{"id":"2705b75c-bbe5-480f-8446-e8fb7eaa6ea3","arxiv_id":"2505.05631","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A generalized denoising score matching loss enables MRI denoisers to be trained from noisy observations alone and outperforms other self-supervised methods on M4Raw and fastMRI.","lead":"This paper introduces Corruption2Self, a self-supervised method that denoises MRI images using only noisy scans, with no clean reference data. It reports state-of-the-art results among self-supervised methods on two public MRI datasets and competitive performance against supervised methods.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1 only constrains hθ for t>tdata; the GDSM loss is degenerate at t=tdata, so Eq. 11 evaluates the network at a point where the stated theory provides no guarantee that hθ equals E[X0|Xtdata].","rationale":"The paper's contribution is a self-supervised denoiser whose advertised guarantee is the GDSM theorem, and the empirical tables are strong. The single most load-bearing step is the inference-time evaluation at tdata: the theorem's loss is degenerate there, so no amount of empirical success makes the stated theoretical claim true as written. The fix is either to prove a continuity/limit result and state it, or to reposition Eq. 11 as an empirical heuristic. The coupling issue for σ_ttarget>0 is a second, related mathematical gap: the proof's second Tweedie representation is not justified by the stated assumptions. Both issues are fixable in revision and do not by themselves invalidate the empirical method, so the reader's CONDITIONAL verdict remains appropriate; my recommended test checks whether the network actually extrapolates to tdata. If it does, the practical claim survives even though the theorem needs sharpening. I therefore agree with the reader's weakest assumption and recommend no change to the verdict.","tokens_in":24621,"tokens_out":16553,"duration_ms":176707,"concrete_test":"On 100 held-out M4Raw T1 slices, for τ∈{0.01,0.02,0.05,0.1,0.2} relative to σ_tdata, compute averaged outputs Âτ=(1/M)Σ_{m=1}^M hθ(Xtdata+στ Z_m, t(τ)) with 32 random Z_m, and compare them to the direct inference hθ(Xtdata,tdata) from Eq. 11. If the Âτ do not converge to the direct output as τ→0 (e.g., PSNR gap above 0.3 dB), the network is not extrapolating the learned conditional expectation to tdata, and the central claim that C2S approximates E[X0|Xtdata] is unsupported. This test uses only the trained model and existing test data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that C2S approximates E[X0|Xtdata]. The bridge is Theorem 1/Corollary 2, but the theorem is stated for t sampled uniformly from (tdata,T] (Eqs. 3 and 12). At the inference point t=tdata, the coefficients in Eq. 3 become γ=0 and δ=1, so Dθ(Xtdata,tdata)=Xtdata and the loss J(θ)=0 for every hθ. Hence any minimizer can take arbitrary values at (Xtdata,tdata); the conclusion hθ*(Xt,t)=E[Xttarget|Xt] is proven only for t>tdata. Equation 11 therefore evaluates the network outside the domain of the theorem. A limit argument as t↓tdata would recover E[X0|Xtdata] from E[X0|Xt] under continuity of the conditional expectation, but the paper neither states nor proves such a regularity property, and neural networks do not automatically extrapolate in the time-conditioning argument. A related gap appears in the same proof for σ_ttarget>0: the equality ∇log pt(Xt)=(E[Xttarget|Xt]-Xt)/(σ_t^2-σ_ttarget^2) requires Xt=Xttarget+sqrt(σ_t^2-σ_ttarget^2)Z with Z independent of Xttarget, which is not implied by Xtdata=X0+σ_tdata N and Xttarget=X0+σ_ttarget N0; under independent N,N0 the relevant variance is σ_t^2+σ_ttarget^2, not σ_t^2-σ_ttarget^2. This affects the detail-refinement variant. Thus the theoretical justification for the headline result is incomplete at exactly the inference operation the method uses.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript introduces Corruption2Self (C2S), a self-supervised MRI denoising method. The authors formulate a generalized denoising score matching (GDSM) loss whose minimizer is the conditional expectation E[X_ttarget | X_t] under stated assumptions, and train a U-Net with time conditioning and NVC-MSA using only noisy observations. They reparameterize noise levels, add a detail refinement stage, and extend the framework to multi-contrast inputs. Experiments on M4Raw and fastMRI compare against classical, supervised, and self-supervised baselines, reporting state-of-the-art self-supervised PSNR/SSIM and competitive supervised performance, with appendices on robustness to noise-level misestimation and additional ablations.","tokens_in":25044,"tokens_out":7665,"duration_ms":79933,"significance":"The core idea--learning conditional expectations