{"id":"153b6397-66d4-4fea-81bc-bd0563de44fa","arxiv_id":"2506.16733","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A prior-guided joint diffusion model converts FDG PET sinograms into DOPA PET sinograms by combining a supervised coarse stage with an unsupervised refinement stage.","lead":"This paper describes a two-stage diffusion model that converts FDG PET scans into DOPA PET scans using raw projection data, called sinograms. The goal is to obtain DOPA-like imaging information without needing the difficult-to-produce DOPA radiotracer.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Stage II refinement is trained on degraded real DOPA sinograms but applied to degraded Stage-I outputs; the resulting train/inference condition mismatch is the key unvalidated assumption behind the two-stage improvement claim.","rationale":"The reader's weakest_assumption identifies exactly this load-bearing point, and I agree with it. The concern is not that the mathematics is wrong; the bridge SDE in Eqs. (1)-(3) and the DDPM-style refinement in Eqs. (8)-(13) are standard machinery. The issue is an empirical distribution-shift between the training and inference conditions of the refinement stage, which directly threatens the claimed benefit of adding Stage II. A clean oracle-condition experiment would settle whether the refinement model can actually correct Stage-I errors or merely works when conditioned on real DOPA-like data. Since the paper also reports no error bars and no explicit patient-level split guarantee, this concern strengthens the case for a CONDITIONAL verdict rather than acceptance, but it does not warrant rejection without the proposed test. Availability of code is a positive, but it does not resolve the distribution-mismatch question.","tokens_in":14783,"tokens_out":4074,"duration_ms":48937,"concrete_test":"On the 141-case test set (or a held-out paired subset), run Stage II under three protocols with all else identical: (A) condition d = R(x_0) using the ground-truth DOPA sinogram (oracle condition), (B) condition d = R(x̂_0) with Stage-I output (current inference), and (C) no Stage II (Stage I alone). Report PSNR/SSIM/NRMSE for A, B, and C. If B is materially worse than A (e.g., PSNR drop > 0.5 dB) or B does not beat C, the claimed refinement benefit is condition-distribution-dependent and the two-stage advantage is not established. Additionally, report a two-sample distance (e.g., FID or MMD) between {R(x_0)} and {R(x̂_0)} on the same test set to quantify the mismatch.","verdict_should_be":"UNCHANGED","load_bearing_attack":"PJDM's central two-stage claim (Table II: CE+PR improves over CE alone, PSNR 24.98 vs 24.25, SSIM 0.812 vs 0.751) requires that the prior-refinement model genuinely improves coarse Stage-I outputs at inference. But Eqs. (9)-(10) train Stage II on pairs (x_t, R(x_0)) with x_0 drawn from the real DOPA sinogram distribution, learning p(x_{t-1}|x_t, R(x_0)). During inference (Algorithm 1, Stage II), both the noisy input x_t and the conditioning signal d = R(x̂_0) are derived from x̂_0 = CE(FDG), a Stage-I synthetic DOPA sinogram. Nothing in the training objective or architecture enforces that R(x̂_0) lies in the training condition distribution. If Stage-I outputs are biased or off-manifold, the refinement model is evaluated out-of-distribution, and the reported gain may reflect regression to a learned average rather than genuine detail restoration. The paper provides no analysis of the distance between {R(x_0)} and {R(CE(fdg))}, and does not expose Stage II to synthetic conditions during training, so the two-stage improvement claim currently rests on an untested distributional assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a prior-guided joint diffusion model (PJDM) for converting 18F-FDG PET sinograms into 18F-DOPA PET sinograms. The method has two stages: a supervised diffusion bridge model (built on DDBM) performs a coarse FDG-to-DOPA conversion using a higher-order hybrid sampler; a second, \"prior refinement\" stage uses a DDPM conditioned on a degraded (blurred and contrast/brightness-perturbed) version of the Stage-I output to refine the sinogram. Experiments on a dataset of 196 PD patients, with 2,643 paired FDG/DOPA scans and 3,877 unpaired DOPA scans for training and 141 paired test scans from an all-digital PET system, report that PJDM achieves PSNR 24.98 dB, SSIM 0.812, and NRMSE 0.064, outperforming U-Net, CycleGAN, Pix2Pix, and cold diffusion. An ablation study (Table II) shows that combining coarse estimation (CE) and prior refinement (PR) improves PSNR from 24.25 to 24.98 and SSIM from 0.751 to 0.812 compared