{"id":"61cc444c-5139-4f11-ad2c-4c91db2836b4","arxiv_id":"2412.04339","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A likelihood-scheduled diffusion method reconstructs low-count PET images by matching the reverse-diffusion likelihood to a precomputed MLEM schedule, reducing hyperparameters and enabling real 3D reconstruction.","lead":"This paper introduces a way to use pre-trained AI image generators for PET scan reconstruction, replacing several hard-to-tune settings with a single schedule derived from a standard algorithm. It reports matching or better image quality than prior diffusion-based methods with faster reconstruction, and shows the first fully 3D reconstruction from real PET data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The method enforces only a scalar Poisson log-likelihood at each diffusion step; since the log-likelihood is degenerate (Sec. IV-A), this does not establish full sinogram consistency or posterior sampling, so the central practical claim rests on an unvalidated constraint.","rationale":"I agree with the reader's conditional verdict and with the identification of the scalar-PLL constraint as the weakest assumption. The empirical 2D results in Table I and the hyperparameter-stability experiments in Section VI-C provide credible support for the practical claim that the method can match PET-DDS while reducing tuning burden. However, the posterior-sampling interpretation and the sufficiency of a scalar likelihood constraint are not established, and the manuscript's own admission of PLL degeneracy makes this a structural concern rather than a mere implementation detail. The proposed residual check would directly test whether enforcing equal total PLL also produces data-consistent images. This does not change the verdict: the paper should remain CONDITIONAL, with the condition being that the scalar-PLL mechanism is validated against full sinogram consistency before the posterior-sampling claim is accepted.","tokens_in":14874,"tokens_out":4887,"duration_ms":55452,"concrete_test":"Recompute the 2D comparison of Section VI-A adding a per-realization normalized sinogram residual ||A x - m||_2 / ||m||_2 for Ours, PET-DDS, and MLEM at matched PLL. If Ours has substantially larger residual than PET-DDS or MLEM despite equal scalar PLL, the equal-likelihood constraint is leaving real data misfit; if residuals are comparable, the degeneracy concern is not empirically damaging.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing step is in Sec. IV-A/IV-B. The stated goal is to \"sample x such that x ~ D and L(x|m) = c\", and the algorithm enforces this by gradient ascent on Tweedie's estimate until the scalar PLL exceeds a schedule derived from MLEM. But the paper itself notes in Sec. IV-A that the PLL is degenerate: a whole manifold of images has equal likelihood. Matching one scalar therefore conditions on a summary statistic, not on the measured sinogram; images with equal total PLL can have very different per-detector residuals and clinically important features. The stronger claim that the method \"provides samples from the posterior distribution ... conditioned on both a likelihood value and noisy measured data\" is asserted rather than derived: no argument connects the gradient-ascent trajectory to p(x|m, L=c) or p(x|m). The 2D numerical gains in Table I show the constraint is practically useful, but they do not validate the mechanism; a method that hits the PLL target while violating detailed consistency could still pass Table I yet fail on lesions or in out-of-distribution settings. The MLEM-derived c is also heuristic: it is the log-likelihood of an early-stopped MLEM image, and the paper's own Fig. 14 shows that for large N_MLEM the target is not reachable on the SGM's image manifold, producing excess variance.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript proposes a likelihood-scheduled score-based generative modeling method for PET image reconstruction. The method first runs MLEM on the measured sinogram to produce a scalar Poisson log-likelihood schedule, then interleaves DDIM-style reverse diffusion steps with gradient ascent on Tweedie's estimate so that the reconstructed image's PLL matches the schedule value at each generative step. The authors compare the method with PET-DDS, OSEM, MAP-EM, and two FBSEM-net variants on simulated 2D [18F]DPA-714 data, reporting NRMSE, SSIM, and reconstruction times, and they demonstrate 3D reconstruction on real [18F]DPA-714 data