of cleaner images from further corrupted noisy observations--is a natural and potentially useful extension of ADSM and Noisier2Noise, and the paper provides a broad experimental comparison on real and simulated MRI data, including low-field M4Raw, multiple contrasts, and multi-contrast fusion. Strengths include the explicit robustness study in Appendix H, the clear positioning relative to prior self-supervised methods, and the reproducibility-oriented details on datasets and training. If the theoretical gap at the inference point is fixed, the method would be a solid contribution to self-supervised MRI denoising; as written, the headline theoretical claim is incomplete in a way that affects the central inference operation.","major_comments":[{"comment":"The theorem is stated and proved for t sampled uniformly from (tdata, T], and the proof divides by gamma(t, sigma_ttarget), which is positive only for t > tdata. At t = tdata, gamma = 0 and delta = 1 in Eq. (3), so J(theta) = E[||Xtdata - Xtdata||^2] = 0 for every h_theta, and h_theta*(Xtdata, tdata) is unconstrained. Equation (11) nevertheless evaluates the network exactly at t = tdata and asserts it approximates E[X0 | Xtdata]. The paper needs an explicit continuity/limit argument as t decreases to tdata, or a modified training loss that also constrains t = tdata; as written, the central theoretical claim does not cover the inference operation.","section":"Section 3.1, Theorem 1/Corollary 2 vs. Section 3.2, Eq. (11)"},{"comment":"For sigma_ttarget > 0, the proof uses the identity Xt = Xttarget + sqrt(sigma_t^2 - sigma_ttarget^2) Z2 with Z2 independent of Xttarget to write the score as (E[Xttarget | Xt] - Xt)/(sigma_t^2 - sigma_ttarget^2). This identity is a coupling assumption that is not stated in Assumptions 3-5: under the natural model Xttarget = X0 + sigma_ttarget Z_ttarget and Xt = X0 + sigma_t Z_t with Z_ttarget and Z_t independent, the conditional variance of Xt - Xttarget given Xttarget is sigma_t^2 + sigma_ttarget^2, not sigma_t^2 - sigma_ttarget^2. Consequently the detail-refinement extension, which relies on sigma_ttarget > 0, is not justified by the stated theorem.","section":"Appendix B, Theorem 4 proof"},{"comment":"The detail-refinement stage trains the network to satisfy h_theta*(Xt, t) = E[Xttarget | Xt] with sigma_ttarget sampled from (0, sigma_tdata], while Eq. (11) evaluates h_theta*(Xtdata, tdata) as a clean estimate E[X0 | Xtdata]. These are different quantities, and the paper does not specify how the nonzero-target predictor is converted into the clean estimate whose PSNR/SSIM is reported in Tables 1-3. Please clarify the inference protocol for the refined model or add the missing derivation.","section":"Appendix G and Section 3.2, Eq. (11)"},{"comment":"The fastMRI reparameterization comparison reports a 'Without Reparam.' row described as 'estimated baseline results.' Since the main text presents reparameterization as an empirical improvement (Table 4a), the provenance of the estimated values should be disclosed in detail, and ideally the baseline should be run under identical conditions; otherwise the fastMRI reparameterization claim is not directly supported.","section":"Appendix E, Table 6 and Section 4"}],"minor_comments":[{"comment":"The text says 'proof provided in Appendix 4' for Theorem 1 and 'proof provided in Appendix 5' for Corollary 2, but the appendices are lettered; update the cross-references.","section":"Section 3.1"},{"comment":"Equation (2) uses Xt for t > tdata, while Eq. (10) and Algorithm 1 construct X_tau from Xtdata + sigma_tau Z; the relationship between t and tau should be made explicit in the main text rather than only in Appendix B.","section":"Section 3.2, Eq. (10) and Algorithm 1"},{"comment":"The paired t-tests are reported without the number of validation subjects/slices or any correction for multiple contrasts; please provide these details.","section":"Table 1"},{"comment":"The Introduction claims multi-contrast C2S achieves state-of-the-art among supervised methods, but Table 5 only compares BM3D, Noise2Noise, and single-contrast C2S; supervised transformers from Table 2 are not included, so the claim should be qualified.","section":"Section 4 and Table 5"},{"comment":"There are several typos, including 'Noise2V oid' in the text, 'F ouguier' in the references, and 't target' in Section 3 where 'sigma_ttarget' is meant.","section":"References and text"},{"comment":"The suggestion that T can be chosen as the maximum pairwise distance between training points is imported from score-based generative modeling; please discuss whether this bound is needed for the denoising objective rather than for generative score estimation.","section":"Appendix J.1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a strong empirical contribution and the main theorem is correct on its stated domain t > tdata, but the inference-time gap at t = tdata and the unstated coupling for sigma_ttarget > 0 are load-bearing and should be fixed in revision. The empirical results are extensive and the method is clearly positioned relative to prior work; I recommend major revision rather than rejection. No concerns about citation practices or novelty disclosure; the relation to Daras et al. and Moran et al. is acknowledged."