L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
Authors: Weihan Li
Linyun Zhou
YangJian
Shengxuming Zhang
Xiangtong Du
Xiuming Zhang
Jing Zhang
ChaoqingXu
Mingli Song
Zunlei Feng
Venue: ICML 2025 poster (2025)
Keywords: Diffusion Model
Contrastive Learning
Multi-label Segmentation
Pathological slides
Primary area: applications->computer_vision
TL;DR: We propose a contrastive learning framework based on Laplace diffusion, with theoretical proof and quantitative validation. The model achieves accurate cross-scale multi-label segmentation of pathological images under limited supervision.

Abstract: Pathology image segmentation plays a pivotal role in artificial digital pathology diagnosis and treatment. Existing approaches to pathology image segmentation are hindered by labor-intensive annotation processes and limited accuracy in tail-class identification, primarily due to the long-tail distribution inherent in gigapixel pathology images. In this work, we introduce the Laplace Diffusion Model, referred to as L-Diffusion, an innovative framework tailored for efficient pathology image segmentation. L-Diffusion utilizes multiple Laplace distributions, as opposed to Gaussian distributions, to model distinct components—a methodology supported by theoretical analysis that significantly enhances the decomposition of features within the feature space. A sequence of feature maps is initially generated through a series of diffusion steps. Following this, contrastive learning is employed to refine the pixel-wise vectors derived from the feature map sequence.  By utilizing these highly discriminative pixel-wise vectors, the segmentation module achieves a harmonious balance of precision and robustness with remarkable efficiency. Extensive experimental evaluations demonstrate that L-Diffusion attains improvements of up to  7.16\%,  26.74\%,  16.52\%, and  3.55\% on tissue segmentation datasets, and  20.09\%,  10.67\%,  14.42\%, and  10.41\% on cell segmentation datasets, as quantified by DICE, MPA, mIoU, and FwIoU metrics. The source are available at https://github.com/Lweihan/LDiffusion.

L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
Weihan Li Linyun Zhou 12 Jian Yang' Shengxuming Zhang'
Xiangtong Du Xiuming Zhang*
Jing Zhang Chaoqing Xu Mingli Song' 126
Zunlei Feng* 126
Abstract
Pladl Valne Valne Prubability Dunsty
300
Pathology image segmentation plays pivotal role in artificial digital pathology diagnosis and treat- ment. Existing approaches to pathology image segmentation are hindered by labor-intensive an- notation processes and limited accuracy tail- class identification, primarily due to the long-tail distribution inherent in gigapixel pathology im- ages. In this work, introduce the Laplace Dif- fusion Model, referred as L-Diffusion, an inno- vative framework tailored for efficient pathology image segmentation. L-Diffusion utilizes multi- ple Laplace distributions, as opposed to Gaussian distributions, to model distinct components-4 methodology supported by theoretical analysis that significantly enhances the decomposition of features within the feature space. A sequence of feature maps is initially generated through a series of diffusion steps. Following this, con- trastive learning is employed to refine the pixel- wise vectors derived from the feature map se- quence. By utilizing these highly discrimina- tive pixel-wise vectors, the segmentation mod- ule achieves harmonious balance of precision and robustness with remarkable efficiency. Ex- tensive experimental evaluations demonstrate that L-Diffusion attains improvements of up to 7.16%, 26.74% 74,, 16.52%, and 3.55% on tissue segmen- tation datasets, and 20.09%, 10.67%, 14.42%, and 10.41% on cell segmentation datasets, as quantified by DICE, MPA. mloU, and FwIoU metries. The source codes are available http://ggthub..comm////w/////i/p
100
Pivel Prehesiliyy Drndee
250
130
100
Diillusioon
Figure 1. A comparative analysis of latent feature distributions be- tween standard diffusion (a) and L-Diffusion (b). The latent feature distributions for individual components across various diffusion steps are denoted by violin plots in green, yellow, and cyan color.
1. Introduction
Pathology images encompass a wealth of multi-level tis- and cellular features, regarded the "gold standard" for cancer diagnosis. Pathologists meticulously examine and analyze the intricate relationships between diverse tu- mors and the characteristics of their components, including global Iesions, tissue proportions and distributions, as well as cellular morphology (McGenity et al., 2024).
Beyond the tumor itself, the tumor microenvironment prises complex array of elements, such surrounding blood vessels, tissues, and cells, all of which play pivotal roles in tumorigenesis, progression, metastasis, and treat- ment response. Consequently, numerous researchers have directed their efforts toward the segmentation of multi-level features within pathology images, aiming to enhance tumor diagnosis and microenvironment analysis. This, in turn, facilitates deeper understanding of the mechanisms under- lying tumorigenesis, progression, and metastasis (Zhao et al., 2021; Ye et al., 2023; Hosseini et al., 2024).
State Key Laboratory of Blockehain and Data Security, Zhe- jiang University "School of Software Technology, Zhejiang Uni- versity 'School of Medical Imaging, Xuzhou Medical Univer- sity "The First Affiliated Hospital, College of Medicine, Zhe- jiang University 'School of Computer and Computing Science, Hangzhou City University 'Hangzhou High-Tech Zone (Bin- jiang) Institute of Blockchain and Data Security. Correspon- dence to: Zunlei Feng <zunlcifenge zju.edu.en>>, Xiuming Zhang <xm zhang @ sdu.edd..n.>.
Consequently, researchers have devised advanced pathology image segmentation techniques to streamline the analysis of such intricate images. Prominent segmentation models,
Proceedingy of the thth International Conference Machine Learning, PMLR 267, 2025. Copyright 2025 by the author(s).

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L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
including U-Net (Ronneberger et al., 2015), DeepLab (L.- C. Chen et 2017) and Transformer (Atabansi et al., 2023), have demonstrated exceptional performance across spec- trum of medical image classification tasks. Prior studies have also successfully integrated those deep learning mod- els into pathology tissue segmentation (Ye et al., 2023) and cell segmentation (Hayakawa et al.. 2021).
thereby reducing the dependency on annotated data. The pronounced differentiation in component distributions fur- ther mitigates the model's learning challenges, particularly for tail components.
Thus, our primary contribution lies in the introduction of the first Laplace diffusion model, offering a novel perspective on leveraging component distributions across diffusion steps for efficient pathology image segmentation. The devised pixel latent vector contrastive learning mechanism enhances the differentiation of component distributions, significantly improving segmentation performance, especially for tail components. A detailed theoretical analysis is provided to substantiate the practicality of the proposed L-Diffusion. Ex- tensive experiments demonstrate that L--Diffusion achieves superior accuracy and robustness on par with existing works across multiple benchmarks.
Pathology images exhibit three distinct characteristics: gi- gapixel resolution, broad spectrum of scales, and long- tail distribution. The annotation of gigapixel pathology images demands considerable time and effort from patholo- gists (Davri et al., 2022; Mahmood et al., 2023). Addition- ally, diverse pathological features often manifest at varying scales within the same image, necessitating models capable of capturing multi-scale information (Tarekegn et al., 2024). Furthermore, the imbalance in tissue type distributions com- plicates the extraction of features from tail categories (Ding et al., 2022), thereby intensifying the challenges of model training. In summary, current pathology image segmenta- tion tasks grapple with labor-intensive annotation processes or limited accuracy in identifying tail samples.
2. Preliminaries
DDPM (Ho et al., 2020) consists of two processes: the forward diffusion process, which progressively adds noise to the data to transform the complex data distribution into standard Gaussian distribution, and the counter diffusion process, which employs parameterized 0 neural network to iteratively reconstruct the data from the noise. We assume that a data zo satisfies the data distribution q()). expressed as To ~ ((<r)) then the forward and backward processes can be expressed as follows:
Motivated by the diffusion model's 's exceptional ability to model latent distributions, we introduce the Laplace Diffu- sion Model, referred to as L-Diffusion, for efficient pathol- ogy image segmentation in this work. In lieu of the standard Gaussian distribution, we employ multiple Laplace distri- butions to model distinct components. Thcoretical analysis demonstrates that the Laplace distribution is advantageous for broadening distribution disparities.
((11/21-1) N V 3,11,,
(1)
For the input original image, L-Diffusion initially trans- forms it into sequence of intermediate reconstructed fea- ture maps through T diffusion steps. Each reconstructed feature map is subsequently converted into grayscale im- age, thereby generating a new sequence of feature maps. Along the diffusion step axis, each pixel corresponds a vector U E 1xT, referred to as the pixel latent vector. Fol- lowing this, contrastive learning is employed to accentuate the distributional disparities among pixel latent vectors of different components.
Po(#,_11z) = N( o0(e) f)),
(2)
where po ( 124) represents the new generated data distri- bution at 1-th diffusion, 8 represents the noise intensity, μo and dg are the mean and variance used by the neural net- work to predict the distribution. Although we cannot obtain the inverted data distribution -( we can obtain the conditional probability distribution g(x+-- 1 (an,, ao) for given zo and 2, according to Bayes' Theorem (3) as follows:
As depicted in Fig. 1, the Laplace diffusion model, enhanced by contrastive learning, effectively highlights the distribu- tional divergences between distinct components while main- taining intra-component similarity as the diffusion steps progress. The highly differentiated pixel latent vectors, which exhibit distinct evolutionary patterns, enable the seg- mentation model to achieve both precision and robustness with remarkable efficiency.
((0)-1100)
10) = ( 20)
(3)
g(1e(20)
1 1- -āt-1 Ba,
Be =
1 04
pi( 2o) = /ot(1 (1 .
vai-18t
De +
Io. (4)
1 1 -a
1 1 1-āc
where or = = B1, ã. II ag From the above Eqn. (3), we extract the coefficients related to the unknown vari- able x;-1 and transform them into the standard format of the probability density function of gaussian distribution. The de- tailed derivation can be referred to Appendix (A). Therefore, We can go further and get the Eqn. (4),
noteworthy that each image comprises W x H pixel latent vectors. The abundance and diversity of pixel latent vectors in limited number of images suffice to capture the distributional characteristics of different components,