using three perpendicular pre-trained 2D SGMs. The central practical claims are that the method matches or improves on PET-DDS's NRMSE/SSIM while reducing reconstruction time and the number of critical hyperparameters, and that it gives the first SGM-based fully 3D PET reconstruction from real data.","tokens_in":15175,"tokens_out":5892,"duration_ms":64555,"significance":"If the practical claims hold, this is a valuable contribution to unsupervised SGM-based PET reconstruction: it replaces several per-step likelihood hyperparameters with a single MLEM-iteration knob, makes 3D reconstruction tractable, and removes the axial slice-inconsistency artifacts of prior 3D approaches. The strengths of the paper include a real 3D data demonstration, perpendicular score averaging across sagittal, coronal, and transverse slices, robustness studies over the number of generative steps and the gradient step size, lesion recovery experiments, bias-variance and likelihood-variance assessments, and the use of a public forward projector. The main 2D comparison against PET-DDS in Table I and Fig. 4 is credible and supports parity or mild improvement. However, the paper's theoretical framing as posterior sampling conditioned on a likelihood value is not established: the algorithm enforces only a scalar Poisson log-likelihood, which is degenerate and does not by itself condition on the full measured sinogram.","major_comments":[{"comment":"The problem formulation in Eq. (9), \"Sample x such that x~D and L(x|m)=c\", is asserted rather than derived as a posterior sampling scheme, yet the Introduction and Discussion claim that the method \"provides samples from the posterior distribution of image reconstruction conditioned on both a likelihood value and noisy measured data.\" The algorithm enforces only the scalar PLL, and Section IV-A itself notes that the PLL is degenerate, so a whole manifold of images with different per-detector residuals share the same likelihood value. No argument connects the gradient-ascent trajectory on Tweedie's estimate to p(x|m, L=c) or p(x|m). The empirical gains in Table I show practical utility but do not validate the mechanism. Please either provide a formal derivation of the posterior-sampling claim or restate the contribution as constrained sampling from the learned prior at a prescribed scalar likelihood value.","section":"Section IV-A/IV-B, Eq. (9)"},{"comment":"The MLEM-derived target likelihood c is not guaranteed to be reachable by the SGM's image manifold. Fig. 14 shows that for N_MLEM > 36 the coefficient of variation of the proposed method exceeds that of MLEM, and the text attributes this to the absence of images with such high likelihood on the SGM's manifold. This is an acknowledged failure mode of the central tuning parameter N_MLEM. The paper should characterize the admissible range of N_MLEM or propose a reachability criterion; otherwise the claim that N_MLEM is a single intuitive knob that can be set to a clinically standard MLEM iteration count is incomplete.","section":"Section VI-H.2, Fig. 14"},{"comment":"The \"reduced hyperparameter tuning burden\" claim is supported structurally by the reduction to N_MLEM and N_gen and by the robustness to N_gen and delta shown in Figs. 5 and 6, but the quantitative comparisons still select N_MLEM by a validation sweep to minimize NRMSE, just as the PET-DDS hyperparameters are swept. Since N_MLEM controls the prior-likelihood balance, and the paper does not validate setting it a priori to the clinically used number of MLEM iterations, the tuning-burden advantage is weaker than stated. A fixed-N_MLEM experiment, for example using N_MLEM equal to the vendor-recommended OSEM iteration count, would materially strengthen the claim.","section":"Section V-F, Table I, Figs. 4 and 10"}],"minor_comments":[{"comment":"The notation \"x ~ D\" is informal; please define D explicitly as the learned image distribution and clarify the relationship between D and the SGM's marginal densities p_t(x_t).","section":"Section IV-A, Eq. (9)"},{"comment":"The caption reports 2.7×10^5 counts while Section V-D states an average of 3.14×10^5 counts per reconstructed slice; please reconcile these numbers or explain the difference.","section":"Fig. 12 caption vs. Section V-D"},{"comment":"The caption states that all columns except \"Clinical\" match the PLL corresponding to 21 iterations of MLEM, but PET-DDS does not use a likelihood schedule; please specify how PET-DDS was made to match this