{"id":"3535290f-5c3c-4ab0-98d4-e443c2181f15","arxiv_id":"2501.03430","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A self-supervised diffusion bridge for MRI that trains on undersampled measurements alone and outperforms a self-supervised denoising diffusion baseline on fastMRI.","lead":"SelfDB trains a diffusion-based MRI reconstruction model using only undersampled measurements, with no clean reference images. It creates a training signal by sub-sampling the available measurements two extra times and using those as targets.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reverse update in Algorithm 1 is asserted not derived; the training target may not match the clean endpoint of the forward bridge.","rationale":"I read the paper as claiming that SelfDB trains a diffusion bridge self-supervized from measurements and that its multi-step reverse update is the posterior step of the newly defined forward process. The reader's weakest assumption identifies exactly this point: Algorithm 1 line 11 is asserted to equal E[y_{t-delta}|y_t] but is not derived. I agree with that concern and sharpen it: the training objective in Eq. 12 regresses M A f_theta toward y, while the forward process in Eq. 11 has intermediate measurement M y as its clean endpoint. If the sampling operator in Eq. 12 is the full operator from Eq. 1, then \\hat{y} is being trained to predict the full measurement, not the intermediate measurement that the bridge is supposed to recover. The paper's notation renders both operators as 'M', which obscures this potential mismatch. The empirical results are plausible and the method may well work, but the central mechanism is not yet justified. The proposed oracle test or a retraining test with the corrected loss target would settle whether the reverse update is actually reversing the stated bridge. Since the reader already issued a conditional verdict and my concern is the same one, I recommend keeping the verdict unchanged.","tokens_in":5246,"tokens_out":20626,"duration_ms":180981,"concrete_test":"Run Algorithm 1 with an oracle \\hat{y} = M y (the true intermediate measurement, available during training) in line 11 and compare the resulting y_t trajectory against the forward process of Eq. 11 at matched noise draws; if the update does not reproduce the forward marginals after accounting for the network approximation, line 11 is not the correct posterior step. Alternatively, retrain with the loss target changed to M y (i.e., minimize ||M A f_theta - M y||^2 on the intermediate mask) and check whether Table 1 metrics change materially; if they do, the original loss was not implementing the claimed bridge reversal.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on Algorithm 1 line 11 being the posterior update E[y_{t-delta}|y_t] for the forward process y_t = (1-t) M y + t M' y + sigma_t epsilon (Eq. 11). For this to hold, the quantity \\hat{y} = M A f_theta(y_t,t) must estimate the clean endpoint of the bridge, i.e. the intermediate measurement M y. But the training loss (Eq. 12) minimizes ||M A f_theta(y_t,t) - y||^2 against the original measurement y. Unless M in Eq. 12 is the intermediate sampling operator rather than the full operator from Eq. 1, this loss supervises \\hat{y} toward y, which has support on the full sampling mask, not toward M y. The paper never specifies this distinction, and it provides no derivation connecting the measurement-space regression in Eq. 12 to the conditional expectation required by Eq. 9/Algorithm 1. If the two targets differ, the reverse iteration is not reversing Eq. 11, and the reported gains from small inference steps are heuristic rather than grounded. This is load-bearing because the multi-step refinement is the proposed method's core mechanism.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes SelfDB, a self-supervised training scheme for diffusion bridges in MRI reconstruction. The method defines a new diffusion process in k-space by applying two additional subsampling operators to the available measurements, so that the forward process interpolates between an intermediately subsampled measurement and a more aggressively subsampled measurement. A network is trained without ground-truth images using the available measurement as its own training target; at inference, iterative refinement is performed in measurement space. Experiments on fastMRI brain data report that SelfDB with four inference steps outperforms a