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a look if you care about self-supervised denoising for low-field or accelerated MRI. The main idea is a continuous-noise generalization of Noisier2Noise and ADSM: train a denoiser on progressively noisier versions of the observed noisy image and use score-matching identities to recover the clean-image conditional mean. The reparameterized schedule, detail refinement, and multi-contrast fusion are useful engineering, and the experiments on M4Raw and fastMRI are credible: C2S beats the self-supervised baselines by a clear margin and lands close to supervised methods, with nice robustness to noise-level misestimation. The paper deserves a serious referee.\n\nThe soft spots are mostly in the theory section. Theorem 1 is stated for t sampled from (tdata, T], and the proof shows h* = E[Xttarget | Xt] for t > tdata. But the inference step (Eq. 11) evaluates the network at t = tdata, where the loss coefficients degenerate (gamma = 0, delta = 1) and every h_theta is a minimizer. So the headline claim that C2S approximates E[X0 | Xtdata] is not actually delivered by the theorem; it relies on an unstated continuity or extrapolation assumption. This is likely fixable, because training uses tau arbitrarily close to 0 and a limit argument should work, but as written the guarantee stops short of the operation used at test time.\n\nThere is a second, more substantive gap: for sigma_ttarget > 0, the detail-refinement variant, the proof assumes Xt can be written as Xttarget plus independent Gaussian noise with variance sigma_t^2 - sigma_ttarget^2. If Xttarget = X0 + sigma_ttarget N0 with N0 independent of the noise in Xtdata, that representation does not hold; the variance algebra gives a different target. Without an extra coupling assumption, the proof does not go through for that variant. The empirical gain from detail refinement may still be real, but the theoretical justification is not there.\n\nMinor issues: Table 6 labels a baseline row as \"estimated\" without saying how it was obtained, and the \"state-of-the-art among supervised methods\" claim in the multi-contrast section is not supported by Table 5, which compares only BM3D, Noise2Noise, and single-contrast C2S. Also, no code is visible in the arXiv version, though the project website may host it.\n\nIf the authors add a continuity or extrapolation statement for t = tdata, fix or weaken the sigma_ttarget > 0 claim, and clean up the Table 6 labeling, I would be comfortable with the paper. As it stands it is a useful empirical contribution whose formal story is a bit looser than the abstract suggests.","headline":"C2S is a credible, useful self-supervised MRI denoiser, but the theory does not cover the t=tdata inference point or the sigma_ttarget>0 variant, and a few claims outrun the tables.","tokens_in":25547,"tokens_out":8323,"would_cite":true,"duration_ms":88614,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A self-supervised score-matching loss lets MRI denoisers learn the clean-image posterior mean from noisy data alone.","keywords":["MRI denoising","self-supervised denoising","score matching","denoising score matching","conditional expectation","multi-contrast MRI","Gaussian noise","corruption2self"],"falsifier":"On a synthetic dataset with a known Gaussian prior for $X_0$ and known noise level, compute the posterior mean $\\mathbb{E}[X_0\\mid X_{t_{\\mathrm{data}}}]$ by Monte Carlo, train C2S from noisy samples only, and compare the network output at $(X_{t_{\\mathrm{data}}},t_{\\mathrm{data}})$ with that posterior mean; a systematic error that persists when the network is trained only on $t>t_{\\mathrm{data}}$ would show the inference step relies on extrapolation outside the theorem's range.","tokens_in":24430,"feed_emoji":"🧠","tokens_out":10186,"duration_ms":91216,"temperature":0.7,"pith_summary":"Corruption2Self (C2S) sets out to prove that MRI denoising can be learned entirely from noisy acquisitions, without clean or high-SNR labels. The paper's core theoretical claim is that minimizing a generalized denoising score matching (GDSM) loss on pairs of noisy images—the observed image and a further corrupted version—drives the network to the conditional