Noisy Multi-Label Learning through Co-Occurrence-Aware Diffusion
Authors: Senyu Hou
Yuru Ren
Gaoxia Jiang
Wenjian Wang
Venue: NeurIPS 2025 poster ()
Keywords: Multi-label classification; Noisy multi-label learning; Diffusion model; Co-occurrence-aware
Primary area: deep_learning
TL;DR: We propose a Co-Occurrence-Aware Diffusion (CAD) model that improves noisy multi-label learning by using generative methods, achieving over 5% performance improvement.

Abstract: Noisy labels often compel models to overfit, especially in multi-label classification tasks. Existing methods for noisy multi-label learning (NML) primarily follow a discriminative paradigm, which relies on noise transition matrix estimation or small-loss strategies to correct noisy labels. However, they remain substantial optimization difficulties compared to noisy single-label learning. In this paper, we propose a Co-Occurrence-Aware Diffusion (CAD) model, which reformulates NML from a generative perspective. We treat features as conditions and multi-labels as diffusion targets, optimizing the diffusion model for multi-label learning with theoretical guarantees. Benefiting from the diffusion model's strength in capturing multi-object semantics and structured label matrix representation, we can effectively learn the posterior mapping from features to true multi-labels. To mitigate the interference of noisy labels in the forward process, we guide generation using pseudo-clean labels reconstructed from the latent neighborhood space, replacing original point-wise estimates with neighborhood-based proxies. In the reverse process, we further incorporate label co-occurrence constraints to enhance the model's awareness of incorrect generation directions, thereby promoting robust optimization. Extensive experiments on both synthetic (Pascal-VOC, MS-COCO) and real-world (NUS-WIDE) noisy datasets demonstrate that our approach outperforms state-of-the-art methods.

Noisy Multi-Label Learning through
Co-Oceurrence-Aware Diffusion
Senyu Hou School of Computer and Information Technology, Shanxi University housenyuâsxu. edu. cn
Yuru Ren
School of Computer and Information Technology, Shanxi University renyurušsxu. edu. cn
Gaoxia Jiang School of Computer and Information Technology, Shanxi University j aangaaoxia@sxu edu. cn
Wenjian Wang
Key Laboratory of Data
Intelligence and Cognitive Computing of
Shanxi Province #jwang@sxu. edu.
Abstract
Noisy labels often compel models to overfit, especially multi-label classification tasks. Existing methods for noisy multi-label learning (NML) primarily follow discriminative paradigm, which relies on noise transition matrix estimation or small-loss strategies to correct noisy labels. However, they remain substantial optimization difficulties compared to noisy single-label learning. In this paper, propose Co-Occurremce-Aware Diffusion (CAD) model, which reformulates NML from a generative perspective. We treat features as conditions and multi- labels diffusion targets, optimizing the diffusion model for multi-label learning with theoretical guarantees. Benefiting from the diffusion model's strength capturing multi-object semantics and structured label matrix representation, can effectively learn the posterior mapping from features to true multi-labels To mitigate the interference of noisy labels the forward process, guide generation using pseudo-clean labels reconstructed from the latent neighborhood space, replac- ing original point-wise estimates with geighborhood-hase proxies. In the reverse process, we further incorporate label co-occurrence constraints to enhance the model's awareness of incorrect generation directions, thereby promoting robust op- timization. Extensive experiments on both synthetic (Pascal-VOC, MS-COCO) and real-world (NUS-WIDE) noisy datasets demonstrate that our approach outperforms state-of-the-art methods.
Introduction
Multi-label classification is specialized subfield of classification tasks where each instance is assigned multiple labels, making it inherently more complex than multi-class classification [I] Modern multi-label classification methods typically leverage deep neural networks (DNNs) trained iteratively on large-scale, accurately annotated datasets 6]. However, collecting expert-labelled data in real-world scenarios is time-consuming and expensive. Crowd-soureing [7] and model- generated labels [ are commonly employed to mitigate annotation costs, inevitably introducing noisy labels into datasets. Unfortunately, due to their high capacity, DNNs can fit most training data, regardless of whether the labels are clean noisy 19-22 This overfitting to noisy labels prevents
"Coreesooniing author: Wenjian Wang
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Instance
Noisy Multi-labels
Latent
Pscudo-clean Multi-labels
Neighborhood
Space
> Person
Ekglunt
Plaplont
Beot
Boo:
Co-Oecurrence -Aware
Matrixing
Conditional Information
Diffusion-based Model
poyyalyy.x.9)
(
Forward Process
y=-N(O.1)
Figure 1: The illustration of the co so-occurrence-ave aware diffusion model. The example comes from the MS-COCO dataset, where the label set has been comrppted to {Person, Elephant, Boat). The true co-occurrence probability of the label pair < Elephant, Boat > very low, so our intuition is constrain the learning weight of this pair during the reverse process. The pseudo-clean label set (Person, Dog, Boat). estimated through latent neighborhood space, is more suitable as the starting point yo for label diffusion after being transformed into matrix form.
the model from achieving actual empirical risk minimization, making it crucial to address label noise multi-label classification.
To tackle this challenge, researchers have proposed noisy multi-label learning (NML), paradigm that extends the well-established label noise learning (LNL) from single-label settings multi-labo scenarios [7] Existing NML approaches predominanly follow LNL strategies, employing noise transition matrix estimation [8 and correction mechanisms 26 identify and rectify noisy labels. Some studies 27 20 further exploit label dependencies to improve the accuracy of noise estimation or correction. However, most of these methods based on discriminative paradigms, often facing optimization challenges.
28 proposed generative-based method LSNPC, where they used variational autoen- to treat noisy labels as the result of latent space transitions, enabling more accurate label correction. Similarly, in the LNL domain, Bac et al. 33 utilized VAE estimate the transition matrix for post-processing label correction, while Chen et al. (3I) framed label noise as a random generation process and used denoising diffusion probabilistic models (DDPM) [32] to model the uncertainty in noisy label generation, optimizing classification via maximum likelihood estimation. These works demonstrate the feasibility and effectiveness generative models classification tasks. Inspired by this insights, we reformulate the NML problem using DDPM as a robust label generation task.
Huang et al. coders (VAE)
29
We aim to develop universal denoising probabilistic diffusion framework for NML, achieved by modeling multi-labels as diffusion targets and using instance features guided conditions. By representing the labels in matrix form, we strengthen the mapping between features and multi-labels, ultimately optimizing maximum likelihood estimation to obtain the accurate class distribution. A key challenge in this paradigm is that only noisy multi-labels are available. To overcome this issue, reconstruct pseudo-clean labels based each sample's 's latent neighborhood feature space, and estimate meta-label co-occurrence matrix from relatively clean subset to guide the reverse process. Figure T illustrates our intuition: when noisy labels exhibit low co-occurrence probability (e.g.. Elephant vs. Boar), our model learns to steer generation away from such incorrect associations via co-occurrence constraints. The latent neighborhood feature space is extracted using pre-trained encoder, obtained through self- supervised learning large-scale pre-trained models, enhancing robustness against noise. These pre-trained encoders remain frozen during diffusion model training, ensuring flcxibility and broad applicability.

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Our main contributions are summarized as follows: 1) We reframe NML as a robust label generation task based on diffusion models with theoretical deduction, and enhance the mapping between features and multi-labels through matrix-based label representation. 2) We design pseudo-clean label reconstructor and a meta-label co-occurrence matrix estimator, leveraging pre-trained encoders to provide strong priors for diffusion model training. 3) We integrate co-occurrence constraints into the diffusion modeling, proposing the Co-Oceurrence-AAe Aware ware Diffusion (CAD) model, which can robustly learn the generative mapping from features to true multi-labels. 4) Our model achieves state-of-the-art (SOTA) performance in synthetic and real-world noisy datasets, e.g., 5~88 OFI improvement on noisy Pascal- VOC datasets.
2
Related Work
Noisy Multi-label Learning, Previous studies have primarily focused on improving multi-label classification models. BCE (33), ADDGCN (34] and ASL (35) are highly effective for multi-label classification but lack mechanisms to handle label noise. Numerous LNL approaches, such as GCE (30. Co-teaching (37] and DivideMix [8], aim to develop noise-robust classification models but lack specialized techniques for handling noisy malti- Liu et al. [39] highlighted the lack and urgency of research in NML, and only recently have a few studies emerged to address this issue directly. Hu et al. [40] proposes WSIC using clean subsets to regularize network learning, while Xie et al. [41] introduces a unified learning framework called CCMN for learning with class-conditional noise. Xia et al. (27] explored the critical role of label dependencies in noisy label learning and proposed the holistic label correction (HI.C) algorithm to refine multi-label classification under label noise. Our method focuses explicitly on tackling the NML problem and advocates for uising generative models. We model multi-label noise as a stochastic generation process, capturing the uncertainty in multi-label generation to enhance robustness against noise.
Generative Classification Method. Bae et al. 30 introduced VAE to estimate the transition matrix for post- post-processing correction in single-label tasks. At the same time, Huang et al. [28 integrated the VAE with previous NML methods for more accurate label correction. However, their fundamental framework remains limited to discriminative paradigm. Diffusion models 33 42 44
were initially designed for image generation tasks, and classification and regression diffusion models (CARD) 45 first treated classification tasks as conditional generative tasks, generating single-label outputs based on features. Building on this, aabell-retricvallaggmeeett diffusion models (LRAD) [31] addressed the robustness issue of diffusion models in noisy single-label learning by incorporating neighbor retrieval mechanism. Our approach redefines NML as robust generative inference learning and enhances the adaptability of diffusion models in transitioning from single-label to multi-label classification tasks by matrixing labels. We also introduce a unique co-occurrence constraint to alleviate the multi-labe noise problem further.
3 Preliminary
This section introduces the diffusion theoretical framework and training architecture for single-label classification tasks. Similar to traditional DDPM, it consists of a forward diffusion process and a reverse denoising process. The target of diffusion and denoising is the sample labels, with in- stance features embedded as control conditions in the diffusion paradigm. For example, CARD introduces a pre-trained encoder fa- In the forward process, it uses the encoded result of the sample features [x) as the Gaussian noise mean, performing conditional diffusion on the one- hot labels with the diffusion endpoint prior distribution as g(Yr x) = Nyrr; (x). I). Using a time diffusion schedule {6: E 1)T, the conditional distribution of the forward pro- cess is defined as L
= '' (y::: VI= -B.,,1111111 + (1 vi - 3.) fo (x), 3.I). This admits a closed-form sampling distribution with an arbitrary time step t: (Vz Yo. fo (x)) = N (ye: / Vo + (1 v fo (x), (1 a.)) I), where ag := 1 3r and ō II. 0g. Following DDPM's approach, the posterior distribution of the forward process can be derived using Bayes' rule:
(y--1 No, x) q (yz-1 Yo. fo())) = N (y--1;ã (y,, Yo. fo(x)),
(1)
Biyor 1-a,
(1- (1-ār-1) 1Vo l-a:
yx + (1 () (x( and 3. 1-a 1 Br.
where j4,
yo
I-a.
3

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In the reverse process, CARD gradually recovers the label vector Yo from a Gaussian noise distribution p(yr x) (yrr fx(x), I):
po (y:-1 yt, f (x)) [x)) :N (y--1; 3.1)
The primary objective of model learning is to make the predicted posterior distribution py approximate the true noise-added estimated posterior distribution q. According the evidence lower bound (ELBO) and Kullback-Leibler (KL) divergence, the optimization objective can be written as:
L = B,g DE (q (y--1 (yr. fx(x))) || po (y--1 (y,, x, fo (x))))]
Observing that learnable knowledge resides on the distribution's mean term, which can be repa- &,
rameterized 1t8 _
Vol (y, VI-ae Co(Y,, Lo (x) ()). The final loss function simplifies to
Lsimple = ||e - to (yr, x, (x), 4)) which represents the mean squared error between the model- predicted noise 6o and the real random noise
4 Co-Oeeurrenee-waare Diffusion Model
In this section, we first provide an overview our proposed method in Section 4.1 followed by introduction to the theoretical framework and inference mechanism of conditional multi- label diffusion in Section 4.2 Finally, in Section 4.3 we propose replacing point estimation with neighborhood distribution estimation and introducing multi-label co-occurrence-awan in the reverse process.
4.1
Model Overview
Our co-occurrence-awert diffusion (CAD) model addresses the NML problem, with the overall framework shown in Figure [] We use diffusion paradigm to model the multi-label matrix, recovering clean labels from noisy label distribution based on features and co-occurrence awareness. Instead of using point estimates, we replace them with the multi-label distribution of neighboring instances and leverage its stability to extract subset of metadata (i.e., clean subset). This strategy enables the estimation of meta-co-occurrence probability matrix. During the training phase of the diffusion-baset model, the estimated neighborhood label distribution is formatted into a matrix structure to serve as the generation target, Yo. which is progressively corrupted into a standard Gaussian distribution, (0, I) in the forward process. In the reverse process, we not only utilize
guidance but also incorporate co-occurrence-awe aware strategy to prevent the generation of unrealistic label combinations.
4.2 Diffusion-based Multi-label Learning
Inspired by CARD, we redefine NML as stochastic process of conditional label generation (i.e., label diffusion). However, there are two issues can be optimized. First, multi-labels inherently offer greater scalability than single-labels, as multi-label can be extended C one-hot vectors (denoting C as the number of classes). Therefore, we model the label matrix instead of a single-dimensional label vector. Second, when Sa fails to accurately map to the true classes, especially datasets with label noise, it significantly interferes with the learning direction. As result, we discard S and remodel the conditional multi-label diffusion paradigm.
Forward process. In the forward process, we redefine conditional Markov diffusion process similar the unconditional multi-label forward distribution q (detailed theoretical framework in Appendix A). assuming that when conditioned on features x, the prior distribution of q is the same as
q (yvly:-1.x) a (yely.-1)
(4)
= =N 1 1,y -
g (yr: X). II á (ye y2-1,x)
(5)
= (y: Voryo, (1-ā;)