conditional ambient-diffusion baseline and an ambient-diffusion diffusion-bridge baseline on NRMSE, SSIM, and LPIPS. The paper also documents a perception-distortion trade-off controlled by the number of inference steps.","tokens_in":5492,"tokens_out":13803,"duration_ms":132216,"significance":"If the theoretical gaps were resolved, the contribution would be practically significant: it would extend the self-supervised paradigm from denoising diffusion models to diffusion bridges, enabling reconstruction without high-quality references and with few inference steps. The paper explicitly targets CS-MRI, where ground-truth images are often unavailable. The strengths are the clear problem statement, the use of an external benchmark with held-out fastMRI data, and the inclusion of both distortion and perceptual metrics with visual comparisons. However, the significance is currently tempered by an unproven reverse-update step and by empirical evidence from a single split without error bars. The contribution is therefore promising but not yet fully established.","major_comments":[{"comment":"There is a load-bearing mismatch between the forward process and the training target. Eq. (11) defines a bridge whose t=0 endpoint is the intermediate measurement \\bar{M} y, while Eq. (12) trains M A f_theta(y_t,t) to match the full measurement y. In Algorithm 1, line 11 uses \\hat{y} = M A f_theta(y_t,t) as the estimate of the bridge endpoint. Unless the same symbol M in Eq. (12) is intended to denote the intermediate operator rather than the original sampling operator from Eq. (1), the network is trained to predict a richer target than the endpoint of Eq. (11). The paper never specifies this distinction or derives the connection between Eq. (12) and the conditional expectation E[y_{t-\\delta}|y_t]. With the current training loss, the iterative update in Algorithm 1 is not reversing Eq. (11). Please either change the forward process to bridge from the full measurement y to M'y, or change the training loss to compare \\bar{M} A f_theta(y_t,t) with \\bar{M} y, and state the chosen convention explicitly.","section":"Section 3, Eqs. (11)-(12) and Algorithm 1"},{"comment":"The simplification M'A x_t = M' y + sigma_t M' A epsilon requires A A^H = I. For the multi-coil forward operator A = F S with ESPIRiT sensitivity maps used in Section 4, A A^H = F S S^H F^H is not the identity, so the last equality in Eq. (10) does not hold. This invalidates the derivation of Ambient-DB and weakens the stated explanation for why Ambient-DB is suboptimal. Please either restrict the claim to settings with orthogonal A or correct the derivation for the multi-coil CS-MRI setting actually used in the experiments.","section":"Section 2.2 and Section 3, Eq. (10)"},{"comment":"All metrics are reported on a single train/validation/test split of fastMRI with no error bars, multiple training runs, or significance tests. The NRMSE gap between SelfDB and C-Ambient-DDM is 0.005 (0.108 versus 0.113), which is small relative to typical run-to-run variability in deep-learning reconstruction. To support the claim of superior performance, please report mean plus/minus standard deviation over at least three independent training runs, or provide a paired statistical test on the test set.","section":"Section 4, Table 1"},{"comment":"The method cannot be reproduced from the manuscript because the noise schedule sigma_t, the inference step size delta, the network architecture, and the training hyperparameters are not specified. Algorithm 1 depends directly on sigma_t and delta, and the reported perception-distortion trade-off in Table 2 depends on the number of inference steps, so these details are essential. Please provide the missing specifications, and ideally release code.","section":"Section 4 and Algorithm 1"}],"minor_comments":[{"comment":"The sampling rates are listed as '25%, 16.6%, and 12.5% as M, M, and M′', which appears to be a typo: the second operator should be a distinct symbol such as \\bar{M} to avoid confusion with the 25% operator.","section":"Section 4, first paragraph"},{"comment":"The phrase 'read arrow' should be 'red arrow'.","section":"Figure 1 caption"},{"comment":"The sentence 'Once a DNN is trained to reverse the this process' contains a typo and should read 'reverse this process'.","section":"Section 2.2, first paragraph"},{"comment":"Reference [16] describes the fastMRI knee dataset, but the experiments use