised Denoising

551

setup ensures a diverse set of anatomical variations

and noise conditions.

4.2 Preliminary Experiments with

Traditional Methods

Before evaluating our Bayesian approach, we con-

ducted preliminary experiments using methods such

as SURE (Metzler et al., 2020), eSURE (Zhussip

et al., 2019), PURE (Kim et al., 2022), ePURE (Kim

et al., 2022), Noise2Noise (N2N) (Lehtinen et al.,

2018a), BM3D (Dabov et al., 2007), and DnCNN

(Zhang et al., 2017b) trained with standard MSE and

known ground truth. We tested these methods on con-

trolled Gaussian noise levels (σ = 25 and σ = 50) for

both axial and coronal views.

The Peak Signal-to-Noise Ratio (PSNR) results

are presented in Table 1. As shown, eSURE (Zhus-

sip et al., 2019) and N2N methods perform strongly

under known Gaussian conditions, achieving high

PSNR values.

These preliminary results highlight the strengths

and limitations of traditional methods. While some

methods excel under known, controlled conditions,

they are not as robust when noise characteristics differ

from assumptions.

4.3 Bayesian-Enhanced Diffusion

Model Evaluation

We now evaluate our Bayesian-enhanced diffusion

model integrated with DnCNN (Zhang et al., 2017b)

under various unknown noise conditions (Gaussian,

Poisson, and mixed). Unlike the preliminary experi-

ments, our approach does not assume prior knowledge

of noise parameters.

Table 2 summarizes PSNR and SSIM results un-

der unknown Gaussian and Poisson noise levels, as

well as a mixed scenario. Our Bayesian approach

achieves notably higher PSNR and SSIM compared

to baseline methods, demonstrating its adaptability.

To visually illustrate these improvements, Fig-

ure 1 shows denoised axial views under Gaussian

noise. The Bayesian-enhanced model restores ﬁne de-

tails and texture more faithfully than baseline meth-

ods.

Figure 2 highlights denoising performance on

coronal views. Again, our approach demonstrates ro-

bustness and edge ﬁdelity, even under higher noise

levels.

Figure 1: Denoised results for axial views under Gaussian

noise (σ = 25 and 50). Our Bayesian model preserves de-

tails and edges more effectively.

Figure 2: Denoised results for coronal views under Gaus-

sian noise (σ = 25 and 50). The proposed method maintains

structural details better than competitors.

4.4 Visualizing Results on Poisson and

Mixed Noise

To further assess performance in complex scenarios,

we tested on Poisson and mixed noise. Figure 3 pro-

vides a comparison under Poisson noise at different

intensities using ePURE, and Figure 4 shows results

under Gaussian, Poisson, and mixed noise types with-

out prior knowledge of noise parameters. Our model

adapts seamlessly, producing high-quality reconstruc-

tions across all conditions.

4.5 Mixed Noise Scenarios and Gradual

Intensity Changes

In practical MRI settings, noise proﬁles may vary

across scans or within a single volume. Figure 5 illus-

trates our model’s performance on mixed noise with

gradually increasing intensity (from σ = 10 to 50 and

λ = 0.2 to 1.0). Even as noise intensity changes,

the Bayesian-enhanced approach retains stable per-

formance and reconstructs subtle structures that other

methods fail to recover.

Finally, Table 3 presents PSNR and SSIM results

under Poisson noise for ePURE, further validating the

competitiveness and adaptability of our approach.

VISAPP 2025 - 20th International Conference on Computer Vision Theory and Applications

552

Table 1: PSNR results of blind denoisers in preliminary experiments on 3T Knee MRI. Higher is better.

