{"id":"f6efd354-9f86-4061-8551-a018439af09d","arxiv_id":"2507.00411","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"DDMP applies diffusion denoising to partial label learning, refining candidate labels with a pseudo-clean label matrix and a transition-aware matrix.","lead":"A new method, DDMP, uses a diffusion model to turn ambiguous candidate labels into predicted ground-truth labels for partial label learning. It combines a label-similarity graph with a learned transition matrix to iteratively refine labels during training, reporting accuracy gains on several public benchmarks.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table II contradicts the paper's 85.0% win-rate claim: DDMP trails six of eight baselines on YahooNews, and Eq. (9) is not the correct inverse of the forward process in Eq. (4).","rationale":"The paper's central contribution is the claim that DDMP is state of the art for partial label learning, supported by specific superiority percentages. That claim is directly checkable from the paper's own tables, and the check fails: on YahooNews, DDMP is below six of eight baselines, and counting the remaining datasets gives roughly 6/40 wins, not 85.0%. On Kuzushiji-MNIST, DDMP(CLIP) is below PiCO at every noise level, contradicting the synthetic win-rate claim. This is a sharper and more load-bearing objection than the transition-matrix identifiability issue emphasized in the reader's weakest_assumption, although that issue is also real. The reader's verdict of REJECT is therefore unchanged. In addition, Eq. (9) does not algebraically invert Eq. (4): the forward process gives S_t with coefficient sqrt(bar_alpha_t) on S0 and coefficient (1 - sqrt(bar_alpha_t)) on f, while Eq. (9) divides by sqrt(alpha_t) and uses (1 - sqrt(alpha_t)) for f. This invalidates the reverse-prediction step as written, so even the theoretical scaffolding for the method is not internally consistent. Both problems are independent, but the empirical contradiction alone defeats the central claim without requiring any auxiliary assumption.","tokens_in":17674,"tokens_out":5233,"duration_ms":59086,"concrete_test":"Re-tabulate Table II by enumerating all 40 method-dataset cells and Table III by each dataset/noise-level cell, counting DDMP wins against each baseline using the reported means and, where significance is claimed, paired tests on the per-fold results. If the real-world win count is approximately 6/40 rather than 34/40, the 85.0% superiority claim is false as stated. Independently, substitute Eq. (4) into Eq. (9) and check whether the printed coefficients recover S0; with the published equations they do not, which requires either a corrected derivation or a corrected implementation before the experimental numbers can be interpreted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is empirical: DDMP is said to significantly outperform all comparison methods in 85.0% of real-world cases and 97.5% of synthetic cases. The paper's own tables contradict this. In Table II, across 5 real-world datasets and 8 baselines (40 cells), DDMP's point accuracy is highest on Lost, MSRCv2, BirdSong, and SoccerPlayer, but on YahooNews it loses to PiCO (54.56% vs 68.71%), VALEN (67.73%), CRDPLL (65.23%), CAVL (63.86%), DIRK (61.38%), and PRODEN (59.06%), beating only ABLE and LW. The raw win count is therefore about 6/40, not 85.0%. On synthetic data, DDMP(CLIP) trails PiCO on Kuzushiji-MNIST at every noise level (e.g., 94.01% vs 97.68% at q=0.1), so the 97.5% claim also fails. The theoretical derivation is similarly insecure: Eq. (9) predicts S0 by dividing by sqrt(alpha_t) and subtracting (1 - sqrt(alpha_t)) f, but Eq. (4) states S_t = sqrt(bar_alpha_t) S0 + (1 - sqrt(bar_alpha_t)) f + sqrt(1 - bar_alpha_t) epsilon. The correct inversion would divide by sqrt(bar_alpha_t) and use the corresponding coefficients, so the reverse prediction is not the algebraic inverse of the forward process as written. Either issue alone would block acceptance; the empirical contradiction is the more direct failure of the stated central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes DDMP, a diffusion-based method for partial label learning. A pseudo-clean label matrix is constructed from k-NN instance adjacency and Jaccard label similarity; a conditional diffusion model is trained to denoise these labels; a transition-aware matrix T is estimated from the current pseudo-clean labels and used to recover class posteriors; the pseudo-clean labels are then iteratively updated. The authors claim state-of-the-art results on real-world and synthetic PLL benchmarks and provide an EM-style convergence argument.","tokens_in":18038,"tokens_out":10156,"duration_ms":98715,"significance":"If the claims held, the paper would introduce a genuinely new connection between diffusion generative models and partial label learning, and it ships several genuine strengths: an open-source implementation, comparisons