---

where parameters O; and 3, are consistent with those in DDPM, meaning the forward diffusion process of the labels is not influenced by any features, and the endpoint conditional distribution of label diffusion is y (yr x) = .V (yr; 0, T). It is important to note that, unlike single-label classification tasks where the diffusion target is a one-hot vector, our diffusion target is x C one-hot matrix obtained by forming the multi-label into a matrix structure. The nigher-dimensional diffusion target is more stable in generative learning compared to a single vector, facilitating the establishment of a stronger mapping from features to true multi-labels.
We derive the conditional posterior distribution during the forward diffusion process using Bayes' rule and Taylor expansion:
(y Yc: 2) N (yc-1;
(6)
where fr = Biyai-1
1-6; Yo + (1-a,-1)V 1-6; y: of - (xly)-1) and 0r = = VTT_. B.. The last term in Re can be considered deviation to the unconditional distribution mean, guided by the first derivative of p (x yt-),, indicating that during training. the decoding information from yt to x must be introduced, otherwise the predictions of the diffusion model will become completely random, and no generative knowledge will be learned (See Appendix for detailed proof).
Reverse process. During the reverse generation process, we directly use feature information as input for the neural network model to predict the reverse posterior distribution:
Pe (y--1 Yr. t) == N (y--1: po (y,, x,,x,t) t) ..d).
1 Br. Based on the analysis of the forward process, reverse prediction requires training a class decoder p (xly:) for gradient guidance, which may incur additional costs. We adopt a straightforward approach which naturally integrates the decoding process into the diffusion model architecture. Specifically, we use a trainable decoding layer L1 to map Yt. into the feature space of However, this is impractical due to the much lower dimensionality of y, compared to the conditional feature space dimensions. Therefore, we utilize pre-trained encoder to obtain quality information during the label purification process, concatenating it with the labels for joint decoding. This enriches the original label information, effectively improving the learning quality of the decoding layer. Detailed information about the specific diffusion model network structure is shown in Appendix Figure B.1
where 3, = 1-a:
By reparameterizing the training objective, our final training loss is simplified to
C. = || c- EB (Vayo + vI -,,,,,,,,1 x, I1:
(8)
Inference. Since the classification diffusion model is deterministic in inference and the dimensionality of the multi-label vector is much lower than that of features, we mimic the inference process of denoising diffusion implicit models (DDIM) [46] to generate multi-labels in as few steps as possible without affecting the generated results. Appendix C introduces the inference algorithm. its implementation details, and the recorded inference times. In experiments, we use settings of S 10 and T 1000, where the inference efficiency of the diffusion model is on the same order of magnitude as that of traditional classification models (See Appendix Table H.1
4.3 Neighborhood Label Estimation and Co-Oceurrence-Aware
By optimizing the diffusion-based multi-label learning, we can effectively guide the model to learn generative mapping from features to true multi-labels. However, in noisy environments, excessive con- tamination of the generative target can lead to wrong shift in learning target distribution. To mitigate this issue, we propose optimizations from both the forward and reverse process simultancously.
Neighborhood label estimation for forward process. A key challenge in label estimation in noisy environments the reliance on single-point estimates, which may fail capture wrong label distributions. To address this, we adopt neighborhood- based label distribution estimation as proxy for each instance. This approach is grounded in the neighborhood consistency assumption [47], which posits that in a latent space, instances with similar features tend to cluster. Ensuring this assumption holds requires an unbiased latent space, which we achieve by leveraging pre-trained encoders trained via self-supervised learning or on meta-data, thus mitigating the influence of label noise. In fact, pre-training not only significantly enhances adversarial robustness but is also widely used in L.I.. to improve resilience against noisy labels.
5

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Table 1: The mean and standard deviation of results (%) on noisy Pascal- 2007
Metrics
Methods
Sym. 10%
Sym. 30%
Sym. 50%
Asym. 10%
Asym. 30%
Asym. 50%
Standard
70.17=0884
64.50+11.0
48. 0..1
1.166+1.15
60.94:1-.225
46.72:1:2.13
ASL
72.98=0.85
66.79:11.19
1.864.1..11
73.50+0..99
61.99-10.78
45.10:10.15
LRAD-R
7..71=0.61
6..97:111.6
67.44:10.61
74.55:10.79
70.64:10.3
59.27:10.72
HLC
7..59=1.76
72.07:10.67
68.03:10.78
75.72:10.64
69.86-11.61
19.09
mAP 1
LSNPC-R
19.21=1.16
73.27:10.7
70.19:10.93
1..52+11.3
71.33-10.95
58.91110226
CAD-R
80.56=0.69
75.18110.47
72.37-10.29
78.98400.90
74.56:10.45
61.8811005
LRAD-V
82.50=0:24
80.14:1.00
78.9310.77
80.1410.99
79.9411.79
68.72=11005
LSNPC-V
83.71=0.58
80.19=0.80
79.69=0.66
79.90+0..8
80.01=00.55
68.57=1.19
CAD-Vt
0.
86.86:0060
84.61
87.50+10.58
81.24:10.42
69.37:1041
Standard
65.51=1.23
63.52:10.48
18.08
67.34410.78
58.30-2.82
42.19
ASL
68.14-0.60
65.71
1..65=+1.32
1.99
1..0
43.83=11100
LRAD-R
69.75=1.11
1..8
53.30=+0.33
09.99
61.42::0.47
4.5
HLC
1.811=1811
68.71
66.62+11552
1,61
64.75=+0.70
1.35
OFI 1
LSNPC-R
73.96=0.50
67.75+0.66
65,47+1119
1.8
63.08+0066
55.07=0.559
CAD-R
75.22-0.74
71.42+00.2
67.19+1.50
73.24++0.91
65.77+1.72
59.51+0.43
LRAD-V
76.03=1.88
69.47711118
68.3
74.28+00.2
65.37
58.45+1.115
LSNPC-V
1..1
70.78+0.19
69.08
74.05+1.19
1.34
19.35
CAD-Vt
82.00=0.10
76.42:10.11
72.41+0..2
81.40+0.99
70.12::0.85
64.51
Standard
65.65+ 1.52
55.644+.884
13.04++171
67. 17.16+1.00
37.03-+3.43
41,24 1.75
ASL
0.62
57 1.26
43.60++0.13
67. 0..74
08.33=+0.49
1..8411.16
LRAD-R
0.89
60.37:10.53
53.241:.81
68.91
62.05
44,29:1062
HLC
71.66=1.44
62.19:1.42
63.65
70.07:11.37
16,51 1.06
CF1
LSNPC-R
74.11=1.71
63.22:10.22
62.41
71.6711..74
61.4911.09
54,05
CAD-R
75.37=0.57
64.8710.4
64.13
73.00100.81
65.78-10.52
$6.1710.49
LRAD-V
11.19=1.53
70.8710.14
64.3110.11
74.08:1.19
64.671189
19.28-1.69
LSNPC-V
78.31=1.27
69.1910.76
64.9220.555
73.85+:1.25
64.73-11.8
19.18
CAD-V1
82.17=0.83
75.78:10.19
69.33+10772
81.18:0.25
70.25
62.74+10554
Specifically, given a noisy training dataset D = (I; 0:) x E Rd E ER", "-" L..... .n. for each instance x; in the latent space, we assign the label sets of its K nearest neighbors, i.e., y
(vi" {x)). Then we compute the normalized frequency distribution of these labels by Jt DJT E k= (+)),, which estimates distribution then serves as the generation target Yo for diffusion model's 's training. To this end, the model mimies the human annotation process, where labels assigned based on contextual information from similar features. This approach parallels how humans retrieve similar features from memory for semantic labeling, allowing the model learn and infer semantic similarities. While the neighborhood proxy method mitigates errors in the generation target, severe noise contamination can still introduce estimation bias (see detailed analysis in Appendix F). To address this, we incorporate co-occurrence awareness into the reverse process to refine the generation direction.
Co-occurrence-aware in reverse process. Our goal is to pre-estimate a label co-occurrence probabil- ity matrix that captures relationships between label pairs, guiding the diffusion model to to be aware of implausible label combinations and avoid generating them(e.g., elephant vs. boat). Ideally, such estimation would rely on meta-dataset, as seen in meta-learning, to ensure robustness. However, in real-world noisy multi-label learning, directly available meta-data is often lacking. To overcome this, we secondary use the latent neighborhood space extract a clean meta-subset from noisy data. Specifically, for each instance I; we estimate its neighborhood label distribution Ty while measure its instability by = D& E,, (y/ )² To differentiate samples with varying instability, we employ a binary Gaussian mixture model (GMM) to model the distribution of d; and define the meta-subset(clean subset) D' as the subset of samples belonging to the lower mean component in GMM (i.e., lower instability samples). This aligns with our neighborhood consistency assumption, samples with more stable neighborhood distributions more likely to be clean and thus more valuable for estimating the co-occurrence matrix.
For the selected meta-subset D', we estimate the co-occurrence probability of each label category using the co-occurrence matrix C, where Cm,,. = P(y, 1, yy = 1|r E &D). Each element Cm., represents the probability of labels m and n appearing together within the meta-subset. Then, we com-

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Algorithm 1 CAD Training
Input: noisy training set = (X, Y), pre-trained encoder fp
1: Obtain latent feature space by fp and record the K-nearest neighbor of each sample
2: Compute instability scores ó and isolate meta-subset D
3: Estimate co-occurrence matrix C on D'
4: while not converged do
5: Sample batch data (x ~ D; time slice t ~ {1, (1....,T] Ty; and noise ())
6: Estimate y as Yo and convert it to a one-hot matrix
7: Compute learning weight w and take gradient descent step on the loss L2 (Eq.9
8: end while
pute the mean co-occurrence rate across all label pairs for samples xi by C, = 1V. E (m yn J.y, Cm,.e- Note that we use a hard truncation to count co-occurrence label combinations V i.e., a positive label is assigned if its value is greater than 0.5. Finally, we apply Min-Max normalization at the batch level to obtain the learning weight wy for each sample, which is used to adjust the learning weight by modifying Eq. g
-w ca + xx,, 11?
(9)
Algorithm D describes the overall training procedure. Steps 1-3 correspond to data preparation, while steps 4-8 cover diffusion model training. After obtaining the trained diffusion model and its parameters, inference is performed using Appendix Algorithm C. which progressively generates the label matrix from input instances. Finally, the multi-label set recovered through matrix inversion.
5 Experimental Results and Analysis
5.1 Experimental Setup
Datasets and noisy multi-label simulation. We validate the effectiveness of the proposed method on three multi-label synthetic noisy datasets: Pascal-VOC 2007
48) Pascal-VOC 2012 (48 and
MS-COCO 49). as well as on the real-world noisy dataset AUS-WIDE 50 In the synthetic noisy datasets, we randomly retain 10% of the samples as a validation set and introduce simulated multi- label noise into the training set using a noise transition matrix T [1] Specifically, for any i & j. Ti - (y₁ E D A & Vly,, $ y' A V E y) represents the probability r of the i-th class label to be corrupted into the j-th class label. To mimic real-world label noise, we consider both symmetric and asymmetric noise patterns and select noise rates of 10%, 30%, and 50% for each patterns. The details of the transition matrix are provided in Appendix Figure D.I
Baselines. We exploit the following baselines: (1) Standard 33 which trains ResNet with BCE
loss. (2) ASL [35], which operates differently on positive and negative samples. (3) LRAD-R (3I. diffusion model with a pre-trained ResNet encoder. (4) HLC (27). a label correction method using label dependence. (5) LSNPC-R 28), which integrates VAE with pre-trained ResNet encoder. (6) LRAD-V B1I, which builds upon LRAD-R R by replacing the ResNet with Vision Transformer
(ViT) 51 pre-trained encoder for improved feature extraction. (7) LSNPC-V (8), variation of
LSNPC-R, replacing the ResNet with a ViT pre-trained encoder to combine generative modeling with transformer-based representations. Note that Standard, ASL are designed for clean multi-label data. LRAD-R/V is designed for LNI.. HLC and LSNPC-R/V are designed for NMI.
Implementation details and metrics. Our model requires a pre-trained encoder fp. We use two versions, CAD-R and CAD-V, which integrate ResNet-50 and ViT-14/L models pre-trained on ImageNet, respectively. Both remain frozen during the diffusion model training without fine-tuning. For faimess, baselines (1)-(5) are compared with CAD-R, which called the Common group, while baselines (6) and (7) are compared with CAD-V, which called the VIT group. We report the mean and standard deviation of the results from five random experiments. Following the conventional settings (52] we evaluate multi-label classification performance using mean average precision (mAP), overall F1 score (OF1), and per-class Fl score (CF1) as assessment metrics. Notably, the best results in Common group and VIT group are highlighted blue and red, respectively. More details and pre-trained model combinations' results can be found in Appendix D.2 and Appendix B
7