3T Knee MRI Axial View

Methods BM3D DnCNN-SURE DnCNN-SURE* DnCNN-N2N DnCNN-eSURE DnCNN-MSE

σ = 25 29.10 31.56 29.00 33.96 33.96 29.20

σ = 50 27.75 31.55 26.07 31.53 31.63 26.22

3T Knee MRI Coronal View

Methods BM3D DnCNN-SURE DnCNN-SURE* DnCNN-N2N DnCNN-eSURE DnCNN-MSE

σ = 25 29.10 32.55 29.00 32.46 32.56 30.82

σ = 50 27.75 28.75 26.07 28.86 29.99 28.83

Table 2: PSNR and SSIM results of the Bayesian-enhanced diffusion model on MRI data. The method adapts to unknown

and mixed noise scenarios.

Metrics σ = 25 σ = 50 λ = 0.5 λ = 1.0

PSNR 35.05 32.80 33.25 30.00

SSIM 0.95 0.92 0.94 0.90

Figure 3: Visual comparison under Poisson noise at varying

intensities using ePURE. Our Bayesian approach adapts to

different noise levels, enhancing image ﬁdelity.

Table 3: PSNR and SSIM results for ePURE on 3T Knee

MRI Coronal View under Poisson noise.

Noise Level PSNR SSIM

λ = 0.5 31.68 0.934

λ = 1.0 32.45 0.947

4.6 Discussion of Results

Our experiments demonstrate that the Bayesian-

enhanced diffusion framework outperforms tradi-

tional methods that rely on known noise models.

By dynamically estimating noise characteristics, the

model adapts to diverse conditions without ground

truth. The result is a more ﬂexible, generalizable de-

noising tool suitable for real-world MRI scenarios.

The visual and quantitative evidence suggests that

this approach maintains structural integrity and detail

ﬁdelity in conditions that break assumptions made by

Figure 4: Denoised results for Gaussian, Poisson, and

mixed noise (top to bottom) with unknown parameters. Our

method generalizes well, delivering consistent quality.

classical methods. Consequently, it sets a new stan-

dard for unsupervised denoising under complex, vari-

able noise patterns.

5 CONCLUSION

This work presents a novel unsupervised learning

framework for MRI denoising that integrates an en-

hanced diffusion model with a dynamically trained

Deep Convolutional Neural Network (DnCNN)

(Zhang et al., 2017b). By employing adaptive loss

functions that adjust to dynamically estimated noise

characteristics, our approach facilitates robust denois-

ing across a wide range of conditions without requir-

From Noise Estimation to Restoration: A Uniﬁed Diffusion and Bayesian Risk Approach for Unsupervised Denoising

553

Figure 5: Denoised results for mixed noise with gradually increasing intensity. Our model maintains robust denoising quality

despite evolving noise characteristics.

ing prior noise distribution knowledge. Experimen-

tal results validate that our method outperforms tradi-

tional techniques, particularly in complex, real-world

medical imaging scenarios. It achieves high ﬁdelity in

noise reduction while preserving essential image de-

tails, setting new benchmarks in both quantitative and

visual performance.

Future efforts will focus on applying this frame-

work to additional imaging modalities and incorpo-

rating cutting-edge neural architectures like genera-

tive adversarial networks (GANs) (Goodfellow et al.,

2014), potentially redeﬁning the standards for medi-

cal image processing. Our results highlight the trans-

formative potential of advanced machine learning in

enhancing diagnostic accuracy and expanding clini-

cal applications, laying a robust groundwork for fu-

ture innovations in medical imaging technology.

REFERENCES

Anonymous (2013). Creation of fully sampled mr data

repository for compressed sensing of the knee. Proc.

SMRT 22nd Annu. Meeting.

Burger, H. C., Schuler, C. J., and Harmeling, S. (2012).

Image denoising: Can plain neural networks compete

with bm3d? In IEEE Conference on Computer Vision

and Pattern Recognition (CVPR), pages 2392–2399.

Cherry, S. R., Sorenson, J. A., and Phelps, M. E. (2012).

Physics in nuclear medicine. Elsevier Health Sci-

ences.

Dabov, K., Foi, A., Katkovnik, V., and Egiazarian, K.

