{"id":"a1f19bad-e12a-42c9-acf9-456b18b3bdbd","arxiv_id":"2601.09931","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Explicitly modeling and sampling acoustic noise as a latent variable, with either an NMF or a diffusion prior, improves unsupervised diffusion-based speech enhancement over prior implicit-noise methods.","lead":"This paper proposes unsupervised speech-enhancement methods that explicitly sample background noise as a latent variable alongside clean speech, using either a matrix-factorization or a diffusion noise prior. Tests on two speech corpora show that these explicit-noise methods improve quality and intelligibility over prior diffusion-based unsupervised approaches, especially in matched conditions when the noise prior is diffusion-based.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Wiener post-filtering and per-method λ tuning, not explicit noise sampling alone, may explain ParaDiffUSE-EN gains; central claim needs a controlled ablation.","rationale":"The reader identifies Eq. (21), the uninformative-prior pseudo-likelihood approximation, as the load-bearing premise. I agree that Eq. (21) is a limitation and the paper admits it, but it is shared by all compared samplers—both implicit and explicit—so it does not specifically threaten the comparative claim. The comparative claim requires that the compared methods differ in 'explicit noise sampling' and little else; in fact, they differ in Wiener post-processing, λ scheduling, observation-model perturbation σ_r, and algorithmic details (Tweedie/Gibbs updates). These confounds are concretely quantifiable from Table III: Wiener filtering alone accounts for large gains in exactly the headline condition (matched VB-DMD), and removing it flips the PESQ/ESTOI ordering between ParaDiffUSE-EN and ParaDiffUSE-IN. Therefore the central claim is not yet established by the paper's experiments, even though the methods are coherent and the results are promising. This is a causal-attribution weakness, not a mathematical inconsistency, and it is addressable with a controlled ablation. Since the reader already issued CONDITIONAL and my concern does not push the verdict to a different category, I keep the verdict unchanged.","tokens_in":21960,"tokens_out":4968,"duration_ms":56753,"concrete_test":"Run a 2×2 ablation on VB-DMD and WSJ0-QUT (matched and mismatched): ParaDiffUSE-IN with/without the Algorithm-3 Wiener filter, and ParaDiffUSE-EN with/without it, using the same λ schedule for both variants (e.g., λ_i = 5.75·σ_τi) and identical initialization. If ParaDiffUSE-EN without Wiener fails to beat ParaDiffUSE-IN with Wiener on SI-SDR, PESQ, and ESTOI, the claim that explicit noise sampling per se improves SE is unsupported. For the NMF comparison, modify UDiffSE+ only by replacing its E-step with DiffUSEEN's Gibbs E-step (Eqs. 30-35), keeping σ_r=0 and λ=1.5; if the gain disappears, the DiffUSEEN advantage comes from the added perturbation/Tweedie updates rather than latent-noise sampling.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim—'explicit noise sampling consistently improves unsupervised diffusion-based SE'—is supported mainly by two pairwise comparisons: DiffUSEEN vs. UDiffSE+ (Section VI-B.1, Table I) and ParaDiffUSE-EN vs. ParaDiffUSE-IN (Section VI-B.1, Table I). But neither comparison isolates explicit noise modeling. ParaDiffUSE-EN differs from ParaDiffUSE-IN not only by explicit noise sampling but also by a Wiener-filter post-processing step (Algorithm 3, lines 15-16) and a different λ schedule (λ_i = λ·σ_τi, λ=5.75, Section VI-A). Table III shows that Wiener filtering alone adds 0.8–1.0 dB SI-SDR on WSJ0-QUT and 2.49 dB SI-SDR on matched VB-DMD, plus 0.14 PESQ and 0.05 ESTOI in the matched VB-DMD case. Without Wiener, ParaDiffUSE-EN on matched VB-DMD actually has lower PESQ/ESTOI than ParaDiffUSE-IN (3.27/0.81 vs. 3.42/0.83) despite higher SI-SDR. Thus the 'best overall quality and intelligibility' claim depends on a post-processor that is not applied to the implicit-noise baseline. Similarly, DiffUSEEN vs. UDiffSE+ changes the observation model (adding σ_r in Eq. 25), the E-step (Gibbs sampling, Tweedie updates), and the λ value (1.75 vs. 1.5), so the improvement cannot be attributed to latent-noise sampling alone. The paper self-reports that the shared uninformative-prior approximation in Eq. (21) 'is not accurate' (Section V-B), but that approximation is common to both compared arms; the more pressing issue is that the experimental design confounds the variable named in the conclusion. The reader's Eq. (21) concern is real but secondary: even if Eq. (21) were exact, the current experiments would not establish the headline attribution.