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Table 2: The mean and standard deviation of results (%) on noisy Pascal-VOCe 2012
Metrics
Methods
Sym. 10%
Sym. 30%
Sym. 50%
Asym. 10%
Asym. 30%
Asym. 50%
Standard
1.02
66.08++0.68
10.30:1..10
1.50
61.60=0.38
49.61 +00.23
ASL
74.18=1.16
68 68.43:10.23
49.72::1.08
1.59
62.66:t0.61
48.82:1:.077
LRAD-R
75.94=0.11
71.6911.54
70.39:1047
7..97:11551
63 63.68:11.13 71.41+1.20
HLC
77.85=1448
72.84:11.2
69.03:11.34
75.17:10.94
70.62:10.77
64.27:11.22
mAP 1
LSNPC-R
1.95
75.07:10.34
73.26:10.43
77.89:1.113
72.10-11.69
65 1.208:1::26
CAD-R
8128
77.0210.94
75.53:10.17
80,4940.27
75.37-10.99
68.36110.89
LRAD-V
81.1510.39 03.8
80,38:1.88
81677:0.78
79.81=1.67
72.91=1.14
LSNPC-V
85.09=1.41
82.16:10.60
83,17=1.35
81,42-0.60
80.88
73.75=1.49
CAD-Vt
89.27-0.977
88 68.99:00669
88.31
89.17
82.12:1..25
76.63:10.59
Standard
66.09-0.28
64.28:0.79
19.95
68.32:11.45
1..21
43.67
ASL
68.74-0.71
65.89
1.15
1..1
16.18-11.36
0..37
LRAD-R
70.36=0066
61.60+22.00
15.76=+1.10
70.11+0..35
57.49-40.29
46,91=0012
HLC
1..14=1.73
70.19+0.11
1..83+1100
72.37+t0.77
65.56=+0.65
60.64=
OFI f
LSNPC-R
7.08
68.56++0.24
68.01+0.73
1..92+1.39
64.04++0.66
58.01
CAD-R
75.88-0.57
72.27+0.77
69.80++0.94
74.31+0.47
65.71+0071
61.60+0.85
LRAD-V
0..72-0.39
71.3311.44
70.07+F0.64
74.37+1.17
61.53:11222
19.51
LSNPC-V
0.18
72.61
71.76:
75.13++0.84
6..05=:1.14
1.944
CAD-Vt
82.72-0.80
77.33+:0.1
75.2240.89
82.59400.83
70.31
66.78:1122
Standard
1.37
17.74+1.005
44.22+1.18
68 68.98+0.88
56.40+1.222
43.36 1.79
ASL
0.80
11
48.90 0,
69.78++0.6
57.68
46.08
LRAD-R
0.59
60.65:+0.24
70.78 14.70::1.47
1.764 1..36:
HLC
0.65
68.54:11.73
64.37:10.68
65.42.10.74
1.78
CF1
LSNPC-R
7.77
63.61
64.12.1..66
73.61
60.8110.60
58.14110.99
CAD-R
76.63=0.57
68 62.10.1111
64.86110.73
74.98:10.95
65.47-10.88
60.5611141
LRAD-V
14.48=1.49
10
64.07:00.40
13.09:0071
62.93-1037
60.7710.79
LSNPC-V
79.62=0.89
718010.58
70.69
75.85+0.339
65.99=10.46
63.6611138
CAD-V1
83.54=0.13
78.64410.77
71.23+0.21
83.38:00299
72.44+0.94
1..49:11007
5.2 Comparison with SOTA methods
The results on noisy Pascal-VOC 2007, PaScal-VOC 2012. MS-COCO and real-world noisy dataset JUS-WIDD are shown in Table I Table 2 Table Table respectively. Our method (denoted by t) consistently outperforms SOTA methods across synthetic and real-world noisy dataset. We analyze our experimental results in two groups based on different pre-trained encoders.
Compared with the Common group. First, our method consistently outperforms the Standard across all noise settings. For instance, on Pascal-VOC 2007 with 30% symmetric noise, our method improves mAP by 11% and OFI by 8%, demonstrating the necessity of handling noise in NML problem. Second, when combined with a ResNet pre-trained encoder, our approach maintains stable advantage over SOTA methods such as LSNPC-R and HLC, e.g., on Pascal-VOC 2012 with 50% noise, our method surpasses SOTA by an average of 2%. Notably, compared to mAP, the OFI and the CF1 scores of CAD-R show less stability. dataset, the CF1 score is slightly lower than HLC, but still competitive. We attribute this to the bias in neighborhood proxy estimation and the noise leakage from the subset, and analyzes the limitations of the CAD-R version in high-noise environments (see Appendix [T. Therefore, we recommend using the CAD-V version, which offers better performance and stability.
the high-noise setting of the Pascal- VOC 2007
Compared with the ViT group. CAD-V exhibits even greater improvements than Common group. On MS MS-COCO. outperforms LRAD-V and LSNPC-V by an average of 8% and 4%. respectively, highlighting its superior ability to leverage the same prior information more effectively. Compared to the Standard method, our method achieves over 30% improvement in high-noise settings (50% noise rate), validating its robustness. Additionally, we compare the CAD-V version with the respective state-of-te ofiee-oftthe-ee methods on the real-world noisy dataset NUS- WIDE, and the results are provided in the Table further demonstrating that our method can well handle practical scenes. As shown Figure 2 our method not only corrects erroneous labels (e.g., the second image in the first row, where 'tiger' is corrected to 'cat') but also generates missing labels (e.g., the third image in the first row, where 'plants' and "rocks" are added). This underscores our method's practical effectiveness in real-world settings and its potential to extend from noisy label learning to partial label learning.
8

---

Table 3: The mean and standard deviation of results (%) noisy MS-COCO
Metrics
Methods
Sym. 10%
Sym. 30%
Sym. 50%
Asym. 10%
Asym. 30%
Asym. 50%
Standard
59.27=0.86
54.90+0.73
00.75++0.75
61.61+0.69
55.48-0.62
36.85=t:.96
ASL
61.64=1.10
56.85:+0.61
00.29:1:.74
1.532::1.52
56,44:1.322
39.22:1:0.48
LRAD-R
63.1120.45
59.55:1:422
57.03310.78
63.211:0.4
64.31+1.19
45.44:1:.74
HLC
64.69=1.10
6..34.1..95
57.53:11.0
64.20110.57
63.60:10228
49.25:10.55
mAP 1
LSNPC-R
1.891=1886
6..3611.80
59.36:10.86
65.73:11.45
64.9411.56
59.07
CAD-R
6.805=0.87
63.9910.80
61.20:10.32
66.97:10.59
67.88-0.89
60.05500.82
LRAD-V
6..69=1007 69.9111190
66.7510.33
67.9511.66
69.78
68.91
LSNPC-V
70.71=1.35
68.25+1.35
67.39:10.54
67.75+1.19
68.844
67.76=20.4
CAD-Vt
0..18=0011
7..93:1062
71.55
74.19::0.65
73.96:10.57
69.56:10.22
Standard
57.43=0.65
58.5110.64
42.59-10.33
59.46:10.66
54.57-10.27
38 1.88411.88
ASL
59.74=1.48
19.9711144
42.21
6..15+1.79
09.13
01.46:
LRAD-R
61.15=1882
1..08
46.07=1118
61.02:00.20
60.42-:0.6
44.94=10.30
HLC
62.69=0.80
63.29+
59.01#0.72
61.97+0.11
60.60=#1009
58.09
OFI 1
LSNPC-R
14.
62,40+1.74
57.99+1.31
63.46++1.55
1..04+1.50
55.61
CAD-R
65.95-0.24
63.78+0.82
59.52+0.74
64.67+00.39
61.56+06.1
59,01+0.65
LRAD-V
1..41=1880
65.75+1.36
59.46+-0.67
64.59+1.95
63.99:F0.41
55.96+
LSNPC-V
67.64=1.66
64.27:10.34
61.19:1107
65.39:10.37
64.05=10.34
18.85
CAD-Vt
71.89=0.91
70.39:10.45
64.14:10.68
71.84:0.61
69.31
63.97:10.22
Standard
56.42-0065
50.24+0.94
38.65+0.61
58.45+0.11
53.19+
37.36++0.92
ASL
58.68
12.03++1.97
12.75
1..1
54.40=
40.89
LRAD-R
60.07=1.88
54.31
1..81
19.97:1.44
57,87
42.27
HLC
0.25
56.15
56.26.10.25
60.91
59.81
11,81
CF1
LSNPC-R
63.69-0.68
57.0811147
56.05510.13
62.37100.53
57.35
13.59
CAD-R
64.78-0.54
58.5710.50
56.69110.90
63.59110.9
59.86-10.95
54.85
LRAD-V
03.34-0.11
59,9911.06
56.7511.76
62.47:L0.11
611811.16
$1.5810899
LSNPC-V
67.30-1447
62.47
58,2911.39
64.27+11.27
62.2440.70
188
CAD-V1
70.62+0025
68 08.42:10.59
62.26:+0.93
70.65:10.70
68.32:10488
19.8811.006
Table 4: Comparison of our method's result (%) SOTA the NUS-WIDE dataset.
Metries
Standard 3
ASI.
35
HI.C 27
IRAD-V 31
LSNPC-V 28
CAD-Vt
mAP
59,21
63.92
63.14
63.95
64.37
65.13
OFI f CF1 f
71.52
75.03
74.68
72.13
74.92
75.58
57.77
62.69
62.87
60.53
63.43
63.68
5.3 Ablation Studies
We conducted ablation experiments on Pascal-VGs VOC 2012 and MS-COCO assess the effectiveness of three modules: neighborhood label proxy (F), co-occurrence-awar (CA) strategy, and diffusion model (DM). As shown Table 5 disabling all three modules results in the Standard baseline. Enabling only the DM approximates the LRAD model without neighborhood retrieval, causing 9% performance drop. Conversely, disabling the DM reduces the method neighborhood estimation, performing worse than most other settings. Notably, the whole framework's s performance is only closely matched when DM combined with either y or CA. highlighting the importance of the diffusion model. Additional ablation studies on pre-trained fp. neighborhood proxy estimation performance, the impact neighbor K value, and training efficiency analysis are detailed in Appendices E and H respectively.
non-parametric
Table further demonstrates that, compared to neighborhood estimation results under different pretrained encoders, the diffusion paradigm consistently plays a critical role in CAD. For example, when ResNet50-wiin relatively weaker representation capacity-is used as the pretrained encoder, its neighborhood estimation performance falls below that of the baseline HLC. Even with such coarse estimations, CAD is capable of refining the generative feature-label mapping and consistently achieving performance improvements beyond the label estimation stage. Moreover, the CAD model with ViT- still outperforms the baseline, whereas the neighborhood label estimation alone (based on ViT-14/L) performs worse than the baseline across key metrics like OF1 and CF1. This clearly highlights the indispensable role of the diffusion architecture enhancing performance beyond what weak feature spaces can offer.