to CE alone.","tokens_in":1622,"tokens_out":1871,"duration_ms":57446,"significance":"If the reported results are robust, the paper addresses a clinically meaningful problem: generating DOPA-equivalent PET data from widely available FDG scans, motivated by the complex synthesis and short half-life of 18F-DOPA. The projection-domain modeling choice is sensible for PET data, and the two-stage supervised-plus-unsupervised design is a plausible way to reduce the need for large paired datasets. The authors provide a public code repository, which supports reproducibility. However, the evidence for the central two-stage improvement claim rests on an unvalidated distributional assumption in the refinement stage and on metric averages without error bars or significance tests. The contribution is incremental and potentially useful to the PET imaging community, but the findings are not yet convincingly established.","major_comments":[{"comment":"The prior refinement model is trained with the condition d = R(x_0) where x_0 is drawn from the real DOPA sinogram distribution, but at inference the condition is d = R(CE(FDG)), where CE(FDG) is a synthetic DOPA sinogram produced by Stage I. The paper provides no evidence that R(CE(FDG)) lies in the training condition distribution, and no ablation that trains or evaluates Stage II on synthetic conditions. Since Table II attributes a PSNR gain of 0.73 dB and an SSIM gain of 0.061 specifically to the CE+PR combination, this train/inference mismatch is load-bearing for the main claim. Please add a quantitative comparison of the two condition distributions (e.g., distribution distances or per-pixel statistics) and an ablation in which Stage II is exposed to synthetic conditions during training, or otherwise justify that the mismatch is negligible.","section":"Section III-C, Eqs. (9)-(13) and Algorithm 1"},{"comment":"All reported metrics are single averages without error bars, standard deviations, or statistical significance tests. The key improvements—PJDM over CD (PSNR +1.12 dB, SSIM +0.059) and CE+PR over CE alone (PSNR +0.73 dB, SSIM +0.061)—may be within intersubject variability. Please report per-patient or per-scan results with variance, run paired significance tests (e.g., Wilcoxon signed-rank) between methods, and provide confidence intervals for the mean metrics in Tables I and II.","section":"Section IV-D, Tables I and II"},{"comment":"The data description does not state whether the 141 paired test scans are from patients disjoint from the 196 patients used to construct the training/refinement sets. If the test set is not patient-disjoint, the results are optimistically biased. The test set is also identified as coming from an all-digital PET system (Brain PET B320), but the scanner provenance of the training scans is not reported. Please clarify the patient-level and scanner-level split, and assess whether a domain shift between training and test scanners affects the comparison.","section":"Section IV-A"}],"minor_comments":[{"comment":"After Eq. (4), the text says the supervised training performs \"the initial modality conversion from 18F-DOPA sinograms to 18F-FDG sinograms,\" which is the reverse of the stated task (FDG-to-DOPA); please correct the direction throughout.","section":"Section III-B"},{"comment":"In the submitted version, several equations (e.g., Eqs. (1)-(7) and (14)-(16)) appear garbled or mis-rendered, making it impossible to verify the exact definitions and indices. Please ensure the final camera-ready version typesets all equations cleanly.","section":"Equations generally"},{"comment":"The paper refers to the neural network output as noise prediction (epsilon) in Eq. (10), but Eq. (13) uses this output in a manner that mixes epsilon- and x_0-prediction notation. Please state explicitly which parameterization is used for the prior refinement model.","section":"Section III-C, Eq. (13)"},{"comment":"The discretization of the coarse estimation sampler, including the role of the step-ratio parameter m and the Heun step, is not defined unambiguously in the pseudocode; a table of symbols or a more explicit time-stepping description would improve reproducibility.","section":"Algorithm 1"},{"comment":"The claims that PJDM's profile lines are \"closest to the ground truth\" are made qualitatively; please report a quantitative discrepancy metric (e.g., mean absolute error along the profile) to support these statements.","section":"Fig. 8 and Fig. 11"},{"comment":"The ablation shows that PR alone achieves PSNR 22.87, notably worse than CE alone (24.25), yet the narrative only emphasizes that CE+PR is best; a brief