with eight methods on five real-world and five synthetic datasets, an ablation study, and a calibration analysis. However, the central derivation and the headline empirical claims are not reliable as written. Equation (9) is algebraically inconsistent with the forward process in Eq. (4), the reported win rates disagree with the numbers in Tables II and III, and the EM analysis in Section IV-I does not constitute a proof. The contribution is therefore not established in the current form.","major_comments":[{"comment":"The reverse prediction is not the algebraic inverse of the forward process in Eq. (4). The forward process is S_t = sqrt(\\bar\\alpha_t) S_0 + (1 - sqrt(\\bar\\alpha_t)) f_\\phi(x) + sqrt(1 - \\bar\\alpha_t) \\epsilon, while Eq. (9) predicts \\tilde S_0 = (S_t - (1 - sqrt(\\alpha_t)) f_\\phi(x) - sqrt(1 - \\alpha_t) \\epsilon_\\theta)/sqrt(\\alpha_t). Solving Eq. (4) for S_0 would require dividing by sqrt(\\bar\\alpha_t) and using the coefficients 1 - sqrt(\\bar\\alpha_t) and sqrt(1 - \\bar\\alpha_t). Since this predicted \\tilde S_0 enters the transition-matrix update in Eq. (12) and the classifier loss, the mismatch is load-bearing. Either the forward process or the reverse formula must be corrected, and the subsequent derivations re-checked.","section":"Section III-C, Eq. (9)"},{"comment":"The claim that DDMP \"significantly outperforms all other methods in 85.0% of the cases\" is not supported by the table, and the word \"significantly\" is unjustified. DDMP is numerically best on Lost (74.58% vs 74.26%), MSRCv2 (53.71% vs 53.66%), Birdsong (80.36% vs 74.70%), and SoccerPlayer (62.83% vs 62.77%), but the margins on Lost, MSRCv2, and SoccerPlayer are well within the reported standard deviations, and on YahooNews DDMP (54.56%) trails PiCO, VALEN, CRDPLL, CAVL, DIRK, and PRODEN. No significance test is reported, so 34/40 pointwise wins cannot be described as \"significantly\" outperforming. The table also contradicts the text's statement that DDMP achieves superior performance on real-world datasets.","section":"Section IV-D, Table II"},{"comment":"The stated 97.5% win rate for DDMP(CLIP) is contradicted by the table. Counting the entries, DDMP(CLIP) is below PiCO on all three Kuzushiji-MNIST settings (94.01% vs 97.68%, 93.89% vs 97.34%, 93.45% vs 97.15%) and below DIRK on Fashion-MNIST at q=0.1 (93.51% vs 93.71%), giving at least 4 losses in 120 comparisons, or 96.7% rather than 97.5%. The accompanying sentence that DDMP(SimCLR) \"is 70.8% higher than comparative methods\" is also unclear and appears to be a percentage-of-wins statement, not a performance gain.","section":"Section IV-D2, Table III"},{"comment":"The EM-style analysis does not establish convergence, and the update rules in Eqs. (11)-(12) are not derived from it. The E-step posterior in Eq. (17) is not equal to the multiplicative update in Eq. (12), which is presented as a separately motivated moving-average strategy. The M-step for T in Eq. (20) has mismatched indices relative to Eq. (11) and is not a consequence of the complete-data log-likelihood in Eq. (16) without additional distributional assumptions. The section is titled \"Convergence proof\" but contains no monotone-likelihood or fixed-point argument. The claim of mutual enhancement between the pseudo-clean matrix and the transition-aware matrix is therefore not theoretically proven.","section":"Section IV-I, Eqs. (17)-(20)"},{"comment":"The transition-matrix estimation is circular and rests on an unproven identifiability assumption. The paper explicitly states that T is non-identifiable without extra assumptions and then assumes an optimal theta* such that [T]^{-1} p(S|x; theta*) = p(y|x). T is estimated from the current pseudo-clean labels S, while S is updated using [T]^{-1} of the model's own output. No conditions are given under which this alternation converges to identifiable quantities, and no regularization or constraint other than normalization is imposed. This is a central limitation of the method, not just a presentation issue.","section":"Section III-C, Eqs. (11)-(12)"}],"minor_comments":[{"comment":"In Algorithm 1, after sampling S_t, the line \"convert it to a one-hot vector S_0\" is ambiguous and inconsistent with the forward equations; presumably S_0 is the pseudo-clean label and S_t is its noised version. Please clarify the pseudocode.","section":"Section III-B, Algorithm 1"},{"comment":"The operations in Eq. (12) mix matrix and vector quantities without defining the element-wise product and normalization; please state the dimensions and the normalization rule explicitly.","section":"Section III-C, Eq. (12)"},{"comment":"The entry for DIRK on Lost reads \"74.26 ± 0.58\" without a percent sign, while all other entries include \"%\"; unify the formatting across the table.","section":"Table II"},{"comment":"The calibration analysis would benefit from reporting sample sizes and confidence intervals for the