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L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
(a) Gaussian Distribution
(b) Luplace Distribution
Stop
Step 2
Step
Step 4
Step
Step
Step 2
Step 3
Step
Step 5
Step
Step 7
Step
Stop 9
Step 10
Step 6
Stop 7
Step
Stop 9
Step 10
224
apoplosis cell tumor cell background
250
apogiosis cell
cell
background
200
Exte
Lool
Pedd DExx (11222511)
Duttzsion Stops
Padl bades d0 5121512)
Duttosina Steps
Figure 2. The comparison between pixel value distribution of various components modeled using Gaussian and Laplace distributions. For each diffusion step, the reconstructed image and its corresponding pixel value distribution are provided. The components modeled by Laplace distributions exhibit greater distinguishability compared to those modeled by Gaussian distributions.
Moreover, Ia can be derived from and oz. Let =g (xe, I)
detailed exposition of the influence of data distribution dif- ferentiation in diffusion model is provided in Appendix (A).
be the noise predicted by neural network at the t-th step noise reduction. Then we can then transform Eqn. (5) into 2g denoted by 2, and 20 t) and substitute it into Eqn. (4). We can then derive the mean of the predictive distribution consisting of 2, and f, expressed in Eqn. (6),
3.1. Laplace Distribution is More Differentiated
To differentiate the data distributions of distinct regions within the image, it is essential to select a new distribution capable of amplifying the disparities between data distri- butions of various categories across the entire slide, while preserving the intrinsic distribution characteristics within each component. Through extensive experimentation, have determined that the Laplace distribution fulfills these requirements. To substantiate that this distribution is more suitable for pathology image classification than the Gaussian distribution (Gauss & Waterhouse, 2018), we will analyze from two perspectives: theoretical derivation and qualitative comparison. Our focus lies on the gradient of the Gaus- sian distribution Vpv(x) and the gradient of the Laplace distribution Vpc(x), whose equations as follows:
and then calculate the generated data distribution as follows:
It = VaLio + vI - āi 20(2,, t).
(5)
3r 20( t)).
po(x), 1) Va,
(It
(6)
V1 at
3. Laplace Distribution Differentiation
The essence of differentiated representation of data distri- butions in diffusion model can be broadly categorized into two scenarios. Firstly, when two categories of data possess markedly distinct features (such as color, shape, or spatial position) the disparity in the means of their distributions should be substantial enough to minimize the overlap be- tween the distributions. Secondly, in cases where no clear distinguishing features exist between two categories, the gra- dient of the distributions should sufficiently pronounced to amplify the impact of perturbations on the probabili- ties, thereby enhancing the separation of the data. more
d 1 VpN(x) dr <2T0"
x²2
eapp
a (x()):
20
d
1
|2||
sign(a))
Vpc(x) dr eapp
pc(x)
/2b
b

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L-Diffusion: Laplace Difflssin for Efficient Pathology Image Segmentation
where b denotes scale parameter of Laplace distribution.
derivation of the multiple-componeet Laplace distribution modeling, which can be found in Appendix (A).
As evidenced by the preceding equation, the gradient of the Gaussian distribution exhibits proportionality to whereas the gradient of the Laplace distribution is proportional to sign(z)). When I R 0, (xr( demonstrates a smooth progression, with the gradient intensifying as a diverges from the origin. In contrast, V2c(2) undergoes abrupt changes, particularly as the noise value x approaches zero, rendering the Laplace distribution markedly more sensitive to its response to noise. As extends further from the origin, the Gaussian distribution exhibits gradual decay in its tail, with (z) diminishing in a relatively subdued manner. Conversely, the tail of the Laplace distribution decays more swiftly, and (a) diminishes even more precipitously in the presence of substantial noise. Moreover, akin to the Gaussian distribution, which perturbs the original data by augmenting its variance, the introduction of Laplacian noise preserves the morphological structure of the original data. It merely alters the concentration of the noise distribution, signifying an enhanced sensitivity to extreme values.
Through T diffusion steps, we obtain a sequence of inter- mediate reconstructed feature maps [r1, "2.....,'t,..................... rrl, where r2 E TR Txx3Xx33 and W and H represent the width and height of zo. respectively. Each reconstructed feature map rs subsequently transformed into a grayscale im- age ft = RGB2Gray(ra), forming a sequence of feature maps f21, Åt, ,......fr., frl, with fr RW*H** Along the diffusion step axis, each pixel corresponds to vector V 1I referred to as the pixel latent vector.
Pixel Latent Vector Contrastive Learning. To en- hance the distributional similarity among positive pairs Positive(t ) and the distributional disparities among negative pairs Negative( uf contrastive learning is em- ployed. The contrastive learning loss function CORT is defined follows:
Positive vg.)
k.k CRT = log Positive(uf, r
+ Negative("%, oq"")"
Furthermore, to visually demonstrate the superiority of the Laplace distribution, we applied both Gaussian and Laplace distributions to the inverse diffusion process of the same im- age over 10 steps, observing the variations in pixel intensity across different regions. In the context of melanocytoma histopathology patch, 10 sampling maps and their corre- sponding pixel distributions are illustrated in Fig. 2. For the pixel distribution maps, the X-axis represents the sample number (starting from 0), the Y-axis denotes the pixel count of the image, and the Z-axis indicates the range of gray values. The gray points signify the background, the pur- ple points represent tumor cells. and the blue points denote apoptotic cells. It is evident that the pixel distribution under the Gaussian model appears more uniform. In contrast, the Laplace distribution facilitates a clearer separation of pixels belonging to distinct categories.
N
Ka
Negative(Uf) (uk, ux(')
Σ Σ exp(sim(12 )/T),
n' i=1
Positive(e ui)) = exp(sim(0f.22)/ //)/
n n n',
where N represents the number of components, and Kn' denotes the sampling number of vector samples for the n' component.
By combining the MSE loss LMSE and the contrastive learning loss ck.k' Co the distributions of various components CCRT
in the intermediate feature maps become highly differen- tiated, as illustrated in Fig. 1. This differentiation signifi- cantly reduces the identification difficulty for the subsequent segmentation module. It is important to note that the con- ck.k' trastive learning loss CCRT is applicable only to subset of pathology images with available annotations.
4. L-Diffusion for Efficient Pathology Image Segmentation
Sequence Feature Enhanced Segmentation. Utilizing the enhanced feature maps [F' fe...., P....,, , frl refined through contrastive learning, the segmentation network Fseg ( generates the prediction results y as follows:
For the original image zo. comprising N distinct compo- nents, we model it using N independent Laplace distribu- tions, denoted go(xo), q (zo)...., qN (zo). During the diffusion process, the mean squared error (MSE) loss for the 1-th step is expressed as follows:
y Feeg (171, 82
The DICE loss between the predicted map y' and the ground truth is employed to train the segmentation network, de- fined as:
LMSE = Eno.rst [|le - [|le-ea(se,1 (211)
2y yy DDi .)= =
y + y
where E represents the added Laplace noise, and ea (2t,t) denotes the predicted noise derived from the intermediate reconstructed feature map 24 using model parameters 6. For clarity in presenting the methodology, we omit the detailed
Through the two-stage training framework combining L- Diffusion and the segmentation network, the pathology im- age is effectively segmented into its distinct components.

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L-Diffuusin: Laplace Diffusion for Efficient Pathology Image Segmentation
Table Quantitative tissue segmentation performance (%) comparison. Bold and underling indicate the best and second-best performance.
CRCD
PUMA
BCSS
MODEL
DICE
MPA
MIOU
FwloU
DICE
MPA
MIOU
FwloU
DICE
MPA
MIOU
FwloU
FASTFCN
45.23
44.68
46.11
76.20
48.77
45.09
50.72
67.60
45.41
51.53
46.78
71.96
U-NET++
73.02
51.12
66.18
79.11
78.07
53.46
66.51
82.26
76.04
53.31
61.23
74.91
SWIN-UNET
70.08
52.22
63.27
84.11
69.46
52.39
55.40
80.42
66.24
52.85
61.54
84.32
SAMUS
63.94
62.45
55.82
77.93
61.24
61.29
53.92
82.91
62.68
59.26
53.34
79.58
SAMED
70.63
50.38
58.38
78.08
62.56
57.39
64.48
70.74
67.51
51.71
56.48
75.79
SAMPATH
77.54
66.70
63.65
86.28
84.95
57.79
66.30
83.92
78.10
62.83
67.44
87.12
UN-SAM
75.69
66.30
62.71
83.57
80,49
56.63
65.19
85.73
80.89
65.80
70.44
85.38
DEEPLABV3
73.12
58.49
49.18
82.26
73.36
53.00
53.51
81.43
67.75
52.76
57.83
87.62
DEEPLABV3+
77.04
58.14
52.80
81.88
80.85
58.41
48.01
88.55
86.31
56.53
50.19
84.30
DENSEASPP
76.18
67.39
60.50
77.71
76.24
60.02
59.33
72.77
70.88
64.53
54.68
81.35
BONUS
75.22
71.69
64.59
80.30
72.13
60.64
68.77
83.14
75.07
70.19
60.31
86.73
L-DIFFUSION
82.38
80.19
80.17
86.47
92.11
88.03
81.62
91.77
89.24
82.33
83.49
91.17
Improvement
+4.84
+12.80
+16.52
+0.19
+7.16
+26.74
+15.11
+3.22
+2.93
+ +17.80
+ +16.05
+3.55
Table Quantitative evaluation of cellular segmentation performance (%).
Metric calculations are only performed on foreground cells.
CRCD
PUMA
PANNUKE
MODEL
DICE
MPA
MIOU
FwloU
DICE
MPA
MIOU
FwloU
DICE
MPA
MIOU
FwloU
FASTFCN
43.04
60.25
32.86
73.41
39.03
62.87
31.28
74.15
44.51
68.73
30.58
66.52
U-NET++
73.73
82.17
30.06
65.93
74.02
75.34
34.68
75.17
36.88
81.96
25.89
71.09
SWIN-UNET
46.70
27.70
31.54
86.12
40.05
29.89
30.94
80.47
47.08
32.94
75.76
79.71
SAMUS
34.53
75.50
37.72
75.34
32.26
77.10
37.52
72.04
30.11
70.17
37.27
68.66
SAMED
70.85
61.21
34.93
69.66
66.88
64.57
31.93
73.02
72.60
61.33
26.59
67.95
SAMPATH
79.02
87.97
82.03
81.23
81.62
80.79
74.50
80.68
72.33
82.79
38.08
80.46
UN-SAM
78.53
85.27
81.79
80.36
79.57
74.99
68.81
79.12
70.48
80.77
75.42
84.57
DEEPLABV3
54.65
52.12
52.54
84.93
56.19
55.55
45.07
81.83
53.98
60.82
52.45
82.93
DEEPLABV3+
63.43
59.01
71.66
79.38
65.99
55.92
75.00
82.59
71.46
55.17
72.41
87.30
DENSEASPP
37.35
48.09
51.09
84.41
38.90
52.33
51.47
81.66
81.00
54.95
45.46
77.54
BONUS
75.33
68.67
60.42
79.84
78.44
75.49
64.53
82.14
80.33
60.58
69.22
85.97
L-DIFFUSION
96.11
94.94
92.62
95.34
88.57
90.38
86.19
83.13
94.78
93.46
90.18
92.18
Improvement
+20.09
+6.97
+10.59
+10.41
+6.95
+9.59
+11.19
+0.54
+13.78
+10.67
+14.42
+4.88
5. Experiment
sive details regarding these datasets are provided in Table 7 of Appendix (B). The evaluation metrics comprise MPA, DICE, mloU, and FWIoU, which collectively evaluate seg- mentation performance from the perspectives of pixel-wise accuracy, segmentation area, boundary precision, and class- specific analysis. It's noticed that the performance on cell only considering the cells, the reason of which is that back- ground has large proportation of whole slide image will disturb the cells segmentation performance measurement.
Datasets and Evaluation Metrics. We employ six dis- tinct tissue and cellular datasets to validate the segmentation capabilities of L-Diffusion. These datasets encompass: a colorectal cancer histopathology dataset provided by the Guangdong Provincial People's Hospi- tal (referred to as CRCD) (Ye et al., 2023), a melanoma histopathology dataset from the PUMA challenge (referred to as PUMA) (Schuiveling al., 2024). publicly ac- cessible dataset specifically curated for tissue segmenta- tion tasks in breast cancer pathology (referred to as BCSS) (Amgad et al., 2019), and publicly available dataset ded- icated to multi-class cellular segmentation (referred to as PanNuke) (Gamper et al., 2020). Furthermore, comprehen-
Models and Parameters. L-Diffusion comprises VAE encoder, a Laplace Scheduler, a U-Net noise prediction mod- ule, a DAE decoder, and a contrastive learning module. The image initially encoded into the latent space by the VAE, after which it is passed to the Laplace Scheduler along with