discussion of why PR alone underperforms would make the two-stage mechanism more interpretable.","section":"Table II"}],"recommendation":"major_revision","confidential_remarks":"The paper fits the scope of the journal and provides a public code repository, which is commendable. However, the primary technical concern—the mismatch between the Stage II training condition distribution and the inference-time synthetic condition—needs to be addressed with additional analysis or training changes. The authors should also investigate the patient-level split of the test set and report statistical significance. If those issues are resolved, the paper could become acceptable, but in its current form the central two-stage improvement claim is not fully supported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a look. The genuinely new piece is doing FDG-to-DOPA conversion directly in the projection domain, with a two-stage cascade: a supervised diffusion bridge (DDBM-style) that maps FDG sinograms to a coarse DOPA estimate, and an unsupervised DDPM trained on real DOPA sinograms that refines that estimate using a degraded version of it as a condition. The code is released and the baseline comparisons are reasonable. The reported gains over U-Net, CycleGAN, Pix2Pix, and cold diffusion are consistent across PSNR/SSIM/NRMSE, and the ablation shows the refinement stage adds something beyond the coarse estimate. That is a credible engineering contribution.\n\nThe soft spot the stress-test flags is real. Stage II is trained on pairs (x_t, R(x_0)) where x_0 is a real DOPA sinogram, so the condition is a degraded version of the clean target. At inference, both the noisy input and the condition are derived from the Stage I synthetic output. Nothing in the training objective forces the condition distribution to match at inference. The paper gives no analysis of how far R(CE(FDG)) sits from the training conditions. So the refinement gain, while empirically positive on 141 test scans, is not yet explained. It could be genuine detail restoration or it could be regression to a learned average. This is a missing analysis, not a demonstrated contradiction.\n\nThe other weaknesses are the usual ones: no error bars or significance tests, no explicit statement that training and test patients are disjoint, and no sensitivity analysis for the free hyperparameters (guidance strength, step ratio, prior start timestep, degradation function). For a TMI-style paper, that is thinner than I'd like, but all fixable.\n\nThe math is standard diffusion; I see no fatal flaw. The reference list covers the relevant bases, and the self-citations are to the authors' own prior DDBM/DDPM work, which is appropriate. The one typo about the direction of the coarse conversion (DOPA-to-FDG vs FDG-to-DOPA) should be corrected.\n\nBottom line: this deserves a proper referee. I would send it to a medical-image-synthesis reviewer with a request to focus on the Stage II distribution issue and the patient-level data split. If the authors add a small experiment with synthetic conditions or a distance analysis, the claim would be much stronger. I'd be comfortable citing the sinogram-domain formulation.","headline":"Real sinogram-domain tracer conversion with an unvalidated refinement-condition distribution; worth refereeing but needs an extra experiment.","tokens_in":15568,"tokens_out":4574,"would_cite":true,"duration_ms":50769,"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":"A two-stage diffusion model converts 18F-FDG PET sinograms into 18F-DOPA PET sinograms, beating four existing translation baselines on all reported metrics.","keywords":["PET tracer conversion","sinogram synthesis","diffusion model","prior-guided refinement","coarse-to-fine learning","18F-DOPA","18F-FDG","projection domain"],"falsifier":"Compare PSNR and SSIM before and after Stage II on (a) degraded real DOPA sinograms and (b) degraded Stage-I synthetic outputs; if refinement only improves the real inputs or worsens the synthetic ones, the match between training and inference conditioning is the breaking point.","tokens_in":14580,"feed_emoji":"🧠","tokens_out":7492,"duration_ms":83306,"temperature":0.7,"pith_summary":"This paper tries to establish that a two-stage diffusion model called PJDM can convert 18F-FDG PET sinograms into 18F-DOPA PET sinograms more accurately than existing image-translation methods. Working directly on the raw projection data, before image reconstruction, is meant to preserve the scanner's original information and reduce errors that accumulate during reconstruction. The authors propose a coarse-to-fine pipeline: a supervised