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses unsupervised single-channel speech enhancement using score-based diffusion models. It builds on UDiffSE/UDiffSE+/DEPSE by explicitly modeling acoustic noise as a latent variable in the E-step, jointly sampling speech and noise. Two frameworks are presented: DiffUSEEN, which retains an NMF-structured Gaussian noise prior but samples noise from its posterior via Gibbs, and ParaDiffUSE, which trains a single conditional score model on both speech and noise labels and provides an implicit-noise variant (ParaDiffUSE-IN) and an explicit-noise variant (ParaDiffUSE-EN) with Wiener post-filtering. The central claim, stated in Section VII, is that explicit noise sampling consistently improves unsupervised diffusion-based SE irrespective of the noise prior. The evaluation on WSJ0-QUT and VB-DMD compares these methods with several unsupervised and supervised baselines, with matched and mismatched conditions, and includes ablations on Wiener filtering and joint vs separate models.","tokens_in":22477,"tokens_out":6591,"duration_ms":63823,"significance":"If the central claim were cleanly established, the paper would make a useful contribution: it gives a unified derivation of prior EM-based unsupervised diffusion SE, introduces a principled joint speech–noise score model with label conditioning (reducing from two models to one), and demonstrates—in absolute terms—strong results under matched conditions (e.g., 8.49 dB SI-SDR and 2.61 PESQ on WSJ0-QUT, 18.00 dB SI-SDR on VB-DMD). The public release of code and demo is a plus. However, the evidence for the central claim is currently compromised by confounded comparisons and by reliance on an acknowledged approximate likelihood; the paper itself flags these limitations. The practical significance is therefore real but not yet fully supported.","major_comments":[{"comment":"The headline comparison ParaDiffUSE-EN vs ParaDiffUSE-IN does not isolate explicit noise modeling. ParaDiffUSE-EN includes Wiener post-filtering (Alg. 3 lines 15-16) and a different likelihood-guidance schedule (λ_i = λ σ_{τ_i}, λ=5.75) from the constant λ=1 used for ParaDiffUSE-IN (§VI-A). Table III shows Wiener filtering alone contributes 1.0 dB SI-SDR on matched WSJ0-QUT and 2.49 dB SI-SDR, 0.14 PESQ, and 0.05 ESTOI on matched VB-DMD; without it, ParaDiffUSE-EN on matched VB-DMD has lower PESQ/ESTOI than ParaDiffUSE-IN (3.27/0.81 vs 3.42/0.83). Thus the 'best overall quality and intelligibility' claim depends on a post-processor applied to only one arm. Please report ParaDiffUSE-IN with the same Wiener post-filtering, or ParaDiffUSE-EN without, and control the λ schedule.","section":"VI-B.1, Table III, Alg. 3"},{"comment":"The DiffUSEEN vs UDiffSE+ comparison is likewise confounded. DiffUSEEN changes the observation model (adds σ_r^2 I in Eq. 25), replaces the E-step with Gibbs sampling and Tweedie-based estimates (Alg. 1, lines 6–9), and uses a tuned λ=1.75 instead of 1.5. The claimed improvement in SI-SAR/SI-SDR cannot therefore be attributed to explicit noise modeling alone. A controlled ablation—e.g., UDiffSE+ augmented with explicit noise sampling while keeping all other components fixed—is needed to support the central claim.","section":"VI-B.1, Eqs. (12)/(25), VI-A"},{"comment":"The paper explicitly states that the uninformative-prior approximation p(s|s_i) ≈ N(s_i/δ_i, σ_{τ_i}^2/δ_i^2 I) is 'not accurate', yet all proposed likelihood scores (Eqs. 30, 47, 49) rest on it. Because the approximation is common to both implicit and explicit arms, it does not by itself explain the relative gains, but it does cast doubt on the absolute performance and on the theoretical motivation that explicit mixture consistency should improve posterior sampling. I recommend a validation experiment: compare against DEPSE-TL's tractable-likelihood variant on a subset, or replace the approximate likelihood with a more accurate one for a few configurations to test sensitivity.","section":"V-B, Eq. (21) and (47)/(49)"},{"comment":"Table I reports no error bars or confidence intervals; the claim that certain values are 'statistically significant' is based on paired t-tests for selected comparisons, but the reader cannot verify the variance across files. Given that the paper's main conclusion rests on multiple pairwise differences, reporting standard errors or intervals for all metrics in Table I (as already done in Tables III and IV) is necessary.","section":"Table I / VI-B"}],"minor_comments":[{"comment":"Typo: 'approximatation' should be 'approximation'.","section":"V-B"},{"comment":"Typo: 'potentailly' should be 'potentially'.","section":"Figure 4 caption"},{"comment":"The subscript in '∇ nτ logp' should be 'n_i' for consistency.","section":"Algorithm 3, line 11"},{"comment":"The abstract says code/demo/supplementary are publicly available, but the text later says 'Our code will be publicly available.' Please align these statements.","section":"Abstract / Footnote 1"},{"comment":"The RTF unit is described as 'second'; consider reporting 'seconds per second of audio' (or 's/s') for clarity.","section":"Table II"}],"recommendation":"major_revision","confidential_remarks":"The paper draws heavily