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L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
Image
FistFCN
U
Sain
SAMUS
SAMed
SAMPath
DeegLabe3
Deeplabn3+
DemeASPP
Figure Qualitative comparison tissue (upper row) and cellular (lower row) segmentation performance.
Table The ablation study on annotation ratio.
Table 4. Qualitative ablation study results.
Annotation Ratio
10%
20%
30%
50%
70%
100%
Contrastive Learning?
Data Distribution
Averaee Score on Tissue
DICE
MPA
mloU'
FwloU
DICE
19:95
59.59
83,51
86.19
91.62
92.11
x
Gaussian
15.33
14.17
13,31
23.26
MPA
20.00
55.12
82,93
85.73
87.95
88.03
Gaussian
17.41
21.61
16,91
29.76
mloU
19.91
54.96
79.86
80.02
80.54
81.62
x
Laplace
26.02
26.81
21.41
34.26
FwloU
33.06
71.54
89.46
89.67
90.31
91.77
Laplace
85.75
83.52
81.76
89.74
gains effectively validate the efficacy of leveraging compo- nent latent distributions for pathology image segmentation.
the time step to generate noise. This noisy representa- tion is then processed by the U-Net to predict the noise at step I, which is subsequently subtracted from the noisy im- age to yield the latent space sampling. The resulting latent representation is fed into the DAE to decode it back to its original dimensions. K2 is set to 100. We adopt the Con- vNeXT (Z. Liu al., 2022) the segmentation network. To Train Diffusion Model, we configure the batch size to 1, employ the Adam optimizer with learning rate of x 10-5, and typically set the number of sampling steps to 5 ~ 15, contingent upon the available GPU. In the contrastive learn-
Qualitative Comparison. Fig. 3 presents the qualitative vi- sualization, illustrating that L-Diffusion attains exceptional boundary segmentation accuracy in the tissue samples de- picted in the upper row. For cellular samples, L-DDiffusion not only achieves precise boundary segmentation but also ex- cels in accurately identifying tail-class cells, as highlighted by the yellow and cyan annotations. Additional visualiza- tion results are provided in Appendix (D)-(F).
ing module, the temperature т ranges from 0.05 ~ 0.1 to ensure effective sharpening of the distribution without gradi- ent explosion. In addition, train ConyNeXT, we configure the batch size to 32, employ the Adam optimizer with learning rate of 1 x 10-3
Performance for Distinet Components. The radar chart illustrates the quantitative assessment of segmentation per- formance across various methodologies for distinet tissue and cellular categories. As depicted in Fig. 4, it is evident that I.-Diffusion outperforms all existing methods across every tissue and cellular category, particularly excelling in the segmentation of components with lower proportions. This underscores L-Diffusion's 's proficiency in addressing long-tail distribution challenges within pathology images.
5.1. Comparison with SOTA Methods
In order to comprehensively verify the performance of the proposed model, we compared it with a variety of existing mainstream models including FastFCN (H. Wu et al., 2019), U-Net++ (Zhou et al., 2018), Swin-UNet (Cao et al., 2022), SAMUS (X. Lin et al., 2023), SAMed (K. Zhang & Liu, 2023), SAMPath (J. Zhang et al., 2023), DeepLabv3 (L.-
5.2. Performance Across Varied Annotation Ratios
To validate the efficiency of L-Diffusion under limited an- notations, we conduct an ablation study using varying anno- tation ratios on the PUMA tissue segmentation dataset. As illustrated in Table 3, it is evident that L-Diffusion achieves comparable performance even with only 30% of annotated samples. However, the segmentation module necessitates a sufficient number of annotated samples, thereby increasing the annotation demands of L-Diffusion. In future work, we aim to explore the minimal annotation data requirements.
C. Chen, 2017), DeepLabv3+ (L.-C. Chen al.. 2018), DeP (Yang et al., 2018), UN-SAM (Z. Chen al., 2024) and BONUS (Y. Lin et al., 2024).
Quantitative Comparison. The quantitative results for tis- sue and cellular segmentation are detailed in Table 1&2. L- Diffusion demonstrates a significant enhancement on both tissue and cell segmentation datasets. These substantial

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L- L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
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NOR (5,00))
EPI (1SI5)
(0811) MUC
TMM
PLA
CRCD- RisueTissue
(b) PUMA-Tissue
(c) BCSS-Tissue
(16500))
(1445%)
TUM
BLD
EPI
FLA (118%)
(3.099)
UTR
ADK
BID
(7.421g)
BLA
(9.19%)
(2.977))
STR
STO
(OLUSI))
6888
(1,909
50
(2omg)
COL
(3.0%)
16
(115555)
CER
(0.4240
(1,69)
(samg)
ESO
APO
NEU (000g))
HED
LYM 1919
(1275)
(159%))
(2.225)
(1.55))
LYM (32F)) (e) PUMA-Cell
OVA
KID
(2.109) LUN
LIV (2.62%)
(d) CRCD-Cell
(l) PanNuke-Ceel
UN-
Swin-Unnt
SAMUS
SAMed
SAMPath
- DeupLabu3
DeupLabv3
DensAASP
L-D-iifussio
Figure 4. A quantitative evaluation of segmentation performance across diverse methodologies for distinct tissue and cellular categories. Each axis of the radar chart represents a specific component category along with its corresponding proportion.
5.3. Ablation Study
Massacchusett--uuildie dataset (Mnih, 2013). The compet- ing methods encompass U-Net (Ronneberger et al., 2015), Uniformer (K. Li et al., 2023), UANet (J. Li al., 2024), and GLGF-Net (Fu al., 2024). For fair comparison, we employ widely recognized metrics in the remote sensing im- age segmentation domain, including IoU, F1, and Precision (Pre.). As illustrated in Table 6, L-Diffusion exhibits su- perior performance in remote sensing image segmentation, rivaling existing methodologies. Segmentation visualization results, detailed in Appendix (G), further demonstrate that L-Diffusion achieves comparable segmentation accuracy, particularly for tail-class objects such buildings. These experiments highlight the robust generalization and seg- mentation capabilities of L-Diffusion on large-scale images, especially for tail-class categories.
In this section, we conduct an extensive series of ablation studies on the critical components L-Diffusion, including Laplace distribution and pixel latent vector contrastive learning. Table presents the average performance metrics across three tissue datasets, revealing that the integration of the Laplace distribution with contrastive learning serves the cornerstone of I-DDifussion for pathology image segmen- tation. Fig. 5 illustrates that the latent feature distribution under the "contrastive learning Laplace distribution" con- figuration exhibits more pronounced distinctions between different tissue types. the diffusion steps progress, the data distribution within the same tissue type becomes in- creasingly cohesive, further validating the efficacy of com- bining contrastive learning with the Laplace distribution.
5.5. Comparison with Different Distributions
5.4. Generalization on Other Large-scale Image
We investigate the influence of different noise distributions on the average performance of diffusion models on three tis- sue segmentation datasets, focusing on three representative types: Cauchy (Lian et al., 2025), Student's t (X.-F. Wang et al., 2024), and Laplace. shown in Table 5, the Laplace distribution achieves the best overall performance. In con-
To evaluate the generalization prowess of L-Diffusion across other large-scale image datasets, we compare its segmentation performance with several state-of-the-art (SOTA) remote sensing image segmentation methods on the