PLL value.","section":"Fig. 13 caption"},{"comment":"For the real 3D data there is no ground truth; the text refers to a \"ground truth\" when selecting a white-matter region, but this should be called a full-count clinical reference image to avoid ambiguity.","section":"Section VI-H.2"},{"comment":"The phrase \"first methodology to investigate possible reconstructions for a fixed likelihood\" should be qualified as \"to our knowledge\" and should specify \"at a fixed scalar likelihood,\" in light of the degeneracy discussion in Section IV-A.","section":"Section VII"}],"recommendation":"major_revision","confidential_remarks":"The manuscript header indicates it has already been accepted by IEEE TMI; my recommendation should be read as guidance for a revision, correction, or erratum rather than as a gatekeeping decision. The practical reconstruction results are solid and the 3D real-data demonstration is a genuine advance, but the posterior-sampling language in the Introduction and Discussion overstates what a scalar likelihood constraint delivers, and the unreachable-target behavior in Fig. 14 deserves a more prominent and complete treatment."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the likelihood-scheduling idea is genuinely new: instead of tuning a likelihood weight by hand, they run MLEM to get a target log-likelihood curve and enforce that target at each reverse-diffusion step, so the only critical knob left is N_MLEM. That is a real practical contribution for PET. Second, the real 3D demonstration with perpendicular SGMs is a step forward, but the 'first-ever' claim should be read against their own 2024 NSS/MIC conference paper [14]; it is not a clean first.\n\nWhat the paper does well: the 2D comparison to PET-DDS is fair and quantitative. Table I, the bias-variance curves, hyperparameter stability, and lesion CRC all support the claim that the method matches PET-DDS while reducing reconstruction time and tuning burden. The 3D timing table is also useful. They state limitations honestly: hallucinations, unreachable high-likelihood targets in Fig. 14, and the heuristic nature of the schedule.\n\nThe soft spot is the one the stress-test flags, and it is real. Equation (9) poses \"sample x such that x ~ D and L(x|m) = c\", but they never derive gradient ascent on Tweedie's estimate as a way to sample from p(x|m, L=c) or p(x|m). The Poisson log-likelihood is degenerate, so matching a scalar does not enforce per-detector consistency; images with equal total PLL can be clinically different. The paper's own Sec. IV-A acknowledges this manifold. That does not sink the practical contribution, since Table I shows the constraint is useful, but it does mean the posterior-sampling language overclaims. I would treat the method as a heuristic that works empirically, not as a proven conditional sampler.\n\nOther soft spots, in proportion: the 3D evidence is largely qualitative, based on one sample per reconstruction with no uncertainty intervals, and no code or data are provided for the headline 3D result. The MLEM-derived c is partly circular by design, but the independent metrics like NRMSE, SSIM, and lesion CRC are not.\n\nWho gets value: anyone working on unsupervised diffusion-based PET reconstruction, and the scheduling trick could transfer to other modalities. The paper is rigorous enough to deserve a serious referee. I would engage with it, but ask the authors to soften the posterior-sampling claim and release the 3D code and data.","headline":"A practical, well-tested diffusion-PET method whose 'posterior sampling' framing is heuristic; the 2D evidence is solid, the real-3D claim needs qualification.","tokens_in":15731,"tokens_out":2258,"would_cite":true,"duration_ms":22424,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["87.57.nj"],"model":"deepseek-v4-flash","headline":"A likelihood schedule from MLEM guides a pretrained diffusion prior, making fully 3D PET reconstruction practical with a single critical hyperparameter.","keywords":["score-based generative modeling","PET image reconstruction","likelihood scheduling","MLEM","DDIM sampling","fully 3D reconstruction","slice consistency","low-count PET"],"falsifier":"Insert a known lesion into a phantom, reconstruct from low-count sinograms at a fixed likelihood schedule, and compare lesion contrast in the sampled images with lesion contrast in the MLEM images used to set the schedule; if the sampled images fit the likelihood but systematically lose or