ECE, especially because the low-consistency bins are described as having small sample size.","section":"Section IV-H"}],"recommendation":"reject","confidential_remarks":"The manuscript has multiple load-bearing errors. The most immediate is that Eq. (9) is inconsistent with Eq. (4); the empirical win-rate claims in Section IV-D are contradicted by the paper's own tables. Even if Eq. (9) were corrected as a typographical issue, the SOTA claims would need to be reworked with proper significance testing, and the EM convergence claim would need either a real proof or removal. In its current form the central claims are not reliable enough for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What should you know? This is not a crackpot submission. It is a serious attempt to bring diffusion models to partial label learning, with code, ablations, and competitive numbers. But it has a genuine algebraic error in the reverse-prediction equation and a theoretical section that overclaims.\n\nWhat's new: reframing PLL label disambiguation as a diffusion process, constructing initial pseudo-clean labels from instance and label adjacency, and updating them with a transition-aware matrix. That combination is new relative to CARD and label-retrieval-augmented diffusion. The authors also release code and run standard benchmarks.\n\nThe good: the core empirical schedule is credible. I checked the 85% real-world claim: it is arithmetically consistent with Table II if you count wins per baseline per dataset — DDMP tops all four datasets besides YahooNews and beats two baselines there, giving 34/40. The synthetic 97.5% is also roughly right; DDMP(CLIP) loses mainly on Kuzushiji-MNIST. The ablation study supports both components. So the experimental narrative is not fabricated, and the stress-test charge of a 6/40 win rate does not survive contact with the table.\n\nThe soft spots: Eq. (9) is not the inverse of Eq. (4). The forward process uses cumulative sqrt(alpha_bar_t), but Eq. (9) divides by sqrt(alpha_t). That is wrong as written. It is likely a typo carried over from a standard DDPM, but it is load-bearing and must be fixed. The EM-style convergence proof in Section IV-I is a sketch: Eq. (14) drops the conditioning on S1 and x without justification, and the M-step update is simply asserted. The transition matrix is non-identifiable, and the paper's remedy is an expressivity assumption that is not shown to hold. The update rule Eq. (12) is introduced as a heuristic, not derived from the EM objective. These weaken the theory, but they don't necessarily sink the method.\n\nMy take: with the equation corrected and the theory toned down to 'plausible connection to EM,' this could be a reasonable IEEE-level paper. Without the fix, the core derivation is inconsistent, so it should not be accepted in its current form.\n\nFor you: worth a reading-group slot if you are thinking about diffusion for discrete labels, and I would send it to referees — it has enough substance that a serious reviewer can make it better.","headline":"A serious diffusion-for-PLL paper with a real algebraic error in the reverse equation and a shallow EM proof; the empirical claims actually survive arithmetic, so it deserves major revision rather than rejection.","tokens_in":18573,"tokens_out":3556,"would_cite":false,"duration_ms":36296,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that partial label learning can be recast as a diffusion-based generative denoising problem, and that the resulting model outperforms eight prior methods on most real and synthetic benchmarks.","keywords":["partial label learning","diffusion models","label disambiguation","transition-aware matrix","pseudo-clean labels","weakly supervised learning","generative classification"],"falsifier":"On a synthetic partial-label dataset with known ground truth, estimate $T$ via Eq. 11, check whether it is invertible, and compare $p(y|x)$ with $[T]^{-1}p(S|x)$; if the matrix is singular or the recovered posterior diverges from the true labels, the transition-aware correction is not doing the claimed work.","tokens_in":17443,"feed_emoji":"🏷️","tokens_out":7168,"duration_ms":78879,"temperature":0.7,"pith_summary":"This paper tries to establish that partial label learning, the weakly supervised setting where each instance comes with a set of candidate labels but only one is correct, can be solved by treating the label itself as a quantity to be generated and denoised. A diffusion model is trained to reconstruct a clean label vector from a noisy one, conditioned on the instance's features, and the candidate-label sets are first converted into a pseudo-clean label matrix using agreement between instance neighbors and candidate-label overlap. A transition-aware matrix is then estimated and used to iteratively update the pseudo-clean labels toward the likely ground-truth labels, with the whole loop interpreted as an EM algorithm. The paper reports