---

NUS-WIDE Images
ID. 0568, 24587805
DD COSO 438909275
D: 0027 40384C670
ID. 0423, 2254880272
D: 0307 1403218420
[buildings: 'clouds',
Pelouds, "person""
Given
[animal, 'caf'' [xebra]]
l'animal; Yiger]
[animal, Yox]
'rainbow', window]
sky', 'swimmers]
lbbilddings', 'clouds', 'snow. window!
CAD Generated
['animal', 'cat)
('animal, 'catt)
('animal, "plants', 'rocks')
('person', 'sports')
NUS-WIDE Images
10:0574_110000 130851100
1D:0010_143800000 143488800770
ID: 00900
Given
('olouds", locean', 'sky',
[horses' "town']
[lake', 'water', 'whales']
Procks', 'temple]
Froad', 'toy
'vehicle', water]
l'airplane', "llouss 'ocean' 'sky, Vehicle', water"]
[olouds', "plants", Window'
CAD Generated
[buildings', town']
[ccars', 'road', 'vehicle"]
l'horee', Toy']
True noisy multi-label examples from the NUS-WIDE dataset and the prediction results from the proposed CAD model. The noisy items in the ground truth label set are highlighted in red, while the successfully corrected items in the CAD model's generated label set are highlighted in blue.
Figure 2:
Table 5: Ablation study results with 30% noise, reporting the average OFI scores (%).
Modules
Pascal-VOs 2012
MS-COCO
y
CA
Sym.
Gap
Asym.
Gap |
Sym.
Gap +
Asym.
Gap 4
64.28
13.05
58.21
12.10
58.51
11.88
54.57
14.74
X
X
70.31
7.02
60.52
9,97
64.75
5.64
62.98
6.33
V
X
V
74.29
3.04
68.41
1.90
67.35
3.04
66.58
2.73
V
V
75.43
1.90
67.99
2.32
68.13
2.26
65.97
3.34
V
71.66
5.67
64,87
5.44
63.47
6.92
62.53
6.78
V
V
77.33
N/A
70.31
N/A
70.39
N/A
69.31
N/A
Table Comparison of the two phased results of label pre-estimation (y) and CAD with different pre-trained encoders. HLC is presented as the baseline in the first row, while the best and second-bes metries are highlighted in red and blue, respectively.
Methods
Pre-trained
VOC 2007-sym.
50%
VOC 2007-Asym.
50%
VOC 2012-Sym. 50%
VOC 2012-Asym.
50%
Encoders
mAP
OFI
mAP
CFI
mAP
OF1
CF1
mAP
CFI
HLC
66.62
59.09
56.51
67.83
64.27
59.86
ResNet50
63.65
47.42
44.53
45.36
31.62
37.88
65.88
39.69
35.31
59.56
32.62
31.61
CAD
ResNet50
72.37
67.19
64.13
61.88
59.51
56.17
75.53
69.80
64.86
68.36
61.60
60.56
VIT-14/1.
82.20
53.21
55.43
52.38
39.99
46.57
82.27
48.64
47.79
52.17
44.23
48.68
CAD
VIT-14/L
84.61
72.41
69.33
69.37
64.51
62.74
88.31
75.22
71.24
76.63
66.78
67.49
6 Conclusion
In this work, we advocate for deep generative perspective achieve robust multi-label classification, offering a novel insight. We use powerful diffusion models to reformulate NML within a probabilistic denoising label learning and robust inference paradigm, proposing the CAD model. We enhance the reliability of the target distribution in the forward process through neighborhood proxy estimation in the latent feature space, while constraining erroneous generation directions in the reverse process using label co-occurrence rates. To the best of our knowledge, this is the first application of diffusion models to the NMI. problem. The proposed method achieves SOTA performance on both synthetic and real-world noisy datasets, highlighting its strong potential in this domain.
10

---

Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grants U21A20513, 62476157, 62576201, and 62276161.
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[50] T.S. Chua, J. Tang, R. Hong, H. Li, Z. Luo, and Y. Zheng, "Nus-wide: a real-world web image database from national university of singapore," in Proceedings of the ACM International Conference on Image and Video Retrieval, ser. CIVR '09. New York, NY, USA: Association for Computing Machinery, 2009.
[51] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner, M. Dehghani, M. Min- derer, G. Heigold, S. Gelly al., "An image is worth 16x16 words: Transformers for image recognition scale," " arXiv preprint arXiv:2010.1 1999,, 2020.
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[54] G. Hlumblot-Renaux. S. Escalera, and T. Moeslund, "A noisy elephant the room: your out-of- distribution detector robust to label noise?" in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024, pp. 22 626 22 636.
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Appendix
A Unconditional Multi-label Diffusion Models
In this section, we model unconditional label generation following the theoretical framework of denoising diffusion probabilistic models (DDPM) [32]. We start by defining the data distribution yo ~ (30) and a Markovian forward (diffusion) process which progressively adds Gaussian noise N (0,1) I) the labels based diffusion strength Br, diffusing label yo yr:
q (ye yt-1) = N (y:: /1 Beyc-1. 8.).
(10)
According to the derivation of the Markov chain, the joint probability distribution from yo to yi can be computed, which is also a Gaussian distribution:
(ye yo) = N (ye: Voryoo (1 -++
(11)
/oyyo + v1 dce, <~ C~N(0.1) (0.1)
(12)
where 0₁ == 1 3g and āg II. ag. Under Bayes' theorem. one finds that the posterior distribution of the forward process can be represented as Gaussian distribution with mean jú (yt, yo) and variance B,
(Vt-1 1 vc, Ve, vo) =N
Vt- i (yt, (0t, BB.I)
(13)
D4 (Br:yo) Uo) vaa-
Voi (1 11-00-0 Ō1-1)
y0 +
Vc:
(14)
1 04
1 αe
8. 1 1 āc-1 Brr
(15)
Ctt.
In the reverse process, we naturally employ a neural network to perform Markovian inference from ((rr), fitting the posterior distribution (Vt-1 ye) through to yu- Since the variance of the posterior Gaussian distribution depends only on the diffusion strength corresponding to time f, the neural network focuses primarily on predicting and learning the mean:
po (yt-1 v.) == N (y--1: 14 (ye, (,,
(16)
To train this model such that pa (yo) closely approximates g (yo), we optimize the variational lower bound (VLB):
LVLB == Lo + L1 +... LT- LT:
(17)
Lo = llg pa (yo v1),
(18)
Lt-1 == DKL (q (y:-1 yt: vo) || pe (Vt-1 3c)),
(19)
L = DEL (g (yT vo) || ((r)).
(20)
However, Ho et al. 132 found that directly predicting the mean was not effective, so they reparam- eterized the estimation target, constraining the neural network to estimate the actual noise of the diffusion process and simplified the loss function:
[| c- - cn (ve,t) t) 12]]
Tsimple = (00=11,.T:10000uuo....
(21)
During inference, we utilize the label noise estimated by the model, restoring the mean of the label at time 1 to retrieve its distribution form, and then gradually performing random sampling until generating the label yo:
1 ar en (ve, 1)) + / Boz. v1
8/
(22)
Vas
where z (0, Unfortunately, such a label generation process does not incorporate any conditional information, thus for instances with same features, it can generate variety of labels. This characteristic makes the diffusion model impractical for elassification tasks where distinct label assignment is required.
22

---

B Conditional Multi-label Diffusion Models and Feature Embedding
In this section, our main goal is to derive the posterior distribution of the forward diffusion process when features are used as controlling conditions and to analyze its differences and connections with the unconditional posterior distribution. Following the method used in DDPM (2), We first define conditional Markov process : (where q represents the corresponding unconditional process) which Gaussian noise ~ N (0, I) is incrementally added to the labels for diffusion. The addition of noise remains the same whether features are conditioned or not, leading to the following definition:
q (vo) := q (30),
(23)
i (y) 1)) = (wt 1)-1),
(24)
T
(yi. 1o, 2)
II q (3e 1)-
(25)
With knowledge of the forward process's 's prior distribution, we can derive the prior distribution of g:
(v: I 1(-1))
á (yt, (e-1) dx
(26)
/ á (ye ()-1, & (x: 1t-1) dx
(27)
J. q (ye (o--1) 1 (x 11-11) dx
(28)
(ye (3--1) ) (z 11-11) dx
(29)
q (3/ Vt--1) 1)
(30)
(yee 1))1, x),
(31)
which indicates that conditions do not affect the prior distribution in the forward process. Similarly, we can derive the joint distribution of q:
J. 9 (Uher, x yo) dr
@ (yher vo)
=
(32)
[ a (xr (1)) (ViT yo, x) dx
(33)
f ( yo) II q (ye 11-11 xdd
(34)
T
= [. (x vo) II q (ve 1d=
(35)
T
= II (yee I 10-1) / q (z vo) dx
(36)
1=1
T
II (ve 1)-1) t=1
(37)
9 (U (o)-
(38)
23

---

Based on this result, we can further derive the marginal distribution of q:
(yhe =
á (vo, yt) dyo:t-1
(39)
c-
i (vo) á (vi...., Us vo) dyo:--1
(40)
[ yone-
q (y0) 9 (81 ........ ya vo) dya:e-1
(41)
(vo. Me) dyo
(42)
yo.c
9 (3r).
(43)
Using the prior and marginal distributions, we can demonstrate that the unconditional posterior distribution aligns with q:
9 (31-1 y1) (1)
(44)
(yee
q (yr 3t-1) (V6-1)
(45)
(Vb)
9 (v/, 9t-1 1) (Vi-1)
(46)
(yr)
q (V1-1,
(47)
(Ve)
q (yc-1 y/))
(48)
By incorporating features as posterior conditions, we estimate the posterior distribution of the conditional forward process using Bayes' rule:
(v:-1 x)) (vc-1) (x V1-1)
(49)
((x)
Continuing, by adding the known distribution y/ condition for generation, can obtain:
① (3te11
Mee @ (x 3t
i (yt-1
(50)
(ar (r)
4 (3t-1
(1)) i (xr 11-1, Wh)
(51)
(xz (/)))
q (yc-1
1/.) à (x Mt-1)
(52)
9 (3t-1 y/) e log ((mla 1) log (onlas))
(53)
where the derivation of @ (x 11-1, w1) á (x M)-1) from Eq. (1p to Eq. 52
is as follows:
[z (t-1)
② (xr (1-1,1)) (yr. 1t- x))
(54)
② (Ve V/-1)
(y yt-1) 4 (x 1/- 1) (yr 1/-1))
(55)
(x: y)-1))
(56)
note that the term log ((=l0<) in Eq. 53 is independent the distribution 9t-1, thus we set this part as constant A:
g (1h-1 Ve. 2) = (y:-1 ye) log ((x(ve-1).
(57)
where q (y:- v:) is the unconditional posterior distribution of the diffusion process, modeled as Gaussian distribution with mean t4 (yt, yo) and variance 3, in Eq. (14) and Eq. 15 respectively. Simplifying the covariance from the probability density formula,
get:
(yr-1 x) Il FP /28, 1122.-toe +log ((r1)e1)).
(58)

---

Diffusion-based Arwwak-rrrhhilccuurr
yo,
PeffusionPProees
Y1
Embedding
1
La
Le
Embedding fx(x)
ResNet encoder
Concatenation
Hadamard product
Figure B.1: 1: The network architecture of the conditional multi-label diffusion model. Blue components represent trainable network layers, while gray components represent normalization activation layers.
Given that the number of time steps T' in the diffusion process is large enough and the diffusion coefficient 3, small enough, the variance of the distribution q (St-1 yr) is sufficiently small and concentrated near f4, We perform a Taylor expansion around y1-1 jr for log (z 11-1) up to the first derivative, for simplicity, we let V Vn- log & (r 3t-1)) y-- g. which essentially the gradient of the distribution at that point.:
log ((x 9t-1) x log ((x Bc-1)l i- + (Vt-1 (b)g o(V--1).
(59)
Thus, the posterior distribution can be estimated as:
q (yt-1 yt, x) x llue 1- 1
(60)
(lix 1 B.ool 1/28,-0
(61)
= (yt fie, o²
(62)
where f4e =
Biyai I-a; --a; yo + 1-0c
1
1
Yt + of v. log q(x 9t-1) and a; V T-a -- 8r-
To ensure the correct introduction of conditions, the mean during model prediction. The diffusion model's network architecture, depicted in Figure B.T. consists of ResNet encoder and series of feedforward layers. The T, decoding layer plays a crucial role by contributing the gradient V, y. log P (xlW)-1) as guidance. The network inputs are (xr Ja), randomly sampled and where Yo transformed into Yt by forward noise addition and then concatenated with fp (z). After decoding, it merges with the normalized encoding features of ResNet through a Hadamard product, incorporates time positional encoding, and uses series of feedforward networks, batch normalization, and Softplu activation to predict the noise term eg.
need to incorporate the decoding gradient into
C Deterministic Implicit Inference
This section primarily discusses the inference process of the CAD algorithm. Since the diffusion process involves labels and is directed towards classification tasks, it is imperative to reduce the uncertainty in the inference process and expedite much as possible, aligning with the method of denoising diffusion implicit models (DDIM) 46]. With a trained conditional diffusion model, we proceed as follows:
(ye v0) = N (yi / Vāryo. (1- I))
(63)
Yt Vayyo vI āte,
(64)
25