expectation of the cleaner image given the noisier one; with the target noise set to zero, that conditional expectation is the posterior mean of the clean image. On M4Raw and fastMRI, C2S outperforms prior self-supervised denoisers and matches supervised networks trained on higher-SNR references, and with multi-contrast inputs it beats the supervised baselines on M4Raw. The practical payoff is that low-field and accelerated MRI scans, where high-SNR ground truth is expensive or unavailable, could be denoised using only the diagnostic images themselves.","feed_headline":"Self-supervised MRI denoiser beats peers without clean labels","feed_subtitle":"A generalized score-matching loss recovers the clean-image posterior mean, matching supervised denoisers on real MRI.","key_machinery":"The load-bearing object is the GDSM loss $$J'(\\$\\theta$)=\\mathbb{E}\\left[\\left\\|\\gamma'(\\tau,\\sigma_{t_{\\mathrm{target}}})h_\\$\\theta$(X_t,t)+\\delta'(\\tau,\\sigma_{t_{\\mathrm{target}}})X_t - X_{t_{\\mathrm{data}}}\\right\\|^2\\right],$$ with $\\gamma'(\\tau,\\sigma_{t_{\\mathrm{target}}}) = \\sigma_\\tau^2 / (\\sigma_\\tau^2 + \\sigma_{t_{\\mathrm{data}}}^2 - \\sigma_{t_{\\mathrm{target}}}^2)$ and $\\delta' = (\\sigma_{t_{\\mathrm{data}}}^2-\\sigma_{t_{\\mathrm{target}}}^2)/(\\sigma_\\tau^2+\\sigma_{t_{\\mathrm{data}}}^2-\\sigma_{t_{\\mathrm{target}}}^2)$. Re-expressing the doubly-noisy image from the perspective of both the observed image and the target image yields two score identities whose equality gives $\\mathbb{E}[X_{t_{\\mathrm{data}}}\\mid X_t] = \\gamma' \\mathbb{E}[X_{t_{\\mathrm{target}}}\\mid X_t] + \\delta' X_t$, so minimizing the loss against $X_{t_{\\mathrm{data}}}$ forces $h_\\theta$ to output $\\mathbb{E}[X_{t_{\\mathrm{target}}}\\mid X_t]$. This coefficient identity, together with the skip connection $D_\\theta = \\lambda_{\\mathrm{out}} h_\\theta + \\lambda_{\\mathrm{skip}} X_t$ and the $\\tau$-reparameterization, carries the whole method.","core_discovery":"The central discovery is that denoising score matching does not need clean training images. By corrupting the observed noisy image $X_{t_{\\mathrm{data}}}$ with additional independent Gaussian noise to form $X_t$, and training the network to predict $X_{t_{\\mathrm{data}}}$ from $X_t$ through a specially weighted sum of the network output and the input, the minimizer of the GDSM loss satisfies $h_{\\theta^*}(X_t,t) = \\mathbb{E}[X_{t_{\\mathrm{target}}} \\mid X_t]$. When $t_{\\mathrm{target}} = 0$, the right-hand side is $\\mathbb{E}[X_0 \\mid X_t]$, the minimum mean-square-error estimate of the clean image, so the network has effectively learned to denoise despite never seeing a clean image. A reparameterized noise scale $\\tau$ with uniform sampling and a skip-blended output stabilizes training, and a detail-refinement variant with $\\sigma_{t_{\\mathrm{target}}} > 0$ retains fine textures. On the M4Raw and fastMRI datasets, the method attains the best PSNR and SSIM among self-supervised methods and competitive numbers against supervised ones, with multi-contrast C2S exceeding all baselines on M4Raw.","pith_inferences":["If the same Gaussian score identity is validated outside MRI, the GDSM construction transfers directly to other imaging modalities with additive white noise, or to Rician data after a variance-stabilizing transform; the authors point to VST but do not test it.","The theory's proof only covers $t > t_{\\mathrm{data}}$, while inference evaluates the network at $t = t_{\\mathrm{data}}$; a Monte Carlo check of $h_\\theta(x,t_{\\mathrm{data}})$ against the true posterior mean under a known Gaussian prior would quantify how much of the method's success depends on extrapolation.","Because $\\sigma_{t_{\\mathrm{target}}}$ is sampled uniformly in detail refinement, treating it as a tunable per-contrast hyperparameter might improve texture retention beyond the reported default; this is a testable extension the paper does not explore."],"forward_implications":["A single noisy acquisition per image is enough to train a denoiser; no clean labels or paired noisy replicates are required, as long as the noise level is known or estimated.","Because the target is the MMSE posterior mean rather than a label-mapped output, C2S generalizes to test data whose SNR is higher than the training labels, a regime where supervised networks trained on averaged labels lose accuracy.","The same loss with $\\sigma_{t_{\\mathrm{target}}}>0$ yields a detail-preserving estimator, giving practitioners a direct trade-off between noise removal and texture retention.","Feeding auxiliary MRI contrasts as conditioning inputs improves denoising of the target contrast, and on M4Raw the multi-contrast variant outperforms every supervised