T2-weighted brain data; please cite the appropriate fastMRI brain data source or clarify the relationship.","section":"Section 4, data description"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the paper reads like a short workshop manuscript rather than a full journal article. The main issue is not novelty or scope but internal consistency: the training loss and the forward bridge in the current write-up point to different endpoints, and the reverse update is asserted rather than derived. This is fixable, so I recommend major revision rather than rejection. If the authors can clarify the notation and provide a correct derivation, the contribution has a reasonable chance of being publishable. I also encourage the editor to ask for error bars or additional seeds, since the headline empirical gain is small."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: SelfDB is a real idea—training a diffusion bridge without paired ground truth by defining a bridge between two levels of measurement subsampling. That is a genuine extension of Ambient Diffusion to bridges, and it is not in the papers they cite. The fastMRI results are encouraging; SelfDB beats the conditional ambient diffusion baseline on all three metrics, and the two-step / four-step / eight-step trade-off is a nice observation.\n\nThe soft spots are real but mostly fixable. The reverse update in Algorithm 1 is asserted as E[y_{t-delta}|y_t] without derivation. For the linear Gaussian bridge in Eq. (11), the conditional expectation is standard, but the substitution of the network estimate for the clean endpoint M y is not justified. The stress-test note flags a possible mismatch between the training target and the endpoint; on reading closely, I think the intended M in Eq. (12) is the intermediate mask, so the loss is comparing M A f to y only on the intermediate mask positions, which matches M y. But the notation is genuinely ambiguous—they reuse M for both the original sampling mask and the intermediate mask, and that should be cleaned up. If they intended the full mask, the training would be inconsistent. The absence of a derivation is still a gap.\n\nEq. (10) says A is orthogonal in CS-MRI. That is not true for multi-coil MRI (A = F S, with S the coil sensitivities); A^H A = S^H S, not identity. It does not sink the main method, but it is the kind of mistake that makes a referee worry.\n\nThe evaluation is thin: one fastMRI split, no error bars, no statistical tests, no code. The reported gains are moderate, and without repeat runs or multiple datasets, the \"superior performance\" claim is plausible but not fully established. Also, the paper does not describe the network architecture or how the measurement vector is fed to a U-Net; that matters for reproducibility.\n\nWho is this for? People working on self-supervised learning for inverse problems, and anyone building diffusion bridges for MRI. It is a solid workshop-to-conference piece that, with a proper derivation and stronger evaluation, could become a good journal paper. I would send it to peer review; a serious referee can help tighten the theory and the experimental reporting.\n\nWorth a read. Not yet a fully supported central claim, but a promising line.","headline":"A clever self-supervised extension of diffusion bridges to measurement-only training, but the reverse update is asserted rather than derived and the evaluation is too thin to fully back the performance claim.","tokens_in":5983,"tokens_out":4892,"would_cite":false,"duration_ms":43413,"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":"SelfDB trains a diffusion bridge for MRI reconstruction without clean references, beating ambient diffusion in few steps.","keywords":["diffusion bridge","self-supervised learning","MRI reconstruction","compressed sensing MRI","inverse problems","diffusion models","ambient diffusion","subsampling"],"falsifier":"Compare one step of Algorithm 1 against the exact conditional expectation $\\mathbb{E}[y_{t-\\delta}\\mid y_t]$ computed by Monte Carlo under the process in Eq. (11) with the same fitted network; if the update deviates systematically from that expectation as $\\delta \\to 0$, the claimed posterior step is not the one being simulated.","tokens_in":1619,"feed_emoji":"🧲","tokens_out":2412,"duration_ms":135197,"temperature":0.7,"pith_summary":"The paper proposes SelfDB, a training scheme that lets a diffusion bridge for image reconstruction be learned when no