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Algorithm C.I CAD inference
Input: Testing set D {X}
Output: 90
1: Sample instance D, Sample multi-label yr ~ N(0.1)
2: for to do
3: z (0, if 1, clse z =0
4: Vrr, Var, I- (Mre) + V ar, - 6
(Fx) (vr,) + 022
Var
5: end for
where c NO, Similar to DDIM, we define a non-Markovian nature for the forward posterior
distribution:
tr (yr, Vr,, 30) = W (vr, 1; Mo + Nyr, 0. 2T)
(65)
where M and N are coefficients to be determined, and 0g 2 0. T is a subsequence of [1,... T. with Ta = T, e.g., i = 1000 and S = 10, then [1, 100, ... 9900, 1000]. From the empirical form of the posterior distribution, we have:
yr.-1 Myo Nyr, +
(66)
Myo + N (Va.yo + VI- + O,E
(67)
= (M + N a..) yo + N a,, o,e,
(68)
where and are independent and identically distributed Gaussian noises with additivity, hence:
yr = (M + a.,) yo + / (1 a.,) 00E
(69)
V 9/u + V -.T.1
(70)
By the method undetermined coefficients, M and N are determined:
M = Vār.-. VI δ. o
aT.
(71)
N /1 Or, o2 VI ar,
(72)
We reorganize the inference distribution. and since the y/ term is unknown during actual inference, we
estimate it using yo v.. .e, (T (y=x) The detailed inference process is outlined in Algorithm
achieve implicit probabilistic diffusion model, turning the inference into a deterministic process given yr by setting a. = 0 [46) This modification reduces the variability during inference, ensuring predictions crucial for classification accuracy. Additionally, since the inferred labels are in matrix form, we apply necessary post-processing step project the matrix-form labels into normalized probability distribution, similar to the SoftMax activation used in classification. To obtain the one-hot label vector, we typically the category with probability greater than 0.5 1.
C.T
For classification tasks, following the DDIM approach,
consistent and reliable label
D Experimental Setup and Details
D.1 Dataset Details
Synthetic noisy datasets. Pascal-VOC 2007 and Pascal-VOC 2012 share the same 20 object categories, with an average of 1.5 labels per image. The Pascal- 2007 dataset consists of 5,01 training images and 4.952 test images, while Pascal- 2012 includes 11,540 training images and 10,991 test images. Since the test set labels for Pascal-VOC 2012 are not publicly available, we follow previous studies and use the Pascal- VOC 2007 test set for evaluation. The MS-COCO dataset contains 82,081 I training images and 40, 1.7 test images, covering 80 object categories with an average of 2.9 labels per image. As shown in the Figure D.I we visualized the noise transition matrix used in the experiments Pascal-VOC 2007 and Rascal-VOCC 2012.
26

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(a) Symmetric noisc
(b) ASymmetric noise
Figure D.I: Synthetic noise transition matrices used in our experiments on Pascal-VOC 2007. The noise rate is set to 30%.
Real-world noisy datasets. NUS-WIDE dataset [50] originally containing 269,648 images from Flickr and manually annotated with 81 visual concepts, is employed to demonstrate the adaptability of our problem setting to real-world scenarios. Since some download URLs have been deleted, we use the version of the dataset provided in B5 Our experiments follow the training/testing splits provided by the original dataset. Figure 2 iillsstatee several real multi-label noisy examples from JUS-WIDE As shown,
method not only corrects erroneous labels (e.g., the second image in the first row, where 'tiger' is corrected to 'cat') but also generates missing labels (e.g., the third image in the first row, where 'plants' and 'rocks' are added). This underscores method's practical effectiveness real-world settings and its potential to extend from noisy label learning to partial label learning.
D.2 Experimental Details
In our experiments, we configured ResNet50 (depicted as blue ResNet blocks in Figure B. as trainable encoders for the diffusion model, where all linear layers have dimensionality of 1024. We use the Adam optimizer for training 30 epochs with a batch size of 128. The initial learning rate is set to 5e-4, and a half-cycle cosine decay is employed. The images in three datasets resize to 224 224. The experimental results on the synthetic noisy datasets are averaged over ten independent random trials. Additionally, results in Appendix [ showed that the mAP remained relatively stable for K values between 30 and relatively insensitive variations within
used range of K values from 1 to 100 the validation set. Experimental
60. Based on these results, we inferred that our CAD this range of K values and consequently set the default K value to 50. Due to the increased difficulty of learning from the real-world noisy NUS-WIDE dataset and its higher computational cost, use ResNet-10 101 as the trainable encoder for the diffusion model and conduct only a single experiment. The rest of the experimental setup remains the same as for the other three datasets.
E More Types of Pre-trained Encoders
We initially conducted research on different settings of the pre-trained encoders fp and performed ablation experiments comparing our method with Standard, LRAD, and LSNPC. Both the LRAD and LSNPC require the integration of a pre-trained model fy. whereas Standard is a baseline method that does not require any pre-trained models. We selected four pre-trained encoders for our experiments:
ResNet-50 is a baseline multi-label classifier, we use the ResNet-50 model pre-trained on ImageNet;
ADDGCN uses a semantic attention module to estimate the content-aware class-label representations for each class from extracted feature map where these representations are fed into graph convolutional network (GCN) for final multi-label classification;
27

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Table E.1: Results (%) Pascal-VOC 2012 and MS-COCO with 30% symmetric noise, using various methods with different pre-trained encoders. (i denotes our method).
Pascal-VOC 2012
MS-COCO
Method
Pre-trained
mAP
OFI
mAP
OFI
Standard
N/A
66.08
64.28
54.90
58.51
LRAD
ResNet50
71.69
61.60
59.55
56,08
LSNPC
ResNet50
75.07
68.56
62.36
62.40
CAD
ResNet50
77.02
72.27
63.99
63.78
LRAD
ADDGCN
73.58
64.05
62.23
58.12
LSNPC
ADDGCN
78.12
71.13
64.65
64.78
CAD
ADDGCN
80,29
74.89
66.54
66.13
LRAD
HLC
75.13
65.36
63.55
59.30
LSNPC
HLC
79.58
72.54
65.82
66.04
CAD
HLC
81,86
76.48
67.76
67.43
LRAD
ViT-L/I4
81.15
71.33
69.91
65.75
LSNPC
ViT-L/14
82.16
72.61
68.25
64.27
CAD
VIT-L/14
88.99
77.33
73.93
70.39
HLC is a noisy multi-label correction approach built on top of ADDGCN. uses the ratio between the holistic scores of the example with noisy multi-labels and its variant with predicted labels to correct noisy labels during training. holistic score measures the instance-label and label dependencies in an example.
ViT-L/14 is a vision transformer (ViT) model with 306 million parameters, pre-trained on the ImageNet containing over 4 million image-text pairs, providing our framework with exceptional feature extraction capabilities.
We evaluate mAP and OF1 the Pascal-VO 2012 and MS-COCO datasets. As shown in Table E.1 Built on feature spaces provided by ADDGCN, designed for multi-label classification, and HLC, optimized for noisy multi-label learning, our CAD method significantly outperforms others, demonstrating superior capability in complex label relationship modeling and noise robustness.
Under ADDGCN pretraining, CAD achieves mAP scores of 80.29% and 66.54% Pascal-VOC 2012 and MS-COCO, respectively, surpassing LSNPC and LRAD, indicating its effectiveness in leveraging graph structures for multi-label modeling. With HLC pretraining, CAD further improves to 81.86% and 67.76% mAP, outperforming all competitors and approaching CAD-V, suggesting its compatibility with other NML-based feature extraction methods. Additionally, under ViT-L/14 pretraining, CAD attains the highest performance (88 99% mAP and 73.93% mAP), reinforcing its efficiency in leveraging prior information. Overall, when the three models use the same pre- trained feature extractor, CAD consistently outperforms the other two methods, indicating that its superior performance not solely due to the effectiveness of feature extraction.
Effects of Neighborhood Estimation Method
We validate the effectiveness of the neighborhood estimation proxy in the proposed CAD framework on the Pascal-VOC 2007 and Pascal-VOCC 2012 datasets. For comparison, we use the label retrieval augmentation (LRA) technique from LRAD as baseline. As shown in Figure F.I both methods are negatively impacted by noise intrusion the noise rate increases. However, our method consistently maintains a significant advantage in mAP. In high-noise environments, however, the OFI and CF1 scores of our approach rapidly degrade to 0%. This is due to the excessive dispersion of label distributions among neighborhood samples, leading to high entropy in neighborhood proxies, making it difficult to distinguish positive samples. Addressing this limitation of our neighborhood estimation method under high noise conditions will be a focus future work.
Fortunately, by integrating co-occurrence constraints and diffusion models, our method achieves 40% performance improvement in high-noise settings (e.g., 50% asymmetric noise), raising OF1 from 30% to 70%. This further validates the importance and necessity of these two additional components.
28

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CAb soyr
JA
LPt mith sym.
wh sy
C40 A-1 EISP!
JAA Syrt
Mac PS
(a) mAP
OFF
(c)
CAB soT
with aggn
LAA wh siam
JM4
wll agm zoin
with sym.
(d) mAP
(e) OFI
(f) CF1
Figure F.1: Comparison the effectiveness of the neighborhood estimation method in our CAD and the label retrieval augmentation (LRA) in LRAD. Subfigures (a)-(c) present results the noisy Pascal-VOC 2007 dataset, while Subfigures (d)-(f) show results on the noisy Pascal-VOC 2012
dataset.
39%
20%
50%
30%
(a) Pascal VOC2007
(b) Pascal VOC2012
Figure G.1: The effect different K values on the best mAP (%) the CAD model under various symmetric noise rates. The gray background highlights the range of K values where the mAP is relatively stable and exhibits robust performance.
G Effects of Different K Value
To analyze the impact of K values on model performance, we conducted tests on the Pascal-VOC 2007 and Pascal-VOC 2012 datasets under varying Symmetric noise rates with ranging from to 100. Figure G.I shows that the CAD's 's mAP remained relatively stable for K values between 30 and 60. We observe that low-noise scenarios, smaller neighborhood radius suffices for accurate estimation, while an excessively large neighborhood can lead to noise leakage. As noise levels increase, the required neighborhood size also grows. This phenomenon can explained by the need to expand the neighborhood size to stabilize label distributions when noisy information becomes prevalent, thereby improving
model's robustness. However, excessively large values K increase computational costs without yielding significant improvements in model performance. Considering these factors, we set K = 50 as the default setting for CAD, as it achieves both stability and high
mAP across various noise conditions.
29