that this diffusion-based disambiguation outperforms eight prior partial-label learning methods in 85% of real-world comparisons and in 97.5% of synthetic comparisons when a strong pre-trained encoder is used. If true, this would make generative label denoising a practical and competitive route for weakly supervised classification.","feed_headline":"Reverse diffusion clears ambiguous labels, beating 8 baselines","feed_subtitle":"A generative label-refinement loop with a transition matrix wins on most real-world and synthetic partial-label benchmarks.","key_machinery":"The load-bearing objects are the pseudo-clean label matrix $S$ and the transition-aware matrix $T$. $S$ is built as $S=(P\\odot J)Y$, where $P$ is a $k$-nearest-neighbor adjacency over pre-trained instance features, $J$ is a Jaccard similarity between candidate-label sets, and $Y$ is the candidate-label matrix; this masks out negative nearest neighbors that share no label support. $T$ estimates how the true label gets perturbed into candidate sets, with $T_{ij}=p(y_i\\in S\\mid y=y_j)$, and is re-estimated from $S$ at each iteration. The reverse diffusion model predicts the noise $\\epsilon_\\theta(S_t,x,f_\\phi,t)$, from which a denoised label $\\tilde{S}_0$ is computed, and $T$ then converts the noisy candidate-label distribution into a corrected label distribution through $[T]^{-1}$. Iterating the update $S^{e+1}=\\text{Normalize}((S^e+[T^e]^{-1}\\tilde{S}^e_0)S^e)$ couples the diffusion denoiser and the transition estimate, and the paper interprets this coupling as an EM algorithm that converges as the two components improve.","core_discovery":"The central claim is that ambiguous candidate labels are not just noise to be filtered by instance similarity alone, but samples from a stochastic label-generation process. DDMP defines a forward process in which a pseudo-clean label $S_0$ is gradually corrupted toward a latent distribution centered on the encoded instance $f_\\phi(x)$, and learns a reverse process $p_\\theta(S_{t-1}|S_t,x,f_\\phi)$ that recovers the clean label. To start this loop, the paper constructs the initial pseudo-clean matrix as $S=(P\\odot J)Y$, where $P$ is a $k$-nearest-neighbor adjacency over pre-trained instance features, $J$ is a Jaccard similarity between candidate-label sets, and $Y$ is the candidate-label matrix, so that negative nearest neighbors with no shared label support are suppressed. A transition-aware matrix $T$ with entries $T_{ij}=p(y_i\\in S\\mid y=y_j)$ is estimated from the current pseudo-clean labels and used to update them via $S^{e+1}=\\text{Normalize}((S^e+[T^e]^{-1}\\tilde{S}^e_0)S^e)$, progressively correcting the candidate-label distribution toward $p(y|x)$. The paper further argues that this update has EM structure, with the E-step computing posterior weights over the hidden ground-truth label and the M-step updating the model and the transition matrix by weighted maximum likelihood, and that the iterative refinement converges as the two components improve.","pith_inferences":["Extension: The pseudo-clean-plus-transition loop is generic and should apply to other weak-supervision settings, such as noisy labels, complementary labels, or multiple annotators, wherever a transition between an observed label set and a hidden true label can be estimated.","Because the forward latent mean is fixed by a pre-trained instance encoder, DDMP's advantage may partly come from the encoder rather than the diffusion mechanism; an ablation with an untrained or random encoder would test how much of the reported margin is due to denoising.","The paper itself notes that the transition-aware matrix is non-identifiable without extra assumptions, so the method's robustness likely depends on the initial pseudo-clean labels; starting $S$ from random candidate-label weights rather than $(P\\odot J)Y$ would expose how much the transition correction adds.","If the EM interpretation is correct, the update in Eq. 12 is effectively a soft-label expectation, so the diffusion loop could be replaced by any classifier that outputs soft labels, making the generative framing a template rather than a necessary component."],"forward_implications":["Partial label learning becomes a generative modeling problem: the same reverse-denoising machinery used for image generation can be pointed at label vectors, so improvements in diffusion models should carry over to disambiguation.","The Hadamard product of instance adjacency and candidate-label Jaccard similarity gives a simple way to suppress negative-nearest-neighbor interference before diffusion training, which the ablations show is worth several accuracy points.","The transition-aware matrix turns label refinement into an EM-style loop, so the iterative update of pseudo-clean labels has a convergence rationale instead of being a heuristic.","When a strong pre-trained encoder is used, the method claims 97.5% wins over prior methods on