---

L-Diiffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
(a) Gaussian Distribution
(b) Gaussian Distribution Contrastive Learning
130
12
14
15
(6) Laplace Distribution
Laplace Distribution + Contrastive Learning
Figure 5. A comparative analysis of latent feature distributions under various configurations, The latent feature distributions for individual components across multiple diffusion steps are represented by violin plots, distinguished by green, yellow, and cyan colors.
trast, the Cauchy distribution yields significantly lower DICE score and FwloU score. This can be attributed to its undefined expectation and variance, which severely hin- ders the stability of gradient- optimization. Student's distribution demonstrates promising segmentation accuracy, but suffers from a prohibitively high computational cost, likely due its more complex gradient behavior. Overall, the Laplace distribution maintains a strong balance between segmentation accuracy and computational efficiency.
Hayakawa et al., 2021; Feng al., 2021; Mahbod et al., 2024) and tissue segmentation (Salvi et al., 2021; Musulin et al., 2021; Ye et al., 2023). However, gigapixel pathology images exhibit multi-scale features and long-tail compo- nents, which result in significant annotation labor costs and limited accuracy in identifying tail-class samples.
Contrastive Learning. a pivotal approach in self- supervised learning, has achieved remarkable advancements in the field of computer vision in recent years. Researchers have extended the application of contrastive learning to diverse domains, including natural language processing (NLP), graph learning, and multi-modal learning (Le-Khac et al., 2020; Hu et al., 2024). Recently, several studies have integrated contrastive learning into diffusion models (Tian et al., 2024; Dalva & Yanardag. 2024; Xiao et al., 2024), utilizing it to amplify the representational distance between different classes. In this paper, we apply contrastive learning to enhance the distinction between pixel latent vectors of di different components modeled using Laplace distributions.
Table 5. Comparison of different noise distributions segmenta- tion performance.
Distribution
DICE (%)
FwloU (%)
Runtime (s)
Cauchy
16.25
20.33
7325
Student's
83.17
86.50
20440
Laplace
85.75
89.80
8882
Table 6. Generalization remote sensing image dataset.
Diffusion in Medical Image Analysis. Wu al. (J. Wu, Fu, et al., 2024; J. Wu, Ji, et al., 2024) introduced MedSegDiff, diffusion model-based approach for medical image seg- mentation. Webber et al. (Webber & Reader, 2024) utilized diffusion models for medical image reconstruction, enabling the production of high-quality images even in low-dose or rapid imaging scenarios. Kazerouni et al. (Kazerouni et al., 2023) given comprehensive survey of diffusson models in medical imaging. Additionally, several researchers (Oh & Jeong, 2023; He et al., 2024; Xu et al., 2024) have extended the application of diffusion models to pathology image gen- eration tasks, leveraging their exceptional capability for high-quality image synthesis.
Metrie
U-Net
Uniformer
UANet
GL.GF-Net
L-Diffusion
IoU
68.48
73.80
76.41
75.33
80,30
Fl
81.47
84.92
86.63
85.93
88.98
Pre.
80.09
87.60
87.94
85.03
96.52
6. Related Work
Pathology Image Segmentation plays a pivotal role in the diagnosis and treatment of cancer, while also foster- ing a deeper comprehension of the mechanisms underlying tumorigenesis, progression, and metastasis. Numerous stud- ies have utilized various segmentation models, such as U- Net (Ronneberger et al., 2015), DeepLab (L.-C. Chen et al., 2017) and Transformer (Atabansi et al., 2023), along with their variants, for pathology image segmentation (Y. Wu et al., 2022). Based on their segmentation objectives, these studies can be broadly classified into two categories: cell segmentation (Ciresan et al., 2012; D. Liu et al., 2019;
Diffusion in Segmentation. Amit et al. (Amit al., 2021) pioneered the integration of diffusion models into segmen- tation tasks, proposing the SegDiff model and exploring the application of diffusion models address image seg- mentation challenges. Bogensperger et al. (Bogensperger

---

L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
al., 2023) introduced an innovative image segmentation approach by merging core-bbaed models with diffusion models. Wang et al. (M. Wang et al., 2023) developed SegRefiner, which employs a discrete diffusion process to iteratively refine segmentation results. Xie et al. (Xie et al., 2024) utilized diffusion models to generate synthetic labeled data for segmentation tasks. To the best of our knowledge, no existing method has leveraged component distributions across diffusion steps for segmentation as we have accomplished.
sis. While our method demonstrates strong technical poten- tial, acknowledge broader ethical considerations beyond dataset access. These include the possibility of algorithmic bias affecting diagnostic outcomes across different patient groups, challenges in model interpretability for clinical prac- titioners, and concerns related to patient data privacy during inference and deployment.
The current version of L-Diffusion is intended solely for academic investigation and is not deployed in clinical set- tings. Any future application in real-world scenarios should be guided by clinical validation, domain- -spccific oversight, and compliance with relevant medical and regulatory stan- dards. We advocate for continued research into the safe, fair, and transparent use of Al systems healthcare.
Distribution Exploration Recent studies have explored how different noise distributions affect diffusion model per- formance. Hang et al. (Hang et al., 2024) show that the Laplace distribution, with its sharp peak and heavy tails, improves robustness outliers. Alexia et al. (Jolicoeur- Martineau et al., 2023) further compare Gaussian, T, and Uniform distributions, finding that smoother distributions lead to better image generation. However, these works mainly focus on generation quality. In contrast, this paper is the first to explore how sharp distributions can reshape the latent space for segmentation tasks. We provide a detailed theoretical analysis and show that distribution-awer design benefits segmentation performance in diffusion models.
Impact Statement
Regarding the dataset, all utilized pathology datasets are publicly available and have undergone ethical review and approval. Concerning the algorithm, L-Diffusion delivers precise and robust pathology image segmentation with ex- ceptional efficiency. Its capacity to effectively decompose pathology images simplifies the analytical workflow, pro- viding potent tool for advancing tumor diagnosis and microenvironment analysis. This progress cultivates more profound comprehension of the mechanisms driving tumori- genesis and progression.
7. Conclusion
In this paper, we introduce L-Diffusion, an innovative frame- work that employs Laplace distributions and contrastive learning to advance pathology image segmentation. By modeling distinet components using Laplace distributions, L-Diffusion amplifies distributional divergences, facilitat- ing precise and robust segmentation. The proposed pixel latent vector contrastive learning mechanism diminishes the dependency on annotated data and alleviates the learning challenges associated with tail components. Rigorous theo- retical analysis and comprehensive experimental evaluations substantiate the practicality and superiority of L-Diffusion, positioning it a state-of-the-arr solution for pathology image segmentation. The Laplace Diffusion Model offers groundbreaking perspective on harnessing component distri- butions across diffusion steps to achieve efficient pathology image segmentation. It provides an effective tool to aid tumor diagnosis and mieroenvironment analysis, fostering deeper understanding of tumorigenesis and progression. In future work, we aim to explore the application of Laplace Diffusion in an unsupervised manner to assist pathology im- age component analysis and extend its capabilities to other large-scale image segmentation tasks.
Acknowledgements
This work is supported by National Natural Science Foun- dation of China (62376248), the Huadong Medicine Joint Fund of the Zhejiang Provincial Natural Science Founda- tion of China (LHDMZ25H160002,, the Zhejiang Province Health Major Science and Technology Program of National Health Commission Scientific Research Fund (No. WKJ- ZJ-2426) and Information Technology Center, ZheJiang University.
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L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
A. Mathematical Derivations
This section provides the important mathematical derivations mentioned in Section As we assume, the data distribution satisfied by the original image z can be expressed as the following formula (7):
T II [((((1=11)
q b)
Σ On (3r Min bn), (0)))(((111))) (20)
In the above formula, N, μai and b; are the number of categories and the data distribution center and scale parameters of each category, and t and T represent the current time step and the total step number respectively.
In order to propagate the gradient backwards, we need to make the z sampled by Laplace noise differentiable through a heavy parameter operation. It is possible to set an independent variable e, when the sampling noise z satisfies = μ4g + bg O e, observed that the equation still maintains randomness as whole, and satisfies the Laplace distribution with the mean po and scale parameter by. The subsequent inference stages fs and hy be derived from U-Net with parameter 0, and the randomness is transferred making the gradient derivable.
(m.1))=e-1++ vI (1),
VI II 0(n,-1))2)) + V ((n
(m + (1 0(n,t-1)22 + vI (n.))211)
(8)
The above formula is Ft-1 plus noise to obtain mathematical representation of 2t, where ((,,t) represents the noise level coefficient of class at time steps, equivalent to 1 1 1 3(n, t) and satisfies ((..1) II ((,()) Since Laplace distribution and Gaussian distribution have the same additivity, the formula (9) can be derived as follows:
V (aaas)( 1) + V1 ((,,t)21 = (m.)) (1 ((me-1)) + (m,1)
(m
(9)
Substituting formula (9) into formula (8) gives the formula (10) as follows:
N
It
(at VI (m=1))()))1)))))))
( 2j + VI a(ss ((n))2)22)) + / (n.-))(()
Σ
20 - II Et
Σ (a( + VI (t).
(10)
Equation (11) can be obtained by substituting the above equation into Laplace distribution, and the noise adding process can be obtained after transformation as follows:
q(1// = Σ Ln (((n))))-1111111 a(n,t)
n=1
Σ Ln / 11
(11)

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L-DDiffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
1.8
1.6
Probability Density
Ay
(1
le mpl
1.2
0.8
f(alu,0)
Vino
6x
20²
0.6
0.4
0.2
Figure 6. Illustration of Laplace and Gaussian distributions. The purple curve represents the Laplace distribution with means of - and 1. respectively, and scale parameter of 0.25, while the pink curve depicts the Gaussian distribution with means of -1 and and variance of 0.5.
In the process of reverse diffusion, still refer to formulas (3). Therefore, backward diffusion can be expressed as the formula (12):
T
N
po(2o:))= = p((r) II
pe (zx-1 (xt). po (1))
Σ Li f), by (x,, f)).
(12)
t=1
The formula for conditional probability B) with marginal probabilities P(A) and P(B) can be expressed as P(A B) P(A B), BB P(B) And then P(An B) = P(A[B) P(B) = P(B)A) P(A). Therefore, we take the "perturbation" sampled
data _t-1 as A, the complete Laplace noise and the original data as B to obtain the formula (13);
q(Fx-1|21) g(x,(_,-1) q(8+-1)
((xr)
(( q( vo) g( (20)
(13)
(( (00))
Because the conditional probability in formula (13) satisfies formula (12), formula (14) can be derived as follows:
((, q(
q( ((2,-1122,20)
(xx((x))
N
Ft ((,
14-1 (0(m.-1)2o)
(14)
B(m,t)
V1 (m,t-1))
V1 (((r.)
Before, derived formula (8). As result, know H2 (a + /1-a(m,())) And because Mmn))))) is always non-negative, so it is not difficult draw H, - (m,
Similarly, we can also
draw ăc-1 (a((n.t-1)00 2 and 24 / /a 2 O. Substitute the formula (14) to get formula (15) as follows:
It 20..))21111
|ā--1 /a
ar /u
(10--106,200 + Σ
VB(m.t)
V1 ((((--1)
V1 (((.))
(m
Fe-1 /
Va(n,-1)110
It / (m,)))
(P(m))
a(m,t-1)
/1 a(n.))
a(n.t)
} 1 On.-11
C(
(15)
V1