baseline tested.","Noise-level misestimation within $\\pm 50\\%$ changes PSNR by at most about 0.1 dB, so the method works with standard noise estimators as a blind denoiser."],"supporting_citations":[{"why":"Supplies denoising score matching and the posterior-expectation relation between the denoiser and the score function that GDSM extends to the noisy-target regime.","marker":"Vincent (2011)"},{"why":"Ambient score matching with noisy data; GDSM recovers it as the $\\sigma_{t_{\\mathrm{target}}}=0$ special case.","marker":"Daras et al. (2024)"},{"why":"Noisier2Noise, shown to be a fixed-noise-ratio special case of GDSM; provides the single-ratio baseline C2S generalizes.","marker":"Moran et al. (2020)"},{"why":"Noise2Noise, the paired-noisy-measurement self-supervised baseline used in comparisons.","marker":"Lehtinen et al. (2018)"},{"why":"Noise2Self, the J-invariance mask-based baseline; its oversmoothing motivates C2S's non-masking approach.","marker":"Batson & Royer (2019)"},{"why":"Provides the M4Raw low-field multi-contrast, multi-repetition dataset used for real-noise training and higher-SNR test evaluation.","marker":"Lyu et al. (2023)"},{"why":"Provides the fastMRI single-coil knee dataset used for simulated-noise robustness experiments.","marker":"Zbontar et al. (2018)"},{"why":"Supplies the DDPM U-Net backbone with time conditioning that the C2S network builds on.","marker":"Ho et al. (2020)"},{"why":"Supplies the NVC-MSA noise-variance-conditioned attention module used for stable conditioning.","marker":"Hatamizadeh et al. (2023)"},{"why":"Variance-stabilizing transform cited to justify Gaussian approximation when MRI noise departs from Gaussianity.","marker":"Foi (2011)"}],"fun_headline_variants":["MRI denoising without clean labels: score matching wins","Self-supervised MRI denoising rivals supervised methods","Score-based self-supervised MRI denoising beats peers","C2S: self-supervised MRI denoising, no clean images","New algorithm cleans MRI noise using only noisy data"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The inference step evaluates the trained network at $t=t_{\\mathrm{data}}$, but the theorem characterizes the loss minimizer only for $t>t_{\\mathrm{data}}$; the method's clean-image estimate therefore rests on the network extrapolating the conditional expectation to the original noise level, and on the added noise being independent Gaussian so the score identity that defines GDSM actually holds.","fun_headline_variants_meta":{"raw":{"variants":["MRI denoising without clean labels: score matching wins","Self-supervised MRI denoising rivals supervised methods","Score-based self-supervised MRI denoising beats peers","C2S: self-supervised MRI denoising, no clean images","New algorithm cleans MRI noise using only noisy data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000242,"raw_usage":{"total_tokens":1597,"prompt_tokens":1088,"completion_tokens":509,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":704,"completion_tokens_details":{"reasoning_tokens":427}},"tokens_in":704,"tokens_out":509,"duration_ms":4627,"temperature":1.0,"reasoning_tokens":427,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:01:06.201472+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a synthetic dataset with a known Gaussian prior for $X_0$ and known noise level, compute the posterior mean $\\mathbb{E}[X_0\\mid X_{t_{\\mathrm{data}}}]$ by Monte Carlo, train C2S from noisy samples only, and compare the network output at $(X_{t_{\\mathrm{data}}},t_{\\mathrm{data}})$ with that posterior mean; a systematic error that persists when the network is trained only on $t>t_{\\mathrm{data}}$ would show the inference step relies on extrapolation outside the theorem's range.","supporting_citations":[{"cited_title":"Noise2noise: Learning image restoration without clean data","cited_arxiv_id":null,"evidence_quote":"Noise2Noise, the paired-noisy-measurement self-supervised baseline used in comparisons."},{"cited_title":"Noise2self: Blind denoising by self-supervision","cited_arxiv_id":null,"evidence_quote":"Noise2Self, the J-invariance mask-based baseline; its oversmoothing motivates C2S's non-masking approach."},{"cited_title":"M4raw: A multi-contrast, multi-repetition, multi-channel mri k-space dataset for low-field mri research","cited_arxiv_id":null,"evidence_quote":"Provides the M4Raw low-field multi-contrast, multi-repetition dataset used for real-noise training and higher-SNR test evaluation."},{"cited_title":"Noise estimation and removal in mr imaging: The variance-stabilization approach","cited_arxiv_id":null,"evidence_quote":"Variance-stabilizing transform cited to justify Gaussian approximation when MRI noise departs from Gaussianity."}],"review_version":1}