first stage produces an initial DOPA sinogram, and an unsupervised second stage refines it using a degraded version of that initial sinogram as guidance. If correct, the method would make DOPA-like PET information available without the costly synthesis and short transport window of the DOPA tracer, and it would demonstrate a practical way to combine a small paired dataset with a large unpaired target-domain dataset.","feed_headline":"Two-stage diffusion beats four rivals on PET tracer conversion","feed_subtitle":"A coarse FDG-to-DOPA sinogram plus prior-guided refinement reaches 24.98 dB PSNR.","key_machinery":"The load-bearing mechanism is a cascaded generative model with two stages. Stage I is a supervised diffusion-bridge network that treats the input 18F-FDG sinogram as the endpoint of a diffusion process and the target 18F-DOPA sinogram as the start, using Doob's h-transform, a conditioning transform that forces the terminal state toward the given sinogram, to guide the bridge; sampling uses a higher-order hybrid sampler combining Euler-Maruyama and Heun steps. Stage II is a conditional denoising diffusion model whose input at each reverse step is the noisy DOPA sinogram concatenated with a degraded version of the Stage-I output, obtained by a degradation function R that applies Gaussian blurring and random contrast and brightness changes. The reverse process starts at an intermediate timestep t_prior = 185 so that only part of the noise is removed, letting the degraded prior hold structural information while the model restores detail. The central conditioning identity is concat(x_t, R(hat{x}_0)), which lets a model trained on real DOPA sinograms pull the coarse synthetic prediction back toward the DOPA manifold.","core_discovery":"On the paper's own terms, the central discovery is that prior-guided refinement in the projection domain improves PET tracer conversion. The proposed PJDM reports PSNR of 24.98 dB, SSIM of 0.812, and NRMSE of 0.064 on a test set of 141 paired scans, outperforming U-Net, CycleGAN, Pix2Pix, and cold diffusion on all three metrics; against the second-best method, cold diffusion, the gain is 1.12 dB in PSNR and 0.059 in SSIM. The ablation supports the two-stage design: coarse estimation alone reaches 24.25 dB PSNR, prior refinement alone 22.87 dB, and the combination 24.98 dB, with SSIM rising from 0.751 or 0.739 to 0.812. The first stage maps an 18F-FDG sinogram to an initial 18F-DOPA sinogram using a supervised diffusion bridge, and the second stage runs a conditional denoising process whose condition is the initial synthetic DOPA sinogram after Gaussian blurring and random contrast and brightness perturbations, with the reverse process started at an intermediate timestep. The paper claims this preserves overall structure while restoring fine detail, and that both the synthesized sinograms and their reconstructed images are the closest to ground truth among the compared methods.","pith_inferences":["A natural stress test the authors did not run: feed Stage II a degraded real DOPA sinogram versus a degraded synthetic one; if the gain over Stage I vanishes or reverses on synthetic inputs, the conditioning distribution is the fragile link.","The same two-stage pattern may transfer to other tracer pairs or projection-domain translation tasks, but the transfer likely depends on how close the coarse stage can get to the target manifold.","If the condition-distribution mismatch is real, a testable extension would be to train Stage II on degraded synthetic outputs from Stage I in addition to degraded real DOPA sinograms.","Reporting sinogram-domain and reconstructed-image metrics separately could reveal whether Stage II's gains are genuine projection-domain improvements or effects that only survive reconstruction."],"forward_implications":["If the result generalizes, clinics could generate DOPA-like PET sinograms from routine FDG scans, reducing the need for the harder-to-produce 18F-DOPA tracer.","The coarse-to-fine recipe provides a way to exploit a small paired dataset plus a large unpaired target-domain dataset, combining supervised structural mapping with unsupervised detail refinement.","Because conversion happens before reconstruction, the method could be integrated into a PET scanner's raw-data pipeline, potentially avoiding errors introduced when translating reconstructed images.","The reported gains over cold diffusion suggest that diffusion-based translation can be improved by adding a learned degradation prior rather than relying on arbitrary forward transforms alone."],"supporting_citations":[{"why":"Supplies the higher-order