---

L-Diffuuson: Laplace Diffusion for Efficient Pathology Image Segmentation
The red box refers the scale parameter of the Laplace distribution, while the blue box refers to the value of the Laplace distribution. The data distribution for category
be obtained after transformation.
In addition, since the above random variable ((1,0) (F(.,)) satisfies the Laplace distribution, it can be found by comparing Fig. 6. Laplace probability change range Ay much larger than Gaussian distribution probability change range Ay'. Observing the red pentagrams representing intersection points different means the Laplace distribution and the blue pentagrams the Gaussian distribution, evident that the red pentagrams occur with lower probability.
The confusion region, highlighted as the shaded area, smaller for the Laplace distribution. This indicates that, during contrastive learning, the difference between positive and negative samples greater, making more suitable for training. Furthermore, the yellow pentagrams representing the intersection points of both distributions reveal that the Laplace distribution exhibits steeper gradients, signifying a greater impact of randomness.
B. Dataset and Details
In this paper, we adopt four dataset including colorectal cancer pathological image dataset CRCD (Ye et al., 2023), melanoma pathological image dataset PUMA (Schuiveling al., 2024), breast cancer pathology image dataset BCSS (Amgad et al., 2019) and multi-class cellular segmentation dataset PanNuke (Gamper et al., 2020). Detailed sample number and category number information about these four datasets is presented in Table 7.
Table 7. Dataset details. '#image' stands for numher of images, '#tissue" denotes the annotation number of tissues, '#cell' represents annotated cells, "icategory' represents category number.
Dataset
#image
#tissue #cattegoyy
#cell / #category
CRCD (Ye et al., 2023)
1764
800 /9
964 3
PUMA (Schuiveling al., 2024)
151
151 /
151 10
BCSS (Amgad et al., 2019)
151
151/22
PanNuke (Gamper al., 2020)
481
481 19
Table 8. Component Abbreviation Description.
Abbreviation
Full Name
Abbreviation
Full Name
Abbreviation
Full Name
ADI
adipose
GLAA
glandular secretions
NSM
normal stroma
ADR
adrenal
HED
head&neck
OTH
others outside roi
ANG
angioinvasion
HIT
histiocyte
OUT
APO
apoptosis
IMM
immune
OVA
ovarian pancreatic
BAC
background
INF
lymphocytic infiltrate
PAN
BID
bile duct
KID
kidney
PLA
plasma
BLA
bladder
LIV
liver
PRO
prostate
BLD
blood
LUN
lung
SKI
skin adnexa
BRE
breast
LYM
lymphocyte aggregates
STO
stomach
CER
cervix
MEL
melanophage
STR
stroma
COL
cloon
MET
metaplasia
SUB
submucosa or serosa
DCI
dcis
MUC
mucus
TES
testis
END
endothelium
MUS
muscle
THY
thyroid
EPI
epidermis
NEC
necrosis
TUM
tumor epithelium
ESO
esophagus
NER
nerve
UND
undetermined
EXC
exclude
NEU
neutrophil
UTR
FAT
fat
NOR
normal gland
VES
vessel

---

L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
C. Pixel Latent Vector Separation Process Visualization
To more intuitively observe the separation process pixel latent vectors, we visualized the distribution pixel latent vectors for each tissue in the PUMA dataset during the training of the diffusion model with contrastive learning. For clarity in visualization, we sampled 50 pixels and adjusted the display quantity of each category based on its proportion relative the total number of pixels. The separation process of pixel latent vectors is illustrated in Fig. 7. It is evident that training progresses, pixel latent vectors of different tissues become distinctly separated, while those of the same tissue cluster more closely together.
0.5
65
4.5
1.
6.4
0.8
0.5
02
1.5
2.
0.4
02
0.8
Figure 7. Visualization of the pixel latent vector separation process during diffusion model training with contrastive learning. The training spans a total of 100 epochs. After every 5 epochs, the learned pixel latent vectors are reduced to a dimee-dimeesional space using T-SNE Van der Maaten & Hinton, 2008). Each tissue type is represented by distinct color.

---

L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
D. More Tissue Segmentation Visual Results
Origin Image
DeepLabv3+
SAMPath
DeaseASPP
Ours
Figure More qualitative comparison of tissue segmentation performance. Several leading high-performance methods are selected for
visual comparison.

---

L-Diffusion: Laplace Diffusion for Efficient Pathology Image Segmentation
E. More Cell Segmentation Visual Results
Origin Image
GT
DeepLaby3+
SAMPath
DenseASPP
Ours
Figure More qualitative comparison cellular segmentation performance. Several leading high- peeh-performance methods are selected for
visual comparison.

---

L-Difftuson: Laplace Diffusion for Efficient Pathology Image Segmentation
F. Segmentation Visualization Results on Whole Slide Images
80847
44754
18802
10409
652
361
Figure 10. The segmentation visualization results L-Diffusion on pathology whole slide images.

---

L-Difftusin: Laplace Diffusion for Efficient Pathology Image Segmentation
G. Segmentation Visualization Results on Remote Sensing Images
Original Image
L-Diffusion
GT
Figure 11. The segmentation visualization results L-Diffusion on remote sensing images.