on the authors' own prior work [20], [21]; this is not a problem per se, but the novelty relative to [20] (which already used UDiffSE+ with Tweedie updates) should be sharpened in the revision. The main concern remains experimental isolation of the claimed mechanism; the confounded comparisons and the acknowledged approximate likelihood require substantial additional evidence before the central claim can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth a serious look, but the central claim needs a cleaner ablation before it can be taken at face value. What's genuinely new: treating noise as an explicit latent variable in the EM/diffusion-posterior-sampling framework, with Gibbs-based joint sampling for the NMF case, and a jointly trained label-conditioned speech/noise score model for the diffusion-prior case. The writing is clear, the unification of prior work is useful, and the authors are honest about some limitations—they explicitly note that the uninformative-prior approximation in Eq. (21) is inaccurate, and they include ablations for Wiener post-filtering and for joint versus separate diffusion models. That honesty earns credit.\n\nThe soft spot is the attribution of the gains. The comparison between ParaDiffUSE-EN and ParaDiffUSE-IN changes two things at once: explicit noise sampling and Wiener post-filtering (plus a different λ schedule). Table III shows the Wiener filter alone adds up to 2.49 dB SI-SDR on matched VB-DMD, and without it ParaDiffUSE-EN actually has lower PESQ/ESTOI than ParaDiffUSE-IN on that condition. Similarly, DiffUSEEN vs. UDiffSE+ differs in the observation model, the E-step, and the λ value. So the conclusion that “explicit noise sampling consistently improves” is not actually supported by the experimental design. The stress-test note has this right; the reader's Eq. (21) concern is real but secondary.\n\nOther issues are minor but worth noting: the main table lacks error bars; λ is tuned per method, which is a hyperparameter choice, not a fatal flaw, but it weakens cross-method comparisons; and ParaDiffUSE-IN's single Monte Carlo sample approximation is rough. These are all addressable in revision. Code is promised but not verifiable from the manuscript.\n\nWho this is for: anyone working on diffusion-based unsupervised speech enhancement or inverse problems with diffusion priors. It's not a field-reorganizing paper, but it pushes a useful line forward and the methodological questions it raises are real.\n\nRecommendation: send it to peer review, but require a controlled ablation where the only difference is explicit noise sampling—same post-processing, same λ schedule, same observation model—and report error bars or confidence intervals. With that, the contribution would be much cleaner.","headline":"A solid incremental contribution whose headline claim—explicit noise sampling is what improves results—is not actually isolated by the experiments.","tokens_in":22940,"tokens_out":1483,"would_cite":true,"duration_ms":18941,"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":"Explicitly sampling acoustic noise as a latent variable, rather than integrating it out, consistently improves unsupervised diffusion-based speech enhancement on both NMF-based and diffusion-based noise priors.","keywords":["unsupervised speech enhancement","diffusion models","score-based generative models","posterior sampling","latent noise modeling","Gibbs sampling","non-negative matrix factorization","domain mismatch"],"falsifier":"Run the matched-condition experiment with the same priors and likelihoods but replace the explicit Gibbs noise sampling with the implicit scheme and check whether the gap in SI-SDR/PESQ persists; or provide oracle NMF noise parameters to both UDiffSE+ and DiffUSEEN and see whether DiffUSEEN still wins — if the advantage disappears under oracle noise, the benefit comes from the noise estimator rather than from explicit sampling per se.","tokens_in":21887,"feed_emoji":"🎧","tokens_out":2986,"duration_ms":29788,"temperature":0.7,"pith_summary":"The paper claims that unsupervised diffusion-based speech enhancement improves when the acoustic noise is explicitly modeled as a latent variable and jointly sampled with the clean speech, instead of being handled only through its covariance as in prior work. This holds whether the noise prior is a Gaussian with NMF-structured covariance (DiffUSEEN) or a learned diffusion prior (ParaDiffUSE-EN). On WSJ0-QUT and VB-DMD, explicit noise modeling systematically raises quality and intelligibility scores, with the diffusion-based variant best under matched conditions and the NMF-based variant most robust under domain mismatch. The practical stake: better unsupervised enhancement, trained without paired clean-noisy data, that degrades less than several supervised systems when test conditions shift.","feed_headline":"Explicit noise sampling lifts unsupervised speech enhancement","feed_subtitle":"Treating noise