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Table H.1: Test Time (sec) for CAD and Discriminative Models on Different Datasets MS-COCO (40,137 test image)
Pascal-VOCC (4925 test image)
CAD 8 Discriminative
CAD 173
Discriminative 102
H Training and Inference Efficiency Analysis
The time expenditure comparison in Figure H.1 highlight the significant cost-effectiveness of our CAD. Compared to LSNPC and HLC. CAD achieves optimal performance while saving half times in training costs, which is groundbreaking. Compared to LRAD, which use similar diffusion model architectures, CAD incurs only about seconds of additional cost. Moreover, its sample preparing process be pre-computed and cached before training, thereby avoiding the need for repeated calculations. other words, it is done once, meaning that when dealing with large-scale datasets, the time cost of this process is negligible compared to model training, yet its contribution to enhancing multi-label classification performance is significant.
Table H.J compares the classification time on the test set between the CAD and discriminative models. Since both Pascal-VOC 2007 and Pascal-VOC 2012 share the test set of Pascal-VOCC 2007, we have combined the results. The Pascal-VOCI test set consists of 4,925 images, while the MS-COCO test set contains 40,137 images, resulting a significant increase testing time. Overall, the diffusion models and discriminative models operate within the same order of magnitude in terms of classification speed. Moreover, classification speed can be further improved with alternative noise scheduling accelerated sampling strategies, slow classification does not pose significant issue.
Training
LSNPC
HLC
ASL
CAD
LRAD
Figure H.1: Time cost (sec) of each method for training epoch NVIDIA A800 GPU,
I Limitations and Future Work
In this work, although demonstrate through experiments that CAD performs strongly noisy benchmark datasets, it still has two main limitations: (1) instability under high-noise conditions, and (2) lack of evaluation more complex noise scenarios, such as instance-dependent noise (IDN), class imbalance [53], or out-of-distribun issue of high variance in OFI and CFI scores and to validate the model's robustness under broader range of noise conditions and real-world multi-label noisy datasets. Additionally, part of CAD's overall performance gain can attributed the use pre-trained encoder. Moving forward, we plan to integrate discriminative and generative paradigms, enabling information generated by the diffusion model to guide various stages of training.
(OOD) noise [54]. In future work, we aim to address the
30