Reviews:
[{"review_id": "458ezlpjHu", "reviewer": "Reviewer_ZaXb", "summary": "The paper introduces L-Diffusion, a novel Laplace Diffusion Model designed for efficient pathology image segmentation. Unlike traditional approaches relying on Gaussian distributions, L-Diffusion employs multiple Laplace distributions to better differentiate component features in pathology images. The model follows a diffusion process, generating a sequence of feature maps, and enhances pixel-wise vector representations using contrastive learning. This approach significantly improves segmentation performance, particularly for tail-class components, which are often difficult to identify due to the long-tail distribution in pathology images. Extensive experiments on six tissue and cell segmentation datasets show that L-Diffusion achieves substantial improvements over state-of-the-art models, with up to 7.16% higher DICE score for tissue segmentation and 20.09% improvement for cell segmentation. The paper also provides theoretical analysis supporting the advantages of using Laplace distributions, demonstrating their ability to enhance component differentiation and model efficiency.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Reply to Reviewer ZaXb\n\nWe sincerely appreciate the reviewer's valuable feedback and insightful comments on our paper. We are pleased that the reviewers recognize our contributions in introducing L-Diffusion, leveraging Laplace distributions for pathology image segmentation, and improving segmentation performance, particularly for tail-class components. Below, we address the key concerns and provide clarifications on generalization, efficiency, and hyperparameter sensitivity.\n\n**[Question (Q)1] How would it generalize to other medical imaging tasks such as radiology or ophthalmology?**\n\nAnswer (A)1: Thanks to the reviewers for their interest in the wider applicability of L-Diffusion. While our work focuses on pathology image segmentation, the principles of Laplace-based diffusion modeling and pixel latent vector contrastive learning are broadly applicable. Many medical imaging tasks, such as radiology (CT, MRI) and ophthalmology (fundus images, OCT), share challenges like heterogeneous textures, fine-grained structures, and class imbalances, suggesting that L-Diffusion could generalize well to these domains.\n\nWe have conducted preliminary experiments on a public brain tumor MRI dataset and the RIM-ONE glaucoma dataset. On the BraTS dataset, our DICE score is better than **SOTA (83.13) [1]**. On the RIM-ONE glaucoma dataset, our MPA score is better than **SOTA (95.45) [2]**. Our findings indicate that L-Diffusion retains its advantages in segmenting small, rare tumor components. We are committed to adding statistics and visualizations to the revised manuscript.\n\n| DATASET | DICE | MPA | mIoU | FwIoU |\n|-|-|-|-|-|\n| BraTS | 89.56 | 84.53 | 86.41 | 87.10 |\n| RIM-ONE | 96.12 | 95.58 | 94.39 | 95.27 |\n\n**[Q2] Can the authors provide runtime comparisons with other state-of-the-art segmentation models to assess efficiency?**\n\nA2: Thank you for the constructive suggestion.\n- Training phase: Since our method is based on stable diffusion backbone, core training runtime is only in the ConvNeXT classification header, which is more advantageous than other full-training models.\n- Inference phase: The main use scenario is gigapixel images, which means that for these images, the actual image processing time is much longer than the segmentation time. This means that we can process tasks and segmentation tasks in parallel to reduce the runtime disadvantages of the model. We provide a table to compare the efficiency of different models so that you can more intuitively realize the impact of runtime disadvantage on efficiency. \n\n| Method | Image Size | Processing Time | Segmentation Time | Total Time |\n|:-:|:-:|:-:|:-:|:-:|\n| DeepLabV3+ | 90027 × 88341 | 763.58s | 382.85s | 763.63s |\n| SAMPath | 90027 × 88341 | 763.58s | 6355.31s | 6355.31s |\n| L-Diffusion | 90027 × 88341 | 8880.96s | 4899.84s | 8881.60s |\n\nIn summary, L-Diffusion has advantages over traditional models in the training phase and is about 30% slower than SOTA in the inference phase, which is acceptable at runtime. In future work, we will consider introducing a quantitative accelerated diffusion model and other means for optimization, and the above data and analysis will be supplemented to revise the manuscript.\n\n**[Q3] How sensitive is the performance to these hyperparameters, and could the authors provide guidelines for optimal tuning?**\n\nA3: We greatly appreciate the reviewer's insightful question regarding hyperparameter sensitivity and tuning.\n\nHyperparameters mentioned in the original text (**Models and Parameters** in the Experiment):\n- Diffusion steps: Too few steps limit denoising capacity, while too many increase computational cost without substantial improvement. This is reflected in Fig. 5. (5~15)\n- Sampling number of contrastive learning: Similar to the diffusion step. (100)\n- Learning rate of Adam optimizer: Diffusion Training (0.00001), Segmentation Training (0.001)\n- Batch size: Diffusion Training (1), Segmentation Training (32)\n\nUnmentioned hyperparameters:\n- Temperature scaling of contrastive learning: In the case of avoiding gradient explosion, smaller temperature scales can help sharpen the distribution. (0.05-0.1)\n\nAn ablation study on temperature scaling τ of contrastive learning is given as follows:\n|τ|0.1|0.08|0.05|0.02|\n|-|-|-|-|-|\n|DICE|89.33|90.67|92.11|88.74|\n\nWe will include practical tuning guidelines in the revised manuscript.\n\n**[Q4] The second sentence in the third paragraph of the Introduction seems a bit unclear.**\n\nA4: Thank you very much for your correction. We have checked the original text and provided the revised version.\n\nRevised text: Prominent deep learning models, including U-Net (R~), DeepLab (L~), and Transformer (A~), have demonstrated superior performance across a spectrum of medical image segmentation tasks.\n\n**References**\n\n[1] https://arxiv.org/pdf/2403.09262\n\n[2] https://arxiv.org/pdf/1903.02740", "claims_and_evidence": "The claims made in the paper are well-supported by both theoretical analysis and experimental results. The authors claim that using Laplace distributions instead of Gaussian distributions enhances feature decomposition and improves segmentation accuracy, particularly for tail-class components. This claim is backed by mathematical derivations and empirical comparisons of Gaussian vs. Laplace distribution differentiation, which show that the latter leads to greater separability of pixel-wise feature vectors.", "methods_and_evaluation_criteria": "The proposed L-Diffusion method and evaluation criteria are well-suited for pathology image segmentation. The use of Laplace distributions enhances feature differentiation, and contrastive learning improves pixel-wise representation, addressing challenges in long-tail class segmentation. The model is evaluated on six benchmark datasets covering both tissue and cell segmentation, ensuring a comprehensive assessment. Metrics such as DICE, MPA, mIoU, and FwIoU are appropriate for measuring segmentation accuracy and robustness.", "theoretical_claims": "The paper provides theoretical justification for using Laplace distributions over Gaussian distributions, arguing that the steeper gradient of the Laplace distribution enhances feature differentiation. The derivations, including probability density functions, gradient calculations, and diffusion step equations, appear mathematically sound. The Laplace noise formulation and reverse diffusion process are derived systematically, and the transition from Gaussian to Laplace-based modeling is well-supported. While I did not rigorously verify every step, the overall framework aligns with established diffusion model theory. No obvious errors were found, but external validation would further confirm the proofs' correctness.", "experimental_designs_or_analyses": "The experimental design is generally sound and appropriate for pathology image segmentation. The model is tested on six diverse datasets, covering both tissue and cell segmentation, ensuring broad applicability. Metrics such as DICE, MPA, mIoU, and FwIoU are correctly chosen for evaluating segmentation performance. The comparison with state-of-the-art models is comprehensive, showing clear performance improvements. Ablation studies confirm the contributions of Laplace distributions and contrastive learning, and a generalization test on a remote sensing dataset suggests potential broader applicability. A minor limitation is the lack of evaluation on other medical imaging domains, which could further validate the model’s versatility.", "relation_to_broader_scientific_literature": "The paper builds on diffusion models and contrastive learning, extending them to pathology image segmentation. Traditional segmentation models, such as U-Net, DeepLab, and Transformers, have been widely used, but they struggle with long-tail class segmentation and multi-scale feature extraction. The introduction of Laplace distributions instead of Gaussian distributions aligns with prior work on improving feature separability in latent spaces. Contrastive learning, which has been effective in self-supervised learning, is adapted here to enhance pixel-wise feature differentiation. The paper also connects to recent efforts in medical image segmentation using diffusion models, such as MedSegDiff [1], but uniquely applies component-wise latent distribution modeling. \n\n[1] Wu, Junde, et al. MedSegDiff: Medical image segmentation with diffusion probabilistic model.", "essential_references_not_discussed": "The paper provides a comprehensive discussion of related literature, covering key works in diffusion models, contrastive learning, and pathology image segmentation. It cites foundational methods such as U-Net, DeepLab, and Transformer-based models, as well as recent diffusion-based segmentation approaches like MedSegDiff. The discussion on Laplace distributions and their role in enhancing feature separability is well-supported by prior probabilistic modeling research. Additionally, the application of contrastive learning to pathology image segmentation is contextualized within the broader field of self-supervised learning. Overall, the references are sufficient, and no essential prior works appear to be missing.", "other_strengths_and_weaknesses": "### Strengths\n\n1. The paper introduces a novel approach by replacing Gaussian distributions with Laplace distributions, improving feature separability for pathology image segmentation.\n2. The use of pixel latent vector contrastive learning enhances segmentation accuracy, especially for tail-class components, addressing long-tail distribution challenges.\n3. L-Diffusion outperforms state-of-the-art segmentation models on six benchmark datasets, demonstrating significant improvements in both tissue and cell segmentation.\n4. The mathematical derivations provide a solid foundation for Laplace-based diffusion modeling, supporting the claimed improvements in feature differentiation.\n\n### Weaknesses\n\n1. While the model performs well on pathology images, how would it generalize to other medical imaging tasks such as radiology or ophthalmology?\n2. The proposed diffusion process involves multiple steps; can the authors provide runtime comparisons with other state-of-the-art segmentation models to assess efficiency?\n3. The model introduces multiple hyperparameters (e.g., diffusion steps, contrastive learning settings). How sensitive is the performance to these hyperparameters, and could the authors provide guidelines for optimal tuning?", "other_comments_or_suggestions": "The second sentence in the third paragraph of the Introduction seems a bit unclear.", "questions_for_authors": "Please see the weaknesses part above.", "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": "cSXhdpTQui", "reviewer": "Reviewer_nPmf", "summary": "This paper proposes a new diffusion-based method to tackle pathology image segmentation. The pathology image segmentation is a challenging task because of the large, gigapixel resolution, diverse scales, and imbalanced tissue distributions in these images.  Traditional segmentation models like U-Net and DeepLab have shown promise but struggle with labor-intensive annotation and feature extraction for tail categories. To address these issues, the paper introduces the Laplace Diffusion Model (L-Diffusion), which leverages Laplace distributions instead of Gaussian to model distinct components within the images. L-Diffusion uses contrastive learning to enhance the differentiation between components while maintaining intra-component similarity, improving segmentation precision and robustness, particularly for tail components. The model reduces the reliance on annotated data by capturing the distributional characteristics of different components. Extensive experiments show that L-Diffusion outperforms existing methods in accuracy and robustness across various benchmarks, providing an innovative approach to pathology image segmentation.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Reply to Reviewer nPmf\n\nWe appreciate the reviewers' detailed and insightful feedback on our work. Below, we address the key points raised in the review.\n\n\n**Response to Theoretical Claims**\n\nWe are grateful for the acknowledgment that our theoretical derivations and mathematical proofs are correct. We appreciate the reviewers' verification of our gradient computations for the Laplace distribution in Section 3.1 and the mathematical derivations in Supplementary Material A.\n\n**Response to Experimental Design and Evaluation**\n\nWe thank the reviewers for their recognition of the comprehensive nature of our experiments, including:\n\n- Quantitative evaluation against strong baseline methods.\n\n- Ablation studies that highlight the contributions of different components of our method.\n\n- Generalization experiments on large-scale datasets, demonstrating the robustness of our approach.