as a latent variable improves quality and mismatch robustness without paired clean–noisy data.","key_machinery":"The load-bearing mechanism is Gibbs sampling over the joint posterior p(s,n|x), alternating between drawing speech from p(s|x,n) and noise from p(n|x,s). For NMF noise, the noise posterior is closed-form Gaussian; for the diffusion noise prior, both draws use reversed-SDE updates whose likelihood terms rely on the uninformative-prior pseudo-likelihood approximation p(s|s_i) ≈ N(s_i/δ_i, σ^2/δ^2 I). The diffusion noise prior is a single score network S_ψ(a_t,t,κ) conditioned on a speech/noise label κ, so one model replaces two.","core_discovery":"The central discovery is that the previously ignored latent structure of noise matters. Where earlier unsupervised diffusion SE sampled only the speech posterior and let the noise enter only through an NMF-structured covariance, the paper formulates SE as joint posterior sampling over speech and noise, alternating Gibbs updates around the observation model x = s + n + r. They show that this explicit sampling step improves mixture consistency and artifact scores across two datasets, and that a single conditional score model can serve as both speech and noise prior. In matched conditions the explicit diffusion-noise variant ParaDiffUSE-EN reaches the best quality and intelligibility among unsu","pith_inferences":["If explicit noise sampling is the true cause of the gains, then any unsupervised generative restoration task with additive nuisance sources — dereverberation, source separation, blind deconvolution — could benefit from the same latent-variable treatment.","The joint conditional score model could be extended to multiple known noise classes without adding models; conditioning on noise-type labels might improve generalization under mismatch.","The uninformative-prior pseudo-likelihood approximation is the most likely accuracy bottleneck; replacing it with a tighter likelihood at higher inference cost could close the matched-condition gap with supervised systems.","The Wiener filtering benefit indicates that a cheap final mixture-consistency projection is a valuable complement to explicit posterior sampling."],"forward_implications":["Explicit noise modeling improves unsupervised speech enhancement consistently for both NMF-based and diffusion-based noise priors.","ParaDiffUSE-EN achieves the best overall quality and intelligibility among unsupervised methods under matched conditions, approaching supervised baselines on WSJ0-QUT and VB-DMD.","DiffUSEEN is more robust under mismatched conditions, with smaller SI-SDR degradation than its diffusion-based counterpart and than several supervised reference systems.","Wiener post-filtering systematically refines ParaDiffUSE-EN outputs, with larger gains in matched settings.","A joint speech-noise score model offers a favorable trade-off between performance and parameter count compared to training separate models."],"fun_headline_variants":["Joint speech-noise sampling beats unsupervised baselines","Explicit noise prior sharpens unsupervised speech enhancement","Modeling noise as a latent lifts speech quality","Diffusion noise prior improves unsupervised SE robustness","Sampling noise explicitly boosts unsupervised enhancement"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The uninformative-prior pseudo-likelihood approximation — treating the speech prior as flat when conditioning on the noised speech — is the load-bearing assumption; the paper itself notes it is not accurate, and if it biases the posterior samples, the reported gains from explicit noise modeling could be artifacts of that approximation.","fun_headline_variants_meta":{"raw":{"variants":["Joint speech-noise sampling beats unsupervised baselines","Explicit noise prior sharpens unsupervised speech enhancement","Modeling noise as a latent lifts speech quality","Diffusion noise prior improves unsupervised SE robustness","Sampling noise explicitly boosts unsupervised enhancement"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000715,"raw_usage":{"total_tokens":3048,"prompt_tokens":741,"completion_tokens":2307,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":485,"completion_tokens_details":{"reasoning_tokens":2240}},"tokens_in":485,"tokens_out":2307,"duration_ms":16169,"temperature":1.0,"reasoning_tokens":2240,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T10:26:12.449183+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the matched-condition experiment with the same priors and likelihoods but replace the explicit Gibbs noise sampling with the implicit scheme and check whether the gap in SI-SDR/PESQ persists; or provide oracle NMF noise parameters to both UDiffSE+ and DiffUSEEN and see whether DiffUSEEN still wins — if the advantage disappears under oracle noise, the benefit comes from the noise estimator rather than from explicit sampling per se.","supporting_citations":[],"review_version":1}