hybrid sampler, with Euler-Maruyama and Heun steps, used for Stage I iterative synthesis.","marker":"[32]"},{"why":"Provides the supervised diffusion-bridge formulation on which the coarse estimation model is built.","marker":"[33]"},{"why":"Supplies the denoising diffusion probabilistic model underlying the prior refinement stage.","marker":"[25]"},{"why":"Provides the fast sampling strategy used in the Stage II refinement process.","marker":"[34]"},{"why":"Provides one of the convolutional baseline methods used as a comparison in the tracer conversion experiments.","marker":"[35]"},{"why":"Provides a GAN-based translation baseline used as a comparison in the tracer conversion experiments.","marker":"[36]"},{"why":"Provides a paired GAN-based translation baseline used as a comparison in the tracer conversion experiments.","marker":"[37]"},{"why":"Provides the cold diffusion baseline that the proposed method is compared against and outperforms.","marker":"[38]"}],"fun_headline_variants":["Prior-guided diffusion beats four rivals on PET tracer conversion","Projection-domain diffusion converts FDG to DOPA PET with 24.98 dB","Two-stage diffusion model improves PET tracer synthesis in sinogram domain","Prior-guided joint diffusion model achieves best PET tracer conversion","Diffusion model in projection domain boosts FDG-to-DOPA PET accuracy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"If the synthetic DOPA sinogram from Stage I is far from the real DOPA sinogram manifold, then the Stage II refiner, which was trained on degraded real DOPA sinograms, may fail to correct it and could even distort the result.","fun_headline_variants_meta":{"raw":{"variants":["Prior-guided diffusion beats four rivals on PET tracer conversion","Projection-domain diffusion converts FDG to DOPA PET with 24.98 dB","Two-stage diffusion model improves PET tracer synthesis in sinogram domain","Prior-guided joint diffusion model achieves best PET tracer conversion","Diffusion model in projection domain boosts FDG-to-DOPA PET accuracy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000223,"raw_usage":{"total_tokens":1527,"prompt_tokens":1083,"completion_tokens":444,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":699,"completion_tokens_details":{"reasoning_tokens":353}},"tokens_in":699,"tokens_out":444,"duration_ms":5429,"temperature":1.0,"reasoning_tokens":353,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T23:37:05.929185+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare PSNR and SSIM before and after Stage II on (a) degraded real DOPA sinograms and (b) degraded Stage-I synthetic outputs; if refinement only improves the real inputs or worsens the synthetic ones, the match between training and inference conditioning is the breaking point.","supporting_citations":[{"cited_title":"Revisiting unreasonable effec- tiveness of data in deep learning era,","cited_arxiv_id":null,"evidence_quote":"Supplies the higher-order hybrid sampler, with Euler-Maruyama and Heun steps, used for Stage I iterative synthesis."},{"cited_title":"Elucidating the design space of diffusion-based genera- tive models,","cited_arxiv_id":null,"evidence_quote":"Provides the supervised diffusion-bridge formulation on which the coarse estimation model is built."},{"cited_title":"st-DTPM: Spatial-temporal guided diffusion transformer probabilistic model for delayed scan PET image pre- diction,","cited_arxiv_id":null,"evidence_quote":"Supplies the denoising diffusion probabilistic model underlying the prior refinement stage."},{"cited_title":"Denoising diffusion bridge models,","cited_arxiv_id":null,"evidence_quote":"Provides the fast sampling strategy used in the Stage II refinement process."},{"cited_title":"Denoising diffusion implicit models,","cited_arxiv_id":null,"evidence_quote":"Provides one of the convolutional baseline methods used as a comparison in the tracer conversion experiments."},{"cited_title":"U-net: Convolutional networks for biomedical image segmentation,","cited_arxiv_id":null,"evidence_quote":"Provides a GAN-based translation baseline used as a comparison in the tracer conversion experiments."},{"cited_title":"Unpaired image-to-image translation using cycle-consistent adversarial networks,","cited_arxiv_id":null,"evidence_quote":"Provides a paired GAN-based translation baseline used as a comparison in the tracer conversion experiments."},{"cited_title":"Image-to-image translation with con- ditional adversarial networks,","cited_arxiv_id":null,"evidence_quote":"Provides the cold diffusion baseline that the proposed method is compared against and outperforms."}],"review_version":1}