displace the lesion while MLEM recovers it, the scalar-likelihood conditioning is insufficient.","tokens_in":1579,"feed_emoji":"🧠","tokens_out":1588,"duration_ms":65683,"temperature":0.7,"pith_summary":"The paper proposes a way to inject a pre-trained score-based generative model—an image prior learned from high-quality scans—into PET reconstruction while keeping only one critical tuning knob. Instead of balancing prior and data terms with several regularization weights, it first runs MLEM to record a 'likelihood schedule' of Poisson log-likelihood values, then guides the reverse diffusion process to match that schedule at every denoising step. On simulated low-count [18F]DPA-714 data, the method matches or improves the NRMSE and SSIM of the previous state-of-the-art SGM method while using far fewer likelihood updates and less tuning. It also extends to real fully 3D PET data for the first time, using three perpendicular pre-trained 2D SGMs to remove the slice-inconsistency artifacts of single-plane SGM reconstruction.","feed_headline":"One knob steers diffusion-based 3D PET reconstruction","feed_subtitle":"An MLEM likelihood schedule replaces four regularization knobs and enables the first real 3D PET reconstructions with score-based priors.","key_machinery":"The mechanism is the likelihood schedule: a sequence of scalar Poisson log-likelihood values obtained by running MLEM and interpolating its per-iteration likelihoods across the diffusion time steps. At each reverse-diffusion step, the algorithm takes one Tweedie denoising step, the estimate of the clean image from the noisy iterate, then performs gradient ascent on the Poisson log-likelihood until the estimate reaches the scheduled value, and finally re-adds noise via the DDIM update. The schedule replaces the multiple regularization hyperparameters of earlier methods: the MLEM iteration count sets the balance between prior and data, leaving only the number of diffusion steps and a step-size parameter that controls schedule accuracy rather than prior-likelihood balance.","core_discovery":"The central claim is that a PET reconstruction can be sampled from a learned image distribution conditioned on a chosen level of data consistency, rather than on a tuned balance of regularization weights. The authors define the target as 'sample $x$ such that $x$ is drawn from the learned distribution and $L(x|m)=c$', with $c$ fixed by a clinically relevant MLEM iterate, and they solve it by following a precomputed Poisson log-likelihood schedule during DDIM-style reverse diffusion. They report that this likelihood-scheduled method matches or improves on PET-DDS, the prior SGM-based PET method, in NRMSE and SSIM, while cutting reconstruction time and lowering the critical hyperparameter count from four to one, the MLEM iteration count. They further report the first SGM-based reconstruction of real fully 3D PET data, using perpendicular pre-trained 2D SGMs whose score estimates are averaged so that no axial regularization prior is needed and slice inconsistency is eliminated.","pith_inferences":["A consequence the authors do not develop is that scalar-likelihood conditioning is weaker than full sinogram consistency; if the equal-likelihood manifold contains anatomically wrong images, samples at the MLEM likelihood value could be confidently wrong, and lesion-insertion phantoms across a range of MLEM iteration counts would test this.","The scheduling concept generalizes beyond likelihood: the same mechanism could schedule other scalar clinical objectives, such as a region-of-interest uptake constraint, without adding hyperparameters.","The paper notes that hyperparameter tuning could be removed entirely by using bootstrap estimates of the optimal MLEM iteration, which would make the method fully automatic given a pretrained SGM.","Because the score prior is fixed and the schedule is recomputed from the measured data, the approach may transfer across scanners with different forward models, a testable extension the paper does not explicitly run."],"forward_implications":["Clinicians can set the main hyperparameter, the MLEM iteration count, to a vendor-recommended clinical value, bringing diffusion priors into reconstruction at a familiar operating point.","Because samples are drawn at the same data-consistency level as MLEM, the spread among sampled reconstructions provides uncertainty information for a fixed clinical likelihood.","Averaging scores from three perpendicular pre-trained 2D