(2007). Image denoising by sparse 3-d transform-

domain collaborative ﬁltering. IEEE Transactions on

Image Processing, 16(8):2080–2095.

Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B.,

Warde-Farley, D., Ozair, S., Courville, A., and Ben-

gio, Y. (2014). Generative adversarial networks.

arXiv.

Ho, J., Jain, A., and Abbeel, P. (2020). Denoising diffusion

probabilistic models.

Jalata, I. K., Khan, R., and Nakarmi, U. (2024). Learn-

ing from oversampling: A systematic exploitation of

oversampling to address data scarcity issues in deep

learning- based magnetic resonance image reconstruc-

tion. IEEE Access, 12:97621–97629.

Kim, H., Yie, S. Y., Chun, S. Y., and Lee, J. S. (2022). Pure-

comb: Poisson unbiased risk estimator based ensem-

ble of self-supervised deep denoisers for clinical bone

scan image. In IEEE 19th International Symposium on

Biomedical Imaging (ISBI), pages 1–5, Kolkata, India.

Kim, K., Soltanayev, S., and Chun, S. Y. (2020). Unsuper-

vised training of denoisers for low-dose ct reconstruc-

tion without full-dose ground truth. IEEE Journal

on Selected Topics in Signal Processing, 14(6):1112–

1125.

Lehtinen, J., Munkberg, J., Hasselgren, J., Laine, S., Karras,

T., Aittala, M., and Aila, T. (2018a). Noise2noise:

Learning image restoration without clean data.

Lehtinen, J., Munkberg, J., Hasselgren, J., Laine, S., Kar-

ras, T., Aittala, M., and Aila, T. (2018b). Noise2noise:

Learning image restoration without clean data. In

Proc. of the 35th Int. Conf. on Machine Learning

(ICML), pages 2965–2974.

Luisier, F., Blu, T., and Unser, M. (2011). Image denoising

in mixed poisson–gaussian noise. IEEE Transactions

on Image Processing, 20(3):696–708.

Manj

on, J. V. and Coupe, P. (2019). Mri denoising using

deep learning and non-local averaging. arXiv.

VISAPP 2025 - 20th International Conference on Computer Vision Theory and Applications

554

Metzler, C. A., Mousavi, A., Heckel, R., and Baraniuk,

R. G. (2020). Unsupervised learning with stein’s unbi-

ased risk estimator. arXiv preprint arXiv:1805.10531.

Ramani, S., Blu, T., and Unser, M. (2008). Monte-carlo

sure: A black-box optimization of regularization pa-

rameters for general denoising algorithms. IEEE

Transactions on Image Processing, 17(9):1540–1554.

Ulyanov, D., Vedaldi, A., and Lempitsky, V. (2018). Deep

image prior. In IEEE Conference on Computer Vision

and Pattern Recognition, pages 9446–9454.

Ulyanov, D., Vedaldi, A., and Lempitsky, V. (2020). Deep

image prior. International Journal of Computer Vi-

sion, 128(7):1867–1888.

Zhang, K., Zuo, W., Chen, Y., Meng, D., and Zhang, L.

(2017a). Beyond a gaussian denoiser: Residual learn-

ing of deep cnn for image denoising. IEEE Transac-

tions on Image Processing, 26(7):3142–3155.

Zhang, K., Zuo, W., Chen, Y., Meng, D., and Zhang, L.

(2017b). Beyond a gaussian denoiser: Residual learn-

ing of deep cnn for image denoising. IEEE Transac-

tions on Image Processing, 26(7):3142–3155.

Zhussip, M., Soltanayev, S., and Chun, S. Y. (2019). Ex-

tending stein’s unbiased risk estimator to train deep

denoisers with correlated pairs of noisy images. In

Proceedings of the 33rd Conference on Neural In-

formation Processing Systems (NeurIPS), Vancouver,

Canada.

From Noise Estimation to Restoration: A Uniﬁed Diffusion and Bayesian Risk Approach for Unsupervised Denoising

555