clean ground-truth images exist. Diffusion bridges normally interpolate between a clean image and its measurement, which requires paired reference images; SelfDB instead builds the bridge directly on the available measurements by sub-sampling them twice. The diffusion process runs from moderately sub-sampled data at $t=0$ to more severely sub-sampled data at $t=1$, and a network is trained, using only the raw measurements as targets, to reverse this degradation. On brain MRI undersampled to 25%, four inference steps reach NRMSE 0.108, SSIM 0.882, and LPIPS 0.036, beating a conditional ambient-diffusion baseline on all three metrics. The practical reason to care is that fast reconstruction with very few steps becomes available in settings where clean references are not routinely collected.","feed_headline":"Diffusion bridge learns MRI reconstruction from raw measurements alone","feed_subtitle":"It sub-samples scans twice, treats the raw measurements as targets, and beats an ambient-diffusion baseline in four steps.","key_machinery":"The load-bearing object is the two-operator subsampled-measurement diffusion process $y_t = (1-t)\\bar M y + t M' y + \\sigma_t \\epsilon$, where a diffusion bridge means a diffusion process built to interpolate between two paired distributions. This process replaces a failed direct adaptation in which applying the ambient-diffusion operator to a bridge state gives $y_t \\approx M'y$ for every $t$, leaving no actual transition to learn; by inserting an intermediate subsampling level, SelfDB creates endpoints that differ and a reverse process that adds information instead of repeatedly solving the same inverse problem. The reverse update in Algorithm 1, patterned on the diffusion-bridge posterior step, uses the network output $\\hat x = f_\\theta(y_t,t)$ through $M A \\hat x$ as a stand-in for the missing measurement, and the training loss in (12) ties that prediction back to the observed $y$.","core_discovery":"On its own terms, the paper's discovery is that a diffusion bridge can be trained self-supervised by making the bridge process a transition between two levels of undersampling of the measured data. Given a measurement $y = MAx + e$, SelfDB introduces two extra subsampling operators, an intermediate $\\bar M$ and a severe $M'$, and defines $y_t = (1-t)\\bar M y + t M' y + \\sigma_t \\epsilon$. Because the two endpoints are different sub-sampled copies of the same measurement rather than an image and Gaussian noise, reversing the process gradually fills in missing k-space information. The network $f_\\theta(y_t,t)$ is trained with the loss $\\mathbb{E}\\|M A f_\\theta(y_t,t)-y\\|_2^2$, and inference iterates the posterior-style update $y_{t-\\delta} = \\frac{\\delta}{t} M A \\hat x + (1-\\frac{\\delta}{t}) y_t + (t-\\delta)\\sqrt{\\sigma_{t-\\delta}^2-\\sigma_t^2}\\,\\epsilon$ with $\\hat x = f_\\theta(y_t,t)$. The paper reports that this measurement-only training outperforms a conditional ambient-diffusion model at four inference steps on brain MRI.","pith_inferences":["A natural test the authors did not run is a comparison against a supervised diffusion bridge with the same architecture; the gap would quantify how much accuracy is traded for removing the need for references.","If the reverse update in Algorithm 1 were replaced by an exactly derived posterior step, SelfDB could in principle extend to non-orthogonal forward operators, such as general CT line-integral models, where the current nested-subsampling identity does not hold.","The observed perception-distortion trend suggests SelfDB could be used as a tunable sampler, with the step count chosen according to whether the downstream task rewards fidelity or human-reader quality."],"forward_implications":["Diffusion bridges no longer require paired clean references, so the method can be trained in settings where only routine undersampled acquisitions are stored.","The few-step speed advantage claimed for supervised diffusion bridges carries over to self-supervised training: four inference steps outperform the conditional ambient-diffusion baseline on NRMSE, SSIM, and LPIPS.","The number of inference steps acts as a tunable perception-distortion knob: two steps give NRMSE 0.101 and LPIPS 0.039, while eight steps give NRMSE 0.118 and LPIPS 0.035.","Because the construction is stated for orthogonal forward operators and nested subsampling, the same argument transfers to other linear inverse