SGMs removes axial slice inconsistency without the blurring effect of an axial regularization prior.","Dynamic likelihood steps reduce compute: fewer gradient updates are spent early and late in diffusion, with reported 2D reconstruction time of 13 seconds versus 35 seconds for the prior SGM method.","The likelihood-scheduling idea transfers to other imaging modalities that combine model-based iterative steps with pre-trained SGMs, as the paper itself notes."],"supporting_citations":[{"why":"Supplies the PET-DDS baseline, the SGM architecture, and the measurement-normalization procedure that the proposed method adapts.","marker":"[12]"},{"why":"Introduces perpendicular pre-trained 2D diffusion models, which the paper adapts by averaging the scores from three orientations.","marker":"[16]"},{"why":"The MLEM algorithm whose per-iteration likelihoods form the schedule and whose iterate sets the target likelihood value.","marker":"[17]"},{"why":"The FBSEM-net supervised reconstruction baseline that the method is compared against in 2D.","marker":"[5]"},{"why":"The ParallelProj projector used as the forward operator in all reconstructions.","marker":"[33]"},{"why":"The DDIM sampling rule that the reverse diffusion updates build on.","marker":"[24]"}],"fun_headline_variants":["Likelihood schedule slashes PET tuning to one knob","First real 3D PET with score-based priors","MLEM-matched diffusion cuts PET reconstruction knobs","Slice-consistent 3D PET from one diffusion knob","One knob, no slice inconsistency in 3D PET"],"cache_read_input_tokens":17792,"weakest_assumption_plain":"The method assumes that forcing each reconstruction to have the same scalar data-fit value as an MLEM image, without enforcing point-by-point agreement with the measured sinogram, is enough to keep the reconstruction faithful—and that the MLEM likelihood value is a sensible target.","fun_headline_variants_meta":{"raw":{"variants":["Likelihood schedule slashes PET tuning to one knob","First real 3D PET with score-based priors","MLEM-matched diffusion cuts PET reconstruction knobs","Slice-consistent 3D PET from one diffusion knob","One knob, no slice inconsistency in 3D PET"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001071,"raw_usage":{"total_tokens":4519,"prompt_tokens":1011,"completion_tokens":3508,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":627,"completion_tokens_details":{"reasoning_tokens":3429}},"tokens_in":627,"tokens_out":3508,"duration_ms":27767,"temperature":1.0,"reasoning_tokens":3429,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:31:26.325957+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Insert a known lesion into a phantom, reconstruct from low-count sinograms at a fixed likelihood schedule, and compare lesion contrast in the sampled images with lesion contrast in the MLEM images used to set the schedule; if the sampled images fit the likelihood but systematically lose or displace the lesion while MLEM recovers it, the scalar-likelihood conditioning is insufficient.","supporting_citations":[{"cited_title":"Score-Based Generative Modeling through Stochastic Differential Equations,","cited_arxiv_id":null,"evidence_quote":"The DDIM sampling rule that the reverse diffusion updates build on."},{"cited_title":"Score-Based Generative Models for PET Image Reconstruction,","cited_arxiv_id":null,"evidence_quote":"Supplies the PET-DDS baseline, the SGM architecture, and the measurement-normalization procedure that the proposed method adapts."},{"cited_title":"Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Models,","cited_arxiv_id":null,"evidence_quote":"Introduces perpendicular pre-trained 2D diffusion models, which the paper adapts by averaging the scores from three orientations."},{"cited_title":"Maximum Likelihood Reconstruction for Emission Tomography,","cited_arxiv_id":null,"evidence_quote":"The MLEM algorithm whose per-iteration likelihoods form the schedule and whose iterate sets the target likelihood value."},{"cited_title":"Model-Based Deep Learning PET Image Reconstruction Using Forward-Backward Splitting Expectation- Maximization,","cited_arxiv_id":null,"evidence_quote":"The FBSEM-net supervised reconstruction baseline that the method is compared against in 2D."},{"cited_title":"PARALLELPROJ—an open-source framework for fast calculation of projections in tomography,","cited_arxiv_id":null,"evidence_quote":"The ParallelProj projector used as the forward operator in all reconstructions."}],"review_version":1}