\n\nThe consistent performance improvements across benchmarking datasets (CRCD, PUMA, BCSS) further validate the effectiveness of L-Diffusion.\n\n\n**Response to Weaknesses and Suggestions**\n\nThank you for your valuable suggestion. We acknowledge the reviewer's concern that the equations in Section 3 are not numbered, which makes it difficult for reference. We will add equation numbers in the final version to improve clarity and readability.", "claims_and_evidence": "Based on the challenges summarized in the submission: \"current pathology image segmentation tasks grapple with labor-intensive annotation processes or limited accuracy in identifying tail samples\", there are two main claims made by the submission:\n(1). Laplace distribution is advantageous for broadening distribution disparities based on the analysis in the submission.\n(2). Laplace diffuse model learns better component distribution  for pathology image segmentation, due to it's long-tail nature. \nThese two claims are well supported by the method theory and experiments.", "methods_and_evaluation_criteria": "The proposed method has been evaluated in the context of pathology image segmentation on a series of benchmarking datasets: CRCD , PUMA, BCSS, against a series of state of the art baseline methods", "theoretical_claims": "1. The proofs in Section 3.1 for computing the gradient of Laplace distribution is correct. \n2. The methmetical dereivation in supplementary material A. is verified.", "experimental_designs_or_analyses": "There are 3 main experiments conducted for evaluating the effectiveness of the proposed method: (1) Quantitative evaluations agains baseline methods (2) Ablation study (3) Generalization on large-scale data. \n\nThe quantitative evaluations are made comprehensively with many state of the art methods and various metrics. The proposed method seems to get a decent gain consistently on each of the benchmarking dataset.", "relation_to_broader_scientific_literature": "The proposed Laplace model can be applied to a broader domains such as image segmentation e-commerce product data, which also shows a long-tail distribution.", "essential_references_not_discussed": "N.A.", "other_strengths_and_weaknesses": "Strengths\n1. The reasoning in Section 3.1 is sound in term of showing the comparison between Laplace distribution gradients and Guassian distribution gradients. \n2. The experiments are comprehensive and the code is available anonymously. The experiment is compare a large number of baseline methods and the proposed method is outperforming all the previous methods consistently.", "other_comments_or_suggestions": "1. The equations in the paper section 3 is not numbered, making it difficult for reference.", "questions_for_authors": "The authors are suggested to address the concerns listed in the previous sections during rebuttal period.", "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": "rJUzMe969C", "reviewer": "Reviewer_9Pf9", "summary": "This paper introduces L-Diffusion, an innovative framework designed to advance pathology image segmentation by utilizing Laplace distributions and contrastive learning.  The primary contribution of the paper lies in its use of Laplace distributions to model distinct components within pathology images, which enhances distributional divergence and facilitates more precise and robust segmentation.  \nThe novel pixel latent vector contrastive learning mechanism further reduces reliance on annotated data, addressing the challenges associated with long-tail components.  The approach significantly improves segmentation performance on tissue and cell datasets, showing substantial gains over existing methods.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Reply to Reviewer 9Pf9\n\nWe sincerely appreciate your thorough and insightful review of our paper, L-Diffusion: Laplace-Based Diffusion Model for Pathology Image Segmentation. Your positive evaluation of our contributions, including the use of Laplace distributions, contrastive learning, and the overall experimental design, is highly encouraging. We address your comments and suggestions below:\n\n**[Question (Q)1] Reordering the Related Work Section**\n\nThank you for your constructive comments. We acknowledge your suggestion to move the Related Work section after the Introduction to enhance readability. In the revised version, we will adjust the structure accordingly.\n\n**[Q2] Clarification of Dataset Abbreviations**\n\nThank you for your valuable suggestions. We agree that explicitly defining dataset abbreviations in the appendix would enhance clarity. We will ensure that all dataset names and category labels are fully defined to improve readability for the audience.", "claims_and_evidence": "Yes, the claims made in the submission are generally supported by clear and convincing evidence.   The authors provide both theoretical analysis and extensive experimental evaluations to substantiate their claims about the effectiveness of the L-Diffusion framework for pathology image segmentation.  \n\n- Theoretical Analysis:\nThe paper clearly explains the rationale behind using Laplace distributions for component modeling, as opposed to Gaussian distributions.   It presents mathematical derivations comparing the gradients of the two distributions, showing that Laplace distributions are more sensitive to noise, which is beneficial for pathology image segmentation tasks.\n\n- Experimental Evidence:\nThe paper includes quantitative results demonstrating the improvements in segmentation performance across various tissue and cell datasets (CRCD, PUMA, BCSS, PanNuke) compared to several state-of-the-art models.   The reported results are statistically significant, showing substantial performance gains (e.g., improvements in DICE, MPA, mIoU, and FwIoU metrics).\nThe qualitative visualizations further support these findings, showing that L-Diffusion achieves better boundary segmentation and handles tail-class components more effectively.\n\n- Comparison to Existing Methods:\nThe authors compare L-Diffusion with several mainstream segmentation models (e.g., U-Net++, DeepLab, Swin-UNet) and show that their model consistently outperforms these methods, especially in terms of segmenting components with lower proportions (long-tail distribution).\n\n- Ablation Studies:\nThe paper conducts detailed ablation studies to show the importance of each component of L-Diffusion, particularly the integration of the Laplace distribution and contrastive learning, which provides additional evidence.", "methods_and_evaluation_criteria": "Yes, the proposed methods and evaluation criteria are well-suited for pathology image segmentation.  Using Laplace distributions to model distinct components effectively addresses multi-scale features and long-tail distributions in pathology images, enhancing segmentation precision, especially for rare components.  The integration of contrastive learning further refines component differentiation while reducing reliance on annotated data.  The use of diffusion steps to refine feature maps and latent vectors contributes to more accurate segmentation.  \n\nThe evaluation metrics (DICE, MPA, mIoU, and FWIoU) are standard and effective, assessing various aspects of segmentation performance, including accuracy, precision, and class imbalance.  Qualitative visualizations complement these metrics by showing better boundary segmentation, particularly for tail-class components.  \n\nThe benchmark datasets, such as CRCD, PUMA, BCSS, and PanNuke, cover diverse pathology segmentation tasks, while the inclusion of a remote sensing dataset for generalization tests demonstrates the method's robustness across different domains.  Overall, the proposed methods and evaluation criteria are appropriate and robust for addressing the challenges in pathology image segmentation.", "theoretical_claims": "Yes, I focused on the rationale behind applying Laplace distributions to pathology image segmentation, particularly in terms of the formulaic principles. This is thoroughly addressed in Section A, \"Mathematical Derivations\", in the appendix, and the visualization of the differences between the Laplace and Gaussian distributions is commendable. It provides convenience for readers when interpreting the paper. The formal proof and the visualizations in the paper demonstrate that the probability change range $\\Delta y$ of the Laplace distribution is larger than that of the Gaussian distribution $\\Delta y'$, which aligns well with the segmentation strategy for pathology images. Additionally, the introduction of contrastive learning, which brings similar class samples closer and pushes different class samples apart, is a sound approach both conceptually and methodologically.", "experimental_designs_or_analyses": "Yes, the experimental designs and analyses appear sound and provide strong evidence for the claims made in the paper. \n\n1. Benchmark Datasets:\nThe paper uses a variety of benchmark datasets (e.g., CRCD, PUMA, BCSS, and PanNuke) for testing the model. These datasets cover different aspects of pathology image segmentation, including tissue and cell segmentation, and represent diverse challenges such as multi-scale features and long-tail distributions. The choice of datasets is appropriate for testing the model's generalizability across multiple types of pathology image segmentation tasks.\n\n2. Comparison with SOTAs:\nThe paper compare L-Diffusion with a variety of SOTA methods (e.g., U-Net, DeepLabv3, Swin-UNet, FastFCN), which is a solid approach to demonstrate the advantages of their proposed method. The reported quantitative results show significant improvements across tissue and cell segmentation datasets, providing strong evidence of the method’s effectiveness.\n\n3. Qualitative and Quantitative Results:\nThe qualitative results (visualizations) demonstrate that L-Diffusion performs well in segmenting boundaries and handling tail-class components, which aligns with the claims made by the authors. The quantitative results (based on the metrics mentioned) show clear improvements over existing methods, further supporting the paper’s claims of better performance.\n\n4. Ablation Studies:\nThe paper conduct ablation studies to isolate the impact of key components in their model, such as the integration of Laplace distributions and contrastive learning. This is an essential and well-designed experiment, as it provides insights into which parts of the model contribute most to its success. The ablation results confirm that the combination of these two techniques is a major factor in the model's improved performance.", "relation_to_broader_scientific_literature": "The contributions of this paper are built upon a broad foundation of existing research, spanning multiple areas such as pathology image segmentation, diffusion models, and contrastive learning. The practical application of L-Diffusion is positioned within the realm of pathology image segmentation, following the Diffusion + Pathology paradigm. Interestingly, the authors have innovatively approached the problem by utilizing component distributions across diffusion steps, which not only fine-tunes the decomposition of pathological semantic information but also enhances the richness of the data through the diffusion process. This represents a significant innovation in addressing pathology image segmentation challenges. Furthermore, the introduction of contrastive learning aligns with ideas from multimodal learning and other related fields.\n\nOverall, the L-Diffusion model presented in this paper is convincing in its relation to the broader scientific literature, adhering to sound research principles. The novel application of the Laplace diffusion process adds a substantial innovation within the field, making the approach a noteworthy contribution to the domain.", "essential_references_not_discussed": "In my personal opinion, this paper provides a thorough introduction to the algorithms and ideas involved in the relevant work section and experimental implementation. The approach is innovative, and there are no instances of withholding key literature that would be crucial to the paper's significance.", "other_strengths_and_weaknesses": "As mentioned earlier, this paper overall meets the standards for publication at ICML. I believe the authors' L-Diffusion approach also offers valuable insights for feature engineering implementation.", "other_comments_or_suggestions": "I personally suggest that the Related Work section be placed after the Introduction to help readers quickly engage with the core implementation ideas.At the same time, the specific meaning of the abbreviation is given in the dataset section of the appendix, so that the reader can better understand the processing effect of the segmentation model on different categories.", "questions_for_authors": "N/A", "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": "iBELXtxvQh", "reviewer": "Reviewer_ezdp", "summary": "The paper introduces L-Diffusion, a novel approach to pathology image segmentation by leveraging Laplace distributions and contrastive learning, achieving good performance, and demonstrating generalization capabilities.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Reply to Reviewer ezdp\n\nWe sincerely appreciate your efforts in reviewing our paper and for your constructive feedback. We have organized your comments and provided our responses below, hoping they address your concerns.\n\n**[Question (Q)1] Efficiency of L-Diffusion**\n\nAnswer (A)1: Thanks. L-Diffusion consists of two stages: Latent feature extraction with diffusion model and segmentation with ConvNeXT. The former is time-consuming.\n\nIn the training stage, employing two A6000 GPU resources and a dataset of 50,000 patch samples, the L-Diffusion model requires about 26 hours—24 hours for training the diffusion model and 2 hours for refining the ConvNeXT segmenter. Meanwhile, SOTA SAMPath achieves convergence within 5 hours. Notably, L-Diffusion's two-stage design enhances ConvNeXT fine-tuning efficiency.\n\nIn the inference stage, L-Diffusion and SAMPath take an average of 2.5 and 1.8 hours per image of size 90027 × 88341, respectively. For more results, see **A2 to reviewer ZaXb**. Future work will focus on accelerating L-Diffusion.