problems with that structure."],"supporting_citations":[{"why":"Supplies the diffusion-bridge reverse iteration and posterior-step formula that SelfDB's update line 11 is patterned on.","marker":"[10]"},{"why":"Provides the ambient-diffusion training-loss idea of using further-subsampled measurements as training targets, which SelfDB adapts to bridges.","marker":"[14]"},{"why":"Motivates the claim that direct diffusion bridges need fewer inference steps than denoising diffusion models.","marker":"[9]"},{"why":"Defines the denoising diffusion model baseline and its reverse-sampling iteration used for the conditional ambient-diffusion comparison.","marker":"[6]"},{"why":"Provides the public brain MRI data from which the undersampled measurements and test references are drawn.","marker":"[16]"},{"why":"Supplies the coil-sensitivity estimation used to build the forward measurement operator in the experiments.","marker":"[17]"}],"fun_headline_variants":["Self-supervised diffusion bridge reconstructs MRI without reference images","MRI reconstruction from raw measurements alone using a diffusion bridge","Diffusion bridge trained on noisy MRI measurements beats unsupervised baseline","SelfDB: self-supervised diffusion bridge for MRI without clean references","Diffusion bridge learns MRI from undersampled data, no ground truth needed"],"cache_read_input_tokens":8192,"weakest_assumption_plain":"The iterative refinement works only if the network's measurement-domain prediction is an accurate enough stand-in for the unmeasured clean data inside the reverse update; the paper does not prove that this substitution is the true conditional expectation.","fun_headline_variants_meta":{"raw":{"variants":["Self-supervised diffusion bridge reconstructs MRI without reference images","MRI reconstruction from raw measurements alone using a diffusion bridge","Diffusion bridge trained on noisy MRI measurements beats unsupervised baseline","SelfDB: self-supervised diffusion bridge for MRI without clean references","Diffusion bridge learns MRI from undersampled data, no ground truth needed"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000167,"raw_usage":{"total_tokens":1241,"prompt_tokens":914,"completion_tokens":327,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":530,"completion_tokens_details":{"reasoning_tokens":241}},"tokens_in":530,"tokens_out":327,"duration_ms":4232,"temperature":1.0,"reasoning_tokens":241,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:52:56.833673+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare one step of Algorithm 1 against the exact conditional expectation $\\mathbb{E}[y_{t-\\delta}\\mid y_t]$ computed by Monte Carlo under the process in Eq. (11) with the same fitted network; if the update deviates systematically from that expectation as $\\delta \\to 0$, the claimed posterior step is not the one being simulated.","supporting_citations":[{"cited_title":"Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration,","cited_arxiv_id":null,"evidence_quote":"Supplies the diffusion-bridge reverse iteration and posterior-step formula that SelfDB's update line 11 is patterned on."},{"cited_title":"Ambient diffusion: Learning clean distributions from corrupted data,","cited_arxiv_id":null,"evidence_quote":"Provides the ambient-diffusion training-loss idea of using further-subsampled measurements as training targets, which SelfDB adapts to bridges."},{"cited_title":"Direct Diffusion Bridge using Data Consistency for Inverse Problems,","cited_arxiv_id":null,"evidence_quote":"Motivates the claim that direct diffusion bridges need fewer inference steps than denoising diffusion models."},{"cited_title":"Denoising Diffusion Probabilistic Models,","cited_arxiv_id":null,"evidence_quote":"Defines the denoising diffusion model baseline and its reverse-sampling iteration used for the conditional ambient-diffusion comparison."},{"cited_title":"fastMRI: A publicly available raw k-space and DICOM dataset of knee images for accelerated MR image reconstruction using machine learning,","cited_arxiv_id":null,"evidence_quote":"Provides the public brain MRI data from which the undersampled measurements and test references are drawn."},{"cited_title":"ESPIRiT-an eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA,","cited_arxiv_id":null,"evidence_quote":"Supplies the coil-sensitivity estimation used to build the forward measurement operator in the experiments."}],"review_version":1}