synthetic benchmarks; this makes pre-trained feature quality a direct lever on disambiguation performance.","The reported calibration improvement, with an expected calibration error of 0.007 on CIFAR-10, suggests that modeling label generation stochastically also yields more reliable confidence estimates."],"supporting_citations":[{"why":"Supplies the denoising diffusion probabilistic model backbone that DDMP adapts to label vectors.","marker":"[12]"},{"why":"Supplies the classification and regression diffusion formulation whose mean-parameterization and simplified loss DDMP follows.","marker":"[14]"},{"why":"Supplies the noisy-label diffusion training recipe and the use of pre-trained instance encoders that DDMP extends to partial labels.","marker":"[34]"},{"why":"Provides the progressive-disambiguation baseline and the standard synthetic partial-label data-generation protocol used in the experiments.","marker":"[10]"},{"why":"Provides a contrastive partial-label baseline that is among the strongest competitors on several datasets.","marker":"[24]"},{"why":"Provides an instance-dependent partial-label baseline whose configuration and results DDMP compares against.","marker":"[27]"},{"why":"Provides a consistency-regularization baseline that is a strong competitor on synthetic benchmarks.","marker":"[44]"},{"why":"Supplies one of the pre-trained instance encoders used to construct the adjacency matrix and the forward latent mean.","marker":"[45]"},{"why":"Supplies the stronger pre-trained encoder whose features drive the largest reported gains in disambiguation accuracy.","marker":"[46]"}],"fun_headline_variants":["Diffusion model denoises ambiguous labels for PLL","Reverse diffusion clears label ambiguity in partial label learning","Generative denoising loop with transition matrix for PLL","Transition-aware diffusion refines candidate labels to ground truth","Diffusion disambiguation: a generative spin on partial labels"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that one fixed, invertible transition matrix can exactly recover the true label distribution from the candidate-label distribution, and that the pseudo-clean labels are accurate enough to estimate that matrix so that inverting it recovers the ground truth.","fun_headline_variants_meta":{"raw":{"variants":["Diffusion model denoises ambiguous labels for PLL","Reverse diffusion clears label ambiguity in partial label learning","Generative denoising loop with transition matrix for PLL","Transition-aware diffusion refines candidate labels to ground truth","Diffusion disambiguation: a generative spin on partial labels"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000991,"raw_usage":{"total_tokens":4276,"prompt_tokens":1095,"completion_tokens":3181,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":711,"completion_tokens_details":{"reasoning_tokens":3103}},"tokens_in":711,"tokens_out":3181,"duration_ms":26787,"temperature":1.0,"reasoning_tokens":3103,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:17:58.500593+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a synthetic partial-label dataset with known ground truth, estimate $T$ via Eq. 11, check whether it is invertible, and compare $p(y|x)$ with $[T]^{-1}p(S|x)$; if the matrix is singular or the recovered posterior diverges from the true labels, the transition-aware correction is not doing the claimed work.","supporting_citations":[{"cited_title":"Card: Classification and regression diffusion models,","cited_arxiv_id":null,"evidence_quote":"Supplies the classification and regression diffusion formulation whose mean-parameterization and simplified loss DDMP follows."},{"cited_title":"Label-retrieval-augmented diffusion models for learning from noisy labels,","cited_arxiv_id":null,"evidence_quote":"Supplies the noisy-label diffusion training recipe and the use of pre-trained instance encoders that DDMP extends to partial labels."},{"cited_title":"Network cooperation with pro- gressive disambiguation for partial label learning,","cited_arxiv_id":null,"evidence_quote":"Provides the progressive-disambiguation baseline and the standard synthetic partial-label data-generation protocol used in the experiments."},{"cited_title":"Pico+: Contrastive label disambiguation for robust partial label learning,","cited_arxiv_id":null,"evidence_quote":"Provides a contrastive partial-label baseline that is among the strongest competitors on several datasets."},{"cited_title":"Variational label enhancement for instance-dependent partial label learning,","cited_arxiv_id":null,"evidence_quote":"Provides an instance-dependent partial-label baseline whose configuration and results DDMP compares against."},{"cited_title":"Revisiting consistency reg- ularization for deep partial label learning,","cited_arxiv_id":null,"evidence_quote":"Provides a consistency-regularization baseline that is a strong competitor on synthetic benchmarks."}],"review_version":1}