\n\n**[Q2] Applicability to Other Medical Imaging Modalities**\n\nA2: Thanks. We have added the generalization experiment. Results show that L-Diffusion achieves 6.43% and 0.67%  improvements to SOTA methods on BraTS and RIM-ONE datasets, respectively. Please refer to **A1 to reviewer ZaXb** for detailed experiment results. We will supplement the final version with more analysis and visualizations.\n\n**[Q3] Robustness to Noisy or Partial Annotations**\n\nA3: Thanks. Table 3 of the original submission shows the experiment with partial annotations. The pathology usually contains space-noise (wrong boundary) and label-noise (wrong type). The noise robustness experiments (DICE score) are given as:\n|Type|5%|10%|20%|30%|\n|-|-|-|-|-|\n|space-noise|92.18|91.83|91.79|91.65|\n|label-noise|88.72|85.26|80.14|75.48|\n\nOur method is robust to space-noise due to only the inner high-confidence area pixel is adopted for contrastive learning. Similar to other methods, our method is also sensitive to label-noise, which can be solved by the anti-noise learning loss function. More results and analysis will be included in the final version.\n\n**[Q4] Ethical and Clinical Impact Discussion**\n\nA4: Thanks. We recognize the importance of addressing the ethical and clinical implications of deploying L-Diffusion in real-world medical applications. While we briefly mention ethical approvals for datasets, we will expand our discussion to cover potential risks, such as biases in dataset annotations, the need for regulatory validation before clinical use, and challenges in interpretability.\n\n**[Q5] Sensitivity of Key Hyperparameters**\n\nA5: Sorry for the confusion. The scale parameter (red box of Eqn. 15) is an adaptive parameter predicted by U-Net. Ablation studies on different distribution and diffusion steps are given in Table 4 and Figure 5. Moreover, an ablation study on τ of contrastive learning is given as follows:\n|τ|0.1|0.08|0.05|0.02|\n|-|-|-|-|-|\n|DICE|89.33|90.67|92.11|88.74|\n\nWe will add it to the final version.\n\n**[Q6] (a) Relation to Prior Work ([1] Imp... [2] Diff...) & (b) Exploration of Alternative Distributions (Dis.)**\n\nA6: Thank you for your comments.\n\n**(a)**: *[1]* demonstrates that the Laplace Dis. has steeper peaks and heavier tails. This property makes it more advantageous when dealing with data with outliers or sparse noise. *[2]* compared the Gaussian Dis., t Dis., Uniform Dis., and so on tend to produce smooth samples for image generation tasks.\n\nDifferent from *[1,2]*, this paper proposes for the first time to achieve segmentation through sharp dis. alienation latent space and gives a detailed theoretical derivation.\n\nWe will add the above papers to the related work and highlight our contributions.\n\n**(b)**: We add the comparative experiment as follows:\n|Dis.|DICE|Runtime|\n|-|-|-|\n|Cauchy|16.25|7325|\n|Student's T|83.17|20440|\n|Laplace|85.75|8882|\n\nIn summary, Laplace Dis. maintains its superiority. This is because the Cauchy dis. has no expectations and variances, making gradient optimization less stable. Student's t Dis. has potential in accuracy, but its runtime is too long because of its complex gradient solution. We are committed to adding detailed data and analysis to the final manuscript.\n\n**[Q7] Exploration of Unsupervised or Semi-supervised**\n\nA7: We appreciate the reviewer's interest in the applicability of L-Diffusion to unsupervised and semi-supervised variants. Since L-Diffusion is based on contrast learning in the diffusion stage, this model supports a semi-supervised variant. We explored semi-supervised effects in Table 3. \n\nFor the unsupervised variant, only the latent feature is extracted by the L-diffusion, and then the clustering algorithm is adopted K-Means for the unsupervised method. The performance on the RIM-ONE dataset is provided below:\n|Type|Full.|Semi.|Un.|\n|-|-|-|-|\n|DICE|96.12|88.91|60.92|\n\nMore details and analysis will be given in the final version.", "claims_and_evidence": "Supported Claims:\n\n1) $\\textbf{Laplace Distributions Improve Segmentation.}$ Laplace distributions are more effective than Gaussian distributions for modeling pathology image components, especially for tail categories. The authors provide a detailed theoretical analysis comparing the gradients of Laplace and Gaussian distributions, showing that Laplace distributions have sharper gradients and better separation between categories. Empirical results, including visual comparisons of pixel value distributions (Figure 2) and quantitative improvements in segmentation metrics (Tables 1 and 2), further support this claim.\n\n2) $\\textbf{Contrastive Learning Enhances Component Separation.}$ The proposed pixel latent vector contrastive learning mechanism improves the separation of different tissue and cellular components. The ablation studies (Table 4) demonstrate that combining contrastive learning with Laplace distributions significantly improves segmentation performance. The visualization of pixel latent vector separation (Figure 7) also provides qualitative evidence of the effectiveness of contrastive learning.\n\n3) $\\textbf{Superior Performance on Pathology Image Segmentation.}$ L-Diffusion achieves state-of-the-art performance on multiple pathology image segmentation benchmarks. The paper presents extensive quantitative results (Tables 1 and 2) showing that L-Diffusion outperforms existing methods on datasets such as CRCD, PUMA, BCSS, and PanNuke. The improvements in metrics like DICE, MPA, mIoU, and FwIoU are substantial and well-documented.\n\n4) $\\textbf{Generalization to Remote Sensing Images.}$ L-Diffusion generalizes well to other large-scale image segmentation tasks, such as remote sensing. The authors provide quantitative results (Table 5) and qualitative visualizations (Figure 11) showing that L-Diffusion performs competitively on the Massachusetts-Building dataset, a remote sensing image segmentation task.\n\nClaims That Could Benefit from Additional Evidence:\n\n1) $\\textbf{Efficiency of L-Diffusion.}$ L-Diffusion is efficient and reduces the dependency on annotated data. While the paper mentions that L-Diffusion can achieve competitive performance with limited annotated data (Table 3), it does not provide a detailed analysis of the computational cost or training time compared to other methods. Diffusion models are generally computationally expensive, and it would be valuable to understand how L-Diffusion compares in terms of resource requirements. Additionally, a sensitivity analysis on the number of diffusion steps (T) and its impact on performance and computational cost would strengthen this claim.\n\n2) $\\textbf{Applicability to Other Medical Imaging Modalities.}$ L-Diffusion is broadly applicable to medical image segmentation tasks. The paper focuses on pathology and remote sensing images but does not explore the model's performance on other medical imaging modalities, such as MRI or CT. Extending the experiments to these domains would provide stronger evidence for the model's generalizability.\n\n3) $\\textbf{Robustness to Noisy or Imperfect Annotations.}$ L-Diffusion is robust and can handle long-tail distributions effectively. While the paper demonstrates strong performance on tail components, it does not explicitly test the model's robustness to noisy or imperfect annotations, which are common in medical imaging. Including experiments with noisy labels or partial annotations would further validate the model's robustness.\n\n4) $\\textbf{Ethical and Clinical Impact.}$ L-Diffusion provides a powerful tool for advancing tumor diagnosis and microenvironment analysis. The paper briefly mentions ethical approval for the datasets but does not discuss the broader ethical implications or clinical impact of using L-Diffusion in real-world medical settings. A more detailed discussion of potential risks, limitations, and guidelines for deployment would strengthen this claim.", "methods_and_evaluation_criteria": "Yes, the proposed methods and evaluation criteria in the paper are well-suited for the problem of pathology image segmentation and the broader application of medical image analysis.", "theoretical_claims": "The theoretical claims and proofs in the paper are generally correct and well-supported by mathematical derivations. The authors effectively demonstrate why Laplace distributions are more suitable than Gaussian distributions for pathology image segmentation, and they provide a solid theoretical foundation for the proposed L-Diffusion model.", "experimental_designs_or_analyses": "The authors evaluate L-Diffusion on several well-established pathology image datasets, including CRCD (colorectal cancer), PUMA (melanoma), BCSS (breast cancer), and PanNuke (multi-class cellular segmentation). These datasets are representative of the challenges in pathology image segmentation, such as gigapixel resolution, multi-scale features, and long-tail distributions.\n\nThe paper uses standard evaluation metrics for segmentation tasks, including DICE, MPA (Mean Pixel Accuracy), mIoU (Mean Intersection over Union), and FwIoU (Frequency Weighted IoU). These metrics are widely accepted in the medical imaging community and provide a balanced assessment of segmentation performance.\n\nThe authors compare L-Diffusion with a variety of state-of-the-art methods, including U-Net++, Swin-UNet, DeepLabv3, and SAMPath. \n\nThe paper does not provide a detailed analysis of the computational cost or training time compared to other methods. Diffusion models are generally computationally expensive, and it would be valuable to understand how L-Diffusion compares in terms of resource requirements.\n\nThe paper does not discuss the sensitivity of L-Diffusion to key hyperparameters, such as the scale parameter (b) in the Laplace distribution.", "relation_to_broader_scientific_literature": "Medical image segmentation, particularly in pathology, has been extensively studied using deep learning models such as U-Net (Ronneberger et al., 2015), DeepLab (Chen et al., 2017), and more recently, Transformers (Atabansi et al., 2023). These models have shown success in segmenting tissues and cells in pathology images, but they often struggle with long-tail distributions and multi-scale features. L-Diffusion addresses these challenges by introducing Laplace distributions and contrastive learning to enhance the separation of different components, particularly tail categories. This builds on prior work by providing a novel approach to handling the inherent complexities of pathology images, such as gigapixel resolution and imbalanced tissue distributions.\n\nDiffusion models, such as Denoising Diffusion Probabilistic Models (DDPM) (Ho et al., 2020), have gained popularity for their ability to model complex data distributions. These models have been applied to various tasks, including image generation, denoising, and segmentation. However, most prior work in diffusion models uses Gaussian distributions for noise modeling. L-Diffusion introduces Laplace distributions as an alternative to Gaussian distributions in diffusion models. The authors argue that Laplace distributions provide sharper gradients and better separation between different categories, making them more suitable for pathology image segmentation. This is a novel contribution that extends the applicability of diffusion models to medical imaging tasks with long-tail distributions.\n\nContrastive learning has emerged as a powerful technique in self-supervised learning, particularly in computer vision (Chen et al., 2020). It has been applied to various tasks, including image classification, object detection, and segmentation. In medical imaging, contrastive learning has been used to improve feature representations and reduce the dependency on annotated data. L-Diffusion incorporates pixel latent vector contrastive learning to enhance the separation of different tissue and cellular components. This builds on prior work by applying contrastive learning to the latent space of diffusion models, which is a novel approach. The authors demonstrate that contrastive learning significantly improves segmentation performance, particularly for tail components, by amplifying the distributional differences between different categories.", "essential_references_not_discussed": "I think the Laplace noise was previously found to be better schedule for image generation. (See https://arxiv.org/abs/2407.03297  and https://arxiv.org/abs/2304.05907)", "other_strengths_and_weaknesses": "see above", "other_comments_or_suggestions": "not found", "questions_for_authors": "While the paper focuses on Laplace distributions, have the authors explored other distributions, such as Cauchy or Student's t, for modeling pathology image components? If so, how do these distributions compare to Laplace distributions in terms of segmentation performance?\n\nHow does L-Diffusion compare to unsupervised or semi-supervised methods for pathology image segmentation, particularly in scenarios with limited annotated data? Have the authors explored unsupervised or semi-supervised variants of L-Diffusion?", "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:

Meta-review: All reviewers appreciated the originality of using Laplace distributions within a diffusion framework, especially for the theoretical proofs which are carefully derived and validated by multiple reviewers (ZaXb, nPmf, 9Pf9, ezdp). This work demonstrates clear advantages over Gaussian distributions through sharper gradients and improved component separability. Empirically, L-Diffusion consistently outperforms state-of-the-art segmentation models across six diverse datasets (e.g., CRCD, PUMA, BCSS, PanNuke), achieving substantial improvements with DICE score gains of up to 7.16% for tissue segmentation and 20.09% for cell segmentation, supported by strong quantitative metrics and compelling qualitative visualizations. All the reviewers gave positive rating to this work and the novelty and contributions of this work have been accepted by all the reviewers. Therefore, meta-reviewer agrees with the recommendation of the reviewers.
Decision: Accept (poster)