Reviews:
[{"review_id": "yFAq2AJe6H", "reviewer": "Reviewer_v11J", "summary": "The paper reframes NML as a robust label generation task based on diffusion models with theoretical deduction, and enhances the mapping between features and multi-labels through matrix-based label representation. The paper designs a pseudo-clean label reconstructor and a meta-label co-occurrence matrix estimator, leveraging pre-trained encoders to provide strong priors for diffusion model training. Besides, the paper integrates co-occurrence constraints into the diffusion modeling, proposing the Co-Occurrence-Aware Diffusion (CAD) model, which can robustly learn the generative mapping from features to true multi-labels.", "questions": "(1) It would be great if the paper can provide some analysis related to the computational costs of the developed approach and the baselines.\n\n(2) It would be great to provide more case study results to illustrate how the developed key components work in practice. Some intermediate results may also be presented.\n\n(3) Some discussed previous works (e.g., [20]) provide theoretical results. Might it be feasible to provide some theoretical results similarly in this paper? Some discussions would be very insightful.", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n(1) The paper is well motivated and is related to an important task in practice.\n\n(2) The paper formulation is novel and the developed approach has good intuitions.\n\n(3) The experiments are comprehensive and the developed approach achieves strong performances. \n\nWeaknesses\n\n(1) It would be great if the paper can provide some analysis related to the computational costs of the developed approach and the baselines.\n\n(2) It would be great to provide more case study results to illustrate how the developed key components work in practice. Some intermediate results may also be presented.", "was_revised": true, "final_justification": "The majority of my questions were answered during the discussion, so I will keep my positive rating.", "rebuttal": "Thank you for your insightful suggestions. Below, we provide point-by-point responses to the weaknesses and questions you raised, hoping to address your concerns regarding our work.\n\n**W1&Q1**: It would be great if the paper can provide some analysis related to the computational costs of the developed approach and the baselines.\n\n**A1**: We have provided a more detailed analysis of the training and inference time costs for our proposed CAD method and the baseline methods in Tables 1 and 2 below (The data originates from Appendix Figure H.1 and Table H.1). Table 1 shows that CAD achieves **better training efficiency** compared to mainstream approaches due to the lightweight diffusion architecture. Table 2 demonstrates that, with the accelerated DDIM sampling strategy, the time cost of generative multi-label inference is on the same order of magnitude as that of discriminative prediction, indicating that CAD is **suitable for large-scale data scenarios**. We will incorporate this part of the Appendix into the main text in the final version.\n\nTable 1:  Time cost (sec) of different method for training one epoch on one NVIDIA A800 GPU.\n|Dataset|LSNPC|HLC|ASL|CAD(Ours)|LRAD|\n|---|:---:|:---:|:---:|:---:|:---:|\n|VOC2007|25|21|13|9|8|\n|VOC2012|40|31|23|20|15|\n|MS-COCO|462|393|379|357|330|\n\nTable 2: Test time cost (sec) for CAD and discriminative (Disc.) models on different test sets.\n|Dataset|CAD|Disc.|\n|---|:---:|:---:|\n|VOC(4.9kimgs)|8|5|\n|COCO(40kimgs)|173|102|\n\n**W2&Q2**: It would be great to provide more case study results to illustrate how the developed key components work in practice. Some intermediate results may also be presented.\n\n**A2**: In our CAD architecture, the neighborhood label estimation in the forward process serves as an initial coarse label guess produced by a non-diffusion model. The subsequent diffusion training process refines this estimate by incorporating feature and co-occurrence constraints. As shown in Table 3 below (The data originates from Table 1 and Table 2 in main text and Appendix Figure F.1), which includes results from our ablation study, **the diffusion training consistently improves multi-label classification performance based on the initial label estimates**. This demonstrates that our training framework enables the diffusion model to effectively learn a robust generative mapping from features to multi-label outputs.\n\nTable 3: Comparison of label pre-estimation (𝑦̄) and full CAD model results (%).\n|Method|VOC2007-sym50%|||VOC2007-asym50%|||VOC2012-sym50%|||VOC2012-asym50%|||  \n|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|  \n| |mAP|OF1|CF1|mAP|OF1|CF1|mAP|OF1|CF1|mAP|OF1|CF1|  \n|𝑦̄|82.20|53.21|55.43|52.38|39.99|46.57|82.27|48.64|47.79|52.17|44.23|48.68|  \n|CAD|84.61|72.41|69.33|69.37|64.51|62.74|88.31|75.22|71.24|76.63|66.78|67.49|  \n\n**Q3**: Some discussed previous works (e.g., [20]) provide theoretical results. Might it be feasible to provide some theoretical results similarly in this paper? Some discussions would be very insightful.\n\n**A3**: Thanks for your constructive suggestion regarding the theoretical aspects of our work. Indeed, [20] provides valuable theoretical insights on using label correlations for estimating the noise transition matrix (LCT). In principle, it is feasible to incorporate such estimation techniques such as T-estimator (_Liu T et al. Classification with noisy labels by importance reweighting. TPAMI, 2015, 38(3): 447-461_) and Dual T-estimator (_Yao Y et al. Dual t: Reducing estimation error for transition matrix in label-noise learning. NeurIPS, 2020, 33: 7260-7271_) into our CAD architecture, since our co-occurrence matrix is also estimated by observing label co-occurrence probabilities within a clean subset. However, these methods typically **require additional network components and warm-up training**. For example, [20] estimates the transition matrix for each class $i$ by considering all other classes $k$ (where $k ≠ i$), which will increase computational overhead.\nThat said, we agree that employing more accurate co-occurrence estimation methods could potentially enhance the performance of our CAD framework. We conducted a small-scale experiment by replacing our co-occurrence constraint with reweighting strategies based on T-estimator and the method proposed in [20]. As shown in Table 4, all these alternatives led to **further performance improvements** for our method. We will include these experimental results in the final version and incorporate theoretical discussions from the matrix estimation literature to improve the interpretability of our co-occurrence modeling.\n\nTable 4: Comparison of the combined performance (%) of different matrix estimation reweighting methods with CAD under a 30% symmetric noise environment.\n|Method|VOC2012||COCO||  \n|---|:---:|:---:|:---:|:---:|  \n||mAP|OF1|mAP|OF1|  \n|CAD|88.99|77.33|73.93|70.39|  \n|CAD+Reweight-T|**89.12**|78.02|74.13|70.52|  \n|CAD+Reweight-LCT|89.07|**78.81**|**74.28**|**71.10**|"}, {"review_id": "pNJSfur372", "reviewer": "Reviewer_UB3E", "summary": "The paper proposes to learn the posterior mapping from features to labels in the noisy multi-label problem using the diffusion model. The noisy issue is constrained by using pseudo-clean labels in the generation process. The pseudo-clean labels are obtained from the latent neighborhood space, replacing the point-wise estimates in traditional methods. The proposed method is evaluated on both synthetic and real-world noisy datasets.", "questions": "1. What happens if the label correlation is less associated with the latent space similarity? What happens when the domain knowledge is very different from pre-trained knowledge?\n\n2. What are the exact theoretical guarantees?\n\n3. What is the performance on rare labels?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper is well written and most information is clearly presented.\n\n2. The idea of using the diffusion model to address the noisy multi-label learning problems is novel and interesting. \n\n3. The experiments show that the proposed method has an advantage compared to existing noisy multi-label learning methods.\n\nWeaknesses:\n\n1. The proposed method seems dependent on the label correlation being associated with the latent space similarity. However, in some tasks and domains, it might not be applicable. In these cases, the diffusion model generation might not meet the requirement for pseudo-clean labels. There might also be issues when there are both noisy labels and out-of-distribution data samples. These are not well discussed in the paper.\n\n2. The paper mentions theoretical guarantees, but it is unclear what the guarantees are referring to.\n\n3. The paper does not discuss other possible ways of mitigating the noise issue using the latent neighborhood space, such as other automatic correction models.\n\n4. The paper does not discuss the possibility of damaging the rare labels, which may occur simultaneously with other unexpected labels.", "was_revised": true, "final_justification": "The paper is technically sound and makes a decent contribution. The rebuttal is adequate but some concerns still remain. Thus I will keep my rating.", "rebuttal": "Thanks for your valuable suggestions. Below, we provide point-by-point responses to the weaknesses and questions you raised, hoping to address your concerns regarding our work.\n\n**W1&Q1**:  What happens if the label correlation is less associated with the latent space similarity? What happens when the domain knowledge is very different from pre-trained knowledge?\n\n**A1**: Thanks for your insightful observation regarding the dependence of the proposed CAD model on the strength of association between label correlations and the pretrained latent feature space. \n\n**First**, Table 1 (originates from Appendix Table E.1) shows that the contribution of different pre-trained models to the latent feature space used in CAD. Both models are pre-trained on ImageNet. From your perspective, it is reasonable to interpret that **ResNet50 exhibits a weaker association between label correlations and its latent space compared to ViT**. This is primarily due to the relatively limited representational capacity of ResNet50’s latent space. Consequently, the performance of **CAD combined with ResNet50 is weaker than when combined with ViT** or other pre-trained models with stronger representational power (e.g., ADDGCN, HLC). However, compared to other methods that also leverage pre-trained models to extract latent space knowledge (e.g., LSNPC, LRAD), **our method consistently makes better use of this coarse-grained feature space**. Through a diffusion paradigm, CAD refines these features into a generative mapping for multi-label classification, resulting in superior performance despite relying on the same latent knowledge. Furthermore, even when CAD is combined with a weaker feature space such as that of ResNet50, it still shows significant advantages over methods that do not utilize pre-trained models at all. **Efficiently leveraging simple, offline, and easily accessible pre-trained models to obtain usable latent feature spaces  is one of the strengths of our method** and aligns with strategies recognized as effective in the current studies (_Ko J et al. Efficient utilization of pre-trained model for learning with noisy labels. ICLR, 2023_ and  _Zhu Z et al. Detecting corrupted labels without training a model to predict. ICML, 2022: 27412-27427_).\n\nTable 1: Results (%) on VOC 2012 and MS-COCO with 30% symmetric noise, using various methods with different pre-trained encoders.\n|Method|Pre-trained|VOC 2012||MS-COCO||  \n|---|---|:---:|:---:|:---:|:---:|  \n|||mAP|OF1|mAP|OF1|  \n|LRAD|ResNet50|71.69|61.60|59.55|56.06|  \n|LSNPC|ResNet50|75.07|66.58|62.40|60.32|  \n|CAD|ResNet50|77.02|72.27|65.78|63.70|  \n|LRAD|ViT-L/14|81.15|71.31|69.91|65.76|  \n|LSNPC|ViT-L/14|82.16|72.21|68.85|64.27|  \n|CAD|ViT-L/14|88.99|77.33|73.93|70.39|  \n\n**Second**, regarding the issue of out-of-distribution noise and potential misalignment between the pre-trained model and domain-specific knowledge, **one possible solution is to apply unsupervised fine-tuning methods**, such as SimCLR, on the pre-trained model before freezing it to obtain the latent feature space. Based on our empirical experiments, combining CAD with the ViT model allows us to effectively utilize a wide range of image datasets, including those involving fine-grained classification tasks. Prior research (_Wei T et al. Vision-language models are strong noisy label detectors. NeurIPS, 2024, 37: 58154-58173_) has also demonstrated the effectiveness of fine-tuning ViT encoders to address noise detection under different data distributions. We will include a discussion of this limitation, along with potential directions for future work, in the revised \"Limitations\" section.\n\n**W2&Q2**: What are the exact theoretical guarantees?\n\n**A2**: Our theoretical contribution primarily lies in the development of a label diffusion paradigm designed to simultaneously address multi-label classification and label noise. While CARD has introduced a label diffusion model for single-label classification, it does not provide a solution for either multi-label settings or noisy labels. For example, CARD’s feature conditioning mechanism relies on training an auxiliary classifier in advance on the dataset to guide the forward diffusion process with injected noise. However, in noisy label environments, this reliance often infeasible. On the other hand, LRAD addresses label noise via label estimation but does not consider label co-occurrence relationships inherent in multi-label tasks, limiting its effectiveness for noisy multi-label scenarios. In contrast, **our work theoretically derives both unconditional and conditional multi-label diffusion processes and proposes a straightforward, noise-robust method for feature conditioning**. This leads to a diffusion network architecture that directly aligns with the proposed theoretical framework. To reduce potential ambiguity, we will revise the final version of the paper by replacing “theoretical guarantees” with “**theoretical applicability guarantees**” in both the abstract and main text. This will clarify that our contribution lies in demonstrating the applicability of diffusion theory to noisy multi-label learning tasks.\n\n**W3**: The paper does not discuss other possible ways of mitigating the noise issue using the latent neighborhood space, such as other automatic correction models.\n\n**A3**: Unlike most methods that iteratively correct labels during model training, our CAD model performs a single-step pre-correction process through the latent feature space, without requiring any additional training or fine-tuning. To further validate this property, we introduced two additional label correction modules that also operate in a training-free and one-step manner: SimiFeat (_Zhu Z et al. Detecting corrupted labels without training a model to predict. ICML, 2022: 27412-27427_) and CLIPCleaner (_Feng C et al. Clipcleaner: Cleaning noisy labels with clip. ACM MM, 2024: 876-885._). SimiFeat leverages a frozen feature extractor and label consistency among similar samples, using a Bayesian thresholding strategy to detect and correct noisy labels. CLIPCleaner aligns image and text embeddings using CLIP’s encoders to perform semantic-based label correction. A preliminary comparison of these two modules with our proposed estimation method (𝑦̄) is presented in Table 2 below. SimiFeat demonstrates superior correction performance, while CLIPCleaner appears to be less effective, possibly due to the limited accuracy of prompt-based semantics in multi-label contexts. When integrated with CAD, we observe that **more accurate pre-correction leads to further performance improvements** of the proposed diffusion paradigm. Our contribution lies in using the diffusion model to refine image features into a generative multi-label mapping based on pre-corrected labels. The integration with different correction modules also demonstrates **the generality and extensibility of the proposed CAD**. We will include a more comprehensive comparison of automatic correction models combined with CAD in the final version, and expand the discussion in the related work section accordingly.\n\nTable 2: Performance (%) comparison of different automatic correction models and their integration with CAD on VOC 2012.\n|Method|Sym. 50%|||Asym. 50%|||  \n|---|:---:|:---:|:---:|:---:|:---:|:---:|  \n||mAP|OF1|CF1|mAP|OF1|CF1|  \n|𝑦̄|82.27|48.64|47.79|52.17|44.23|48.68|  \n|SimiFeat|85.11|50.25|49.22|53.79|45.61|50.17|  \n|CLIPCleaner|80.39|47.63|46.62|50.83|43.01|47.63|  \n|𝑦̄+CAD|88.31|75.22|71.24|76.63|66.78|67.49|  \n|SimiFeat+CAD|89.16|76.13|72.85|77.31|67.82|68.41|  \n|CLIPCleaner+CAD|87.03|74.23|70.04|75.57|65.24|66.38|  \n\n**W4&Q3**: The paper does not discuss the possibility of damaging the rare labels, which may occur simultaneously with other unexpected labels. What is the performance on rare labels?\n\n**A4**: In noisy multi-label settings, rare labels may be mistakenly treated as label noise, which will negatively impact the model’s ability to fit them. In traditional weak supervision scenarios with extreme class imbalance, previous studies have proposed various semi-supervised and active learning approaches to address the challenge of rare label modeling. For example, graph-based label propagation methods (_Pimplikar R et al. Learning to propagate rare labels. ACM CIKM, 2014: 201-210_)  leverage difference-of-convex optimization and k-NN subgraph sampling to improve robustness to extreme imbalance in large-scale graph-structured data. Alternatively, pseudo-labeling and representation-aware active learning techniques can be used to train robust models that mitigate the impact of rare labels (_Mullapudi R T et al. Learning rare category classifiers on a tight labeling budget. ICCV, 2021: 8423-8432_). Although our method is not specifically designed to address the rare label problem, we think the proposed **CAD can partially alleviate this issue by expanding neighborhood search, or strengthening co-occurrence constraints via advanced matrix estimation techniques**. The datasets used in our experiments are popular for evaluating NML methods, and they **usually do not exhibit extreme imbalance**. For instance, in the VOC dataset (excluding the most basic class person), the lowest label frequency (cow, 273 instances) and the highest (chair, 1168 instances) yield a ratio of roughly 1:4. Even if common noise is added to these extreme labels, it is still less likely for rare label situations to occur. In view of this, the proposed **CAD does not include strategies specifically designed to address the rare label problem**.  Alternatively, We will briefly discuss this limitation in the final version of the paper. In future work, we plan to explore both simulated and real-world imbalanced multi-label datasets to better capture rare label scenarios and to develop dedicated solutions that can be integrated with the diffusion paradigm for enhanced performance."}, {"review_id": "nIbnuoWMID", "reviewer": "Reviewer_FnCb", "summary": "This paper proposes a Co-Occurrence-Aware Diffusion (CAD) model, which reformulates noisy multi-label learning (NML) from a generative perspective.  It treats features as conditions and multi-labels as diffusion targets, optimizing the diffusion model for multi-label learning with theoretical guarantees.  To mitigate the interference of noisy labels in the forward process, it guides generation using pseudo-clean labels reconstructed from the latent neighborhood space, replacing original point-wise estimates with neighborhood-based proxies.  In the reverse process, it incorporates label co-occurrence constraints to enhance the model’s awareness of incorrect generation directions, thereby promoting robust optimization.  Experiments demonstrate the effectiveness of the proposed method.  The main contributions of this paper are:\n\n- It reframes NML as a robust label generation task based on diffusion models with theoretical deduction, and enhances the mapping between features and multi-labels through matrix-based label representation.\n- It designs a pseudo-clean label reconstructor and a meta-label co-occurrence matrix estimator, leveraging pre-trained encoders to provide strong priors for diffusion model training.\n- It integrates co-occurrence constraints into the diffusion modeling, proposing the Co-Occurrence-Aware Diffusion (CAD) model, which can robustly learn the generative mapping from features to true multi-labels.", "questions": "1.  Why is a diffusion model preferred over other generative frameworks on the NML problem?\n2.  How does CAD perform when trained from scratch or with a weakly initialized encoder?", "limitations": "The authors could further discuss the potential societal impact of the proposed method.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strength**\n\n- The problem studied in this paper is interesting and valuable.\n- This paper is well written and in good sharp, which is easy to follow.\n- Experimental results are promising and can validate the effectiveness of the proposed method.\n\n\n\n**Weakness**\n\n- For the motivation of this paper, in my opinion, it does not clearly explain why a diffusion model is preferred over other generative frameworks on the NML problem.  Therefore, the practical requirements for CAD are somewhat unclear. The manuscript lacks a detailed discussion of the practical requirements and benefits that CAD fulfills over alternative frameworks. As a result, readers are left without a clear understanding of why the diffusion paradigm was chosen, what specific challenges in modeling noisy label matrices it addresses, and how its properties translate into tangible performance or stability advantages in the multi‑label denoising context.\n- The proposed CAD seems to rely heavily on a strong pre‑trained encoder.  However, the paper does not explore scenarios in which such powerful pre‑trained models are unavailable, such as domains with limited data or modalities without large-scale pre-training assets. There is no evaluation of CAD‘s performance when the encoder is trained from scratch, initialized with random weights, or borrowed from a weaker backbone architecture.  Without such analysis, it remains unclear whether the benefits of CAD stem primarily from the diffusion framework itself or are largely inherited from the strength of the underlying feature representations.", "was_revised": true, "final_justification": "After reading the comments from all reviewers and the authors' responses, I believe that the authors have addressed my concerns. Therefore, I support the acceptance of this paper.", "rebuttal": "Thanks for your valuable suggestions. Below, we provide point-by-point responses to the weaknesses and questions you raised, hoping to address your concerns regarding our work.\n\n**W1&Q1**: Why is a diffusion model preferred over other generative frameworks on the NML problem?\n\n**A1**: Thanks for pointing out the need to clarify our motivation for choosing diffusion models over other generative frameworks for the NML problem. In real-world multi-label annotation scenarios, inherent uncertainty is common due to complex image semantics, ambiguous category boundaries, and subjective differences among annotators. Consequently, incomplete or conflicting annotations often lead to label noise, which is difficult to be avoided. Therefore, it is more realistic to view the multi-label learning process as an uncertainty-aware generation task conditioned on image features. Instead of directly fitting noisy labels, we aim to learn a distributional mapping from the original features to the “most likely true label set,” thereby enhancing robustness to label noise. To this end, we adopt diffusion models as the label generation framework. On the one hand, prior work (_Han X et al.. CARD: Classification and Regression Diffusion Models. NeurIPS, 2022_) has compared the modeling ability of diffusion models against other generative approaches such as GANs (e.g., GCDS, _Xiao Z et al. Tackling the Generative Learning Trilemma with Denoising Diffusion GAN. ICLR, 2022_), showing that **diffusion models are more effective at capturing predictive uncertainty in classification tasks**. This makes them particularly suitable for modeling the noise and ambiguity in label generation. On the other hand, in text-to-image generation, diffusion models have demonstrated the ability to synthesize images that combine multiple target concepts given composite prompts. This suggests that diffusion models are **inherently capable of capturing multiple objectives**. This indicates that in NML tasks, diffusion models may be well-suited to handle input images with multiple target objects, as their inherent ability to capture multiple objectives allows them to generate appropriate combinations of labels, i.e., an ideal characteristic for multi-label classification. Taken together, these characteristics **make diffusion models a natural and powerful choice for addressing the challenges in NML**. We will incorporate a more detailed discussion of these motivation and comparative analysis in the final version of the paper.\n\n**W2&Q2**: How does CAD perform when trained from scratch or with a weakly initialized encoder?\n\n**A2**: We greatly appreciate your concern regarding the use of pre-trained models. Please allow us to address your question from two perspectives. \n\n**First**, it is important to emphasize that our **CAD model does not heavily depend on the pre-trained encoder**, we can train a feature encoder from scratch using unsupervised approaches like SimCLR (_Chen T et al. A simple framework for contrastive learning of visual representations. ICML, 2020: 1597-1607_). Table 1 (to be added in the final version) shows the intermediate neighborhood label estimation and final classification results of CAD when combined with different pre-trained encoders include scratched ResNet50. The ResNet50 trained via unsupervised feature learning on the target dataset surpasses the ImageNet-pretrained counterpart in both label pre-estimation accuracy and performance when integrated with CAD, primarily because it effectively constitutes a form of fine-tuning on the target data distribution. On the other hand, from your perspective, ResNet50 can be viewed as a weakly initialized encoder compared to ViT-L/14, and the neighborhood label estimation alone based on ResNet50 performs worse than the baseline NML method across key metrics like OF1 and CF1. Even with such coarse estimations, CAD is capable of refining the generative feature-label mapping and consistently achieving performance improvements beyond the label estimation stage, outperforming the baseline NML method. This clearly highlights **the indispensable role of the diffusion architecture in enhancing performance beyond what weak feature spaces can offer**.\n\nTable 1: Comparison of label pre-estimation (𝑦̄) and full CAD model results (%) using different pre-trained encoders.\n\n|Method|Pre-trained encoder|VOC2007-sym50%|||VOC2007-asym50%|||VOC2012-sym50%|||VOC2012-asym50%|||  \n|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|  \n| | |mAP|OF1|CF1|mAP|OF1|CF1|mAP|OF1|CF1|mAP|OF1|CF1|\n|𝑦̄|ResNet50 (scratch)|65.49|48.77|45.83|46.78|32.59|38.92|67.62|40.84|36.37|61.18|33.53|32.55|\n|CAD|ResNet50 (scratch)|74.65|69.31|66.19|63.85|61.45|57.93|77.85|71.87|66.83|70.47|63.46|62.33|\n|𝑦̄|ResNet50 (pre-trained)|63.65|47.42|44.53|45.36|31.62|37.88|65.88|39.69|35.31|59.56|32.62|31.61|  \n|CAD|ResNet50 (pre-trained)|72.37|67.19|64.13|61.88|59.51|56.17|75.53|69.80|64.86|68.36|61.60|60.56|  \n|𝑦̄|ViT-14/L|82.20|53.21|55.43|52.38|39.99|46.57|82.27|48.64|47.79|52.17|44.23|48.68|  \n|CAD|ViT-14/L|84.61|72.41|69.33|69.37|64.51|62.74|88.31|75.22|71.24|76.63|66.78|67.49|  \n|HLC(Baseline)|N/A|68.03|66.62|63.65|59.09|58.59|56.51|69.03|67.83|64.37|64.27|60.64|59.86|  \n\n**Second**, recent studies (_Zhu Z et al. Detecting corrupted labels without training a model to predict. ICML. 2022: 27412-27427._; _Ko J, Ahn S, Yun S Y. Efficient utilization of pre-trained model for learning with noisy labels. ICLR 2023_ and _Feng C, Tzimiropoulos G, Patras I. Clipcleaner: Cleaning noisy labels with clip. ACM MM, 2024: 876-885_) increasingly explore how to leverage pre-trained models with noise-free knowledge to handle label noise without additional training. These works, aligned with our view, suggest that **utilizing simple, accessible, and easily integrated pre-trained encoders is a practical and reasonable** strategy. The weights used for both ResNet50 and ViT-L/14 are publicly available and pre-trained on ImageNet—commonly adopted in most classification settings. For instance, using ResNet simply requires setting $pretrained=True$. While it is possible to train a feature encoder from scratch using unsupervised approaches like SimCLR (_Chen T et al. A simple framework for contrastive learning of visual representations. ICML, 2020: 1597-1607_), we believe that, **when high-quality, readily available pre-trained encoders exist, it is both reasonable and efficient to use them**. To ensure fair comparison, we selected LRAD and LSNPC as our main baselines, both of which also use pre-trained encoders. Table 2 (The data originates from Appendix Table E.1) shows that under the same latent feature space conditions, **CAD consistently makes better use of latent knowledge and refines it into more effective multi-label mappings**. We will include Table 1 in the final version to illustrate the model’s non-reliance on specific pre-trained encoders and will add a more detailed discussion on this issue.\n\nTable 2: Results (%) on VOC 2012 and MS-COCO with 30% symmetric noise, using various methods with different pre-trained encoders.\n|Method|Pre-trained|VOC 2012||MS-COCO||  \n|---|---|:---:|:---:|:---:|:---:|  \n|||mAP|OF1|mAP|OF1|  \n|LRAD|ResNet50|71.69|61.60|59.55|56.06|  \n|LSNPC|ResNet50|75.07|66.58|62.40|60.32|  \n|CAD|ResNet50|77.02|72.27|65.78|63.70|  \n|LRAD|ViT-L/14|81.15|71.31|69.91|65.76|  \n|LSNPC|ViT-L/14|82.16|72.21|68.85|64.27|  \n|CAD|ViT-L/14|88.99|77.33|73.93|70.39|"}, {"review_id": "yfegnxpuX6", "reviewer": "Reviewer_kEsb", "summary": "The paper proposes a diffusion-based method coupled with neighborhood-based co-occurrence to handle the multi-label learning problem. In particular, the proposed method is inspired by the previous method CARD designed on single noisy label learning by firstly estimating the noisy multi-label distribution through the K nearest neighbor approach. Secondly, the obtained distribution of noisy multi-label matrix follows the diffusion process, and then reconstructed in the backward diffusion process as done in DDPM. The empirical evaluation on both synthetic and real-world datasets show the remarkable performance of the proposed method compared to the existing ones.", "questions": "Please address the two questions raised in the weaknesses. In particular, please explicitly provide the distinctions between CARD and the proposed method.", "limitations": "The paper briefly discusses the limitations of the proposed method, which are more in the empirical evaluation, such as instance-dependent noise or out-of-distribution noise. There is no explicit discussion on the limitations of the proposed method.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths:\nThe paper is motivated from the real world setting where noisy labels may be contaminated into the set of multi-labels provided. Hence, it is important to address the noisy multi-label learning problem. The paper also provides a good overview and literature review on the previous and existing studies in the field.\n\nThe explanation of the proposed method is easy to follow, especially the visualization. In addition, the paper also presents extensive empirical evaluation to demonstrate the capability of their proposed method.\n\n## Weaknesses:\n- The proposed method is limited in terms of novelty. As described in the paper, it is an adopted version of CARD in noisy single-label learning to apply to the multi-label learning. Due to this similarity, it reduces the originality of the proposed method.\n- Another concern is that diffusion models, in general, are designed to estimate the distribution of data. In this case, the data is the noisy multi-labels. The nearest neighbor step in the forward pass already provides a rough estimation of that distribution. The backward pass is to provide a \"finer grain\" version of that distribution. However, it is considered as the clean label distribution that is \"denoised\" by the diffusion model.\n\n## Minors:\n- Inconsistent English: the majority of the paper follows the American English, but some are in British English. For example, line 24: \"expert-labelled\" ==> \"expert-labeled\"\n- Eqs (4) and (5) have unnecessary line break for a single column paper.", "was_revised": true, "final_justification": "The authors have addressed most of my concerns during the discussion period.", "rebuttal": "Thanks for your valuable suggestions. Below, we provide point-by-point responses to the weaknesses and questions you raised, hoping to address your concerns regarding our work.\n\n**W1&Q1**: The proposed method is limited in terms of novelty. As described in the paper, it is an adopted version of CARD in noisy single-label learning to apply to the multi-label learning. Due to this similarity, it reduces the originality of the proposed method.\n\n**A1**: Thanks for your comment. Compared with CARD, our work **focuses on analyzing and improving practical performance for the specific problem**. Based on the characteristics of the noisy multi-label learning (NML), we conduct targeted theoretical analysis and method design, including: (i) **introducing feature-conditional strategies for noise-robustness and providing theoretical applicability guarantees**, and (ii) **developing diffusion-based embedding and coupling of label co-occurrence constraints**.\n\n**First**, the original feature conditioning mechanism in CARD relies on a supervised classifier $f_\\phi$ to define the forward noisy distribution as $q(y_T|x) \\sim {N}(f_\\phi(x),I)$. However, this mechanism becomes invalid in the presence of noisy labels, as only noisy distributions are available during training, which can lead to a biased $f_\\phi$ early on. In our work, **we redesign the feature conditioning strategy to be robust to label noise with theoretical applicability guarantees**, allowing it to be directly injected into the diffusion process. This improves the model's ability to capture the structured correlation between features and multiple labels.\n\n**Second**, prior work (_Chen J et al. Label-retrieval-augmented diffusion models for learning from noisy labels. NeurIPS, 2023, 36: 66499-66517_) has not addressed label co-occurrence relationships in noisy multi-label settings. To remedy this, **we incorporate label co-occurrence constraints** into the reverse diffusion process, which helps the model identify and avoid generating implausible label combinations (e.g., _Elephant_ and _Boat_), thereby **improving both the plausibility and robustness of the generation path**. \n\n**Finally**, we conduct extensive experiments on both synthetic and real-world noisy datasets, demonstrating that our method significantly outperforms existing SOTA methods across multiple evaluation metrics. These results validate the effectiveness of our proposed improvements. In summary, while our approach is inspired by the foundational ideas in CARD, **the modeling and optimization mechanisms we proposed are clearly novel and practically valuable for the NML setting**, and not a simple application or replication of prior work.\n\n**W2**: Another concern is that diffusion models, in general, are designed to estimate the distribution of data. In this case, the data is the noisy multi-labels. The nearest neighbor step in the forward pass already provides a rough estimation of that distribution. The backward pass is to provide a \"finer grain\" version of that distribution. However, it is considered as the clean label distribution that is \"denoised\" by the diffusion model.\n\n**A2**: Thanks for your insightful observation. As you correctly pointed out, the label estimation in the forward process does provide a coarse-grained version of the label distribution. However, due to the limited representational capacity of the pre-trained encoder’s feature space, **this initial estimation often falls short of ideal performance**. As shown in Table 1 (to be added in the final version, the data originates from Tables 1 and 2 in main text and Appendix Figure F.1) below, even when using a powerful encoder like ViT, the estimated multi-label classification metrics, such as OF1 and CF1, are still far from satisfactory. For example, on the VOC 2007 dataset with 50% symmetric noise, the CF1 score barely reaches 55%. In contrast, **after applying the proposed co-occurrence-aware diffusion process, our method outperforms** advanced NML baselines like HLC (_Xia X et al. Holistic label correction for noisy multi-label classification. ICCV, 2023: 1483-1493._), even when using a coarse-grained feature space and initial label distribution from a weaker encoder like ResNet50. This improvement arises not merely from converting coarse to fine label distributions, **but more importantly from refining the feature space itself under the guidance of image features to achieve a better alignment with the target multi-label set**. In other words, if we draw an analogy between the label diffusion model and a classifier, the diffusion process can be viewed as learning a mapping between extracted features and multi-label targets. However, unlike traditional discriminative models that directly minimize classification loss, our diffusion framework optimizes the L2 distance ($||\\epsilon-\\epsilon_\\theta(y_t,{x},t)||^2$) between the generated denoised label distributions and the noisy ground-truth labels across all time steps. This indirect training objective **encourages the model to learn a probabilistic generation path from features to labels, ultimately building a more robust generative mapping**. We will include Table 1 and the accompanying explanation in the final version of the paper to further clarify the mechanism and contribution of the diffusion paradigm in this context.\n\nTable 1: Comparison of label pre-estimation (𝑦̄) and full CAD model results (%) using different pre-trained encoders.\n|Method|Pre-trained encoder|VOC2007-sym50%|||VOC2007-asym50%|||VOC2012-sym50%|||VOC2012-asym50%|||  \n|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|  \n| | |mAP|OF1|CF1|mAP|OF1|CF1|mAP|OF1|CF1|mAP|OF1|CF1|  \n|𝑦̄|ResNet50|63.65|47.42|44.53|45.36|31.62|37.88|65.88|39.69|35.31|59.56|32.62|31.61|  \n|CAD|ResNet50|72.37|67.19|64.13|61.88|59.51|56.17|75.53|69.80|64.86|68.36|61.60|60.56|  \n|𝑦̄|ViT-14/L|82.20|53.21|55.43|52.38|39.99|46.57|82.27|48.64|47.79|52.17|44.23|48.68|  \n|CAD|ViT-14/L|84.61|72.41|69.33|69.37|64.51|62.74|88.31|75.22|71.24|76.63|66.78|67.49|  \n|HLC(Baseline)|N/A|68.03|66.62|63.65|59.09|58.59|56.51|69.03|67.83|64.37|64.27|60.64|59.86| \n\n**M1**: Inconsistent English: the majority of the paper follows the American English, but some are in British English. For example, line 24: \"expert-labelled\" ==> \"expert-labeled\".\n\n**A3**: Thank you for pointing this out. We appreciate your attention to detail. We will carefully revise the final version to ensure consistent use of American English throughout, including corrections like changing “expert-labelled” to “expert-labeled” and reviewing similar cases across the paper.\n\n**M2**: Eqs (4) and (5) have unnecessary line break for a single column paper.\n\n**A4**: Thanks for your careful review. We agree that the line breaks in Eqs. (4) and (5) are unnecessary, especially for a single-column format, and may affect readability. In the final version, we will revise these equations to be presented in a single line for better clarity and layout consistency."}]

Author rebuttal:

Meta-review: This paper reframes noisy multi-label learning through a co-occurrence-aware diffusion model (CAD) that conditions on image features. 

The reviewers found the motivation clear and the core idea novel; two recommended acceptance and two were borderline-accept. The rebuttal and discussion significantly strengthened the paper by addressing key concerns:
(i) The empirical evaluation is comprehensive, with strong ablations, including tests on encoder sensitivity, where CAD shows improvements even with weaker or randomly initialized encoders.
(ii) Efficiency is well-quantified, with both training and inference times competitive compared to baselines.
Remaining concerns, such as theoretical guarantees and the handling of rare labels, have been acknowledged through clarifications and concrete plans for the camera-ready version.
Overall, the use of a diffusion model to tackle noisy multi-label learning is both novel and promising.
Decision: Accept (poster)