{"id":"581982bc-f161-4662-9841-c9e3f0272e74","arxiv_id":"2604.15459","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"RelativeFlow reformulates flow matching into relative noisier-to-noisy mappings via consistent transport and simulation-based velocity fields to outperform prior methods on CT and MR denoising with noisy references.","lead":"RelativeFlow introduces a flow matching framework that learns medical image denoising from noisy references by breaking the task into relative noisier-to-noisy steps that compose into a unified high-quality target. Smart generalists might read it because clearer CT and MR images without needing perfect clean training data could improve real-world diagnostic accuracy in healthcare.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"CoT composition into unified absolute flow lacks explicit verification that relative velocity fields integrate consistently across noise levels","rationale":"Reader's weakest assumption directly identifies the composition and generalization risk; the abstract-only review correctly flags it as uncheckable. Full-text experiments on CT/MR show performance gains but do not isolate whether gains arise from proper composition or from SVF regularization alone. This single check would decide if the decomposition is load-bearing or incidental.","tokens_in":1697,"tokens_out":321,"duration_ms":21261,"concrete_test":"Construct a 1D Gaussian denoising toy problem with three known noise variances (σ1 > σ2 > σ3 = 0); train RelativeFlow on relative pairs only, integrate the composed CoT paths from σ1 to σ3, and compare the final marginal to the direct absolute flow from σ1 to σ3; if KL divergence exceeds 0.05 the composition claim is unsupported.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that relative noisier-to-noisy mappings (via CoT) compose into one absolute noise-to-clean flow. The abstract states CoT 'constrains relative flows to be components of and progressively compose a unified absolute flow,' yet no section or equation is shown to prove that the learned SVF on heterogeneous pairs yields the same terminal distribution as direct absolute transport, nor that path consistency holds when noise levels are not strictly ordered. If this fails, the method collapses to ordinary flow matching on noisy pairs without the claimed taming benefit.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper proposes RelativeFlow, a flow matching framework for medical image denoising that reformulates the problem by decomposing absolute noise-to-clean mappings into relative noisier-to-noisy mappings. It introduces Consistent Transport (CoT) to constrain relative flows as components that progressively compose a unified absolute flow, and Simulation-based Velocity Field (SVF) constructed via modality-specific degradation operators. The central claim is that this tames the noisy reference problem in MID, enabling learning from heterogeneous noisy references and significantly outperforming SimSDL, SimSGL, and SSL methods on CT and MR data.","tokens_in":1837,"tokens_out":584,"duration_ms":38263,"significance":"If the composition property of relative flows holds and the empirical gains are robust, the work offers a principled way to handle the absence of clean references in medical imaging without restrictive noise assumptions, which could improve practical denoising pipelines. The explicit decomposition into relative mappings and the modality-aware SVF construction represent a clear conceptual advance over treating noisy references as clean targets.","major_comments":[{"comment":"Abstract: the claim that CoT 'constrains relative flows to be components of and progressively compose a unified absolute flow' is load-bearing for the central contribution, yet no equation or derivation is supplied showing that the learned SVF on heterogeneous pairs yields the same terminal distribution as direct absolute transport or that path consistency is preserved when noise levels are not strictly ordered.","section":"Abstract"},{"comment":"Experiments: the assertion of significant outperformance on CT and MR denoising rests on high-level statements without visible error bars, ablation tables, or statistical tests, making it impossible to verify whether the reported gains exceed those of ordinary flow matching on noisy pairs.","section":"Experiments"},{"comment":"Method: the SVF construction is said to support different modalities via degradation operators, but no analysis or constraint is given to guarantee generalization across CT and MR without modality-specific retraining or additional regularization, which directly affects the cross-modality claims.","section":"Method"}],"minor_comments":[{"comment":"Abstract: the inline definitions of CoT and SVF are clear but would benefit from a short enumerated list of the two components to improve scannability.","section":"Abstract"},{"comment":"Notation: the distinction between 'relative noisier-to-noisy mappings' and the final 'unified high-quality target' could be clarified with a simple diagram or one-line recurrence relation.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The abstract is unusually self-contained and high-level; the full manuscript must supply the missing composition proof and experimental details for the claims to be evaluable. Citation pattern appears standard for the area."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive feedback on RelativeFlow. The comments identify important areas for clarification and strengthening, particularly around mathematical rigor, experimental validation, and modality handling. We address each major comment point-by-point below, with proposed revisions where the manuscript can be improved without misrepresenting the work.","responses":[{"response":"We acknowledge that the abstract is high-level and that an explicit derivation for heterogeneous noisy pairs would strengthen the presentation. Section 3.2 defines CoT as a displacement map enforcing composition: for pairs with noise levels satisfying σ_i > σ_j, the relative velocity integrates to the absolute transport map under the SVF. However, the manuscript does not include a full proof for non-monotonic noise ordering or terminal distribution equivalence across arbitrary heterogeneous references. We will add a concise derivation (new paragraph in Section 3.2 and a short appendix) showing that, given consistent degradation operators, the composed relative paths converge to the same high-quality terminal distribution as direct absolute flow matching. Path consistency for non-strictly ordered levels will be addressed by noting that CoT implicitly sorts via pairwise consistency during training.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the claim that CoT 'constrains relative flows to be components of and progressively compose a unified absolute flow' is load-bearing for the central contribution, yet no equation or derivation is supplied showing that the learned SVF on heterogeneous pairs yields the same terminal distribution as direct absolute transport or that path consistency is preserved when noise levels are not strictly ordered."},{"response":"The referee is correct that the current experimental reporting lacks sufficient statistical detail to allow independent verification of the gains over baselines including standard flow matching on noisy pairs. We will revise the Experiments section to include: (i) error bars showing mean ± std over 5 random seeds for all metrics, (ii) an expanded ablation table directly comparing RelativeFlow against vanilla flow matching trained on the same noisy-reference pairs, and (iii) paired t-test p-values for the reported improvements on both CT and MR datasets. These additions will be placed in the main text and supplementary material.","revision_made":"yes","referee_comment":"[Experiments] Experiments: the assertion of significant outperformance on CT and MR denoising rests on high-level statements without visible error bars, ablation tables, or statistical tests, making it impossible to verify whether the reported gains exceed those of ordinary flow matching on noisy pairs."},{"response":"The manuscript does not claim zero-shot cross-modality generalization. SVF is explicitly constructed with modality-specific degradation operators (Section 3.3), and all reported experiments train separate models for CT and MR. The framework's contribution is that the same relative-flow formulation and CoT mechanism apply once the appropriate operator is supplied. We will add a clarifying paragraph in Section 3.3 and the discussion section stating that modality-specific retraining is required and that no cross-modality transfer without adaptation is demonstrated. This removes any ambiguity about cross-modality claims while preserving the unified methodological advance.","revision_made":"partial","referee_comment":"[Method] Method: the SVF construction is said to support different modalities via degradation operators, but no analysis or constraint is given to guarantee generalization across CT and MR without modality-specific retraining or additional regularization, which directly affects the cross-modality claims."}],"tokens_in":1417,"tokens_out":718,"duration_ms":48600,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's main move is to decompose the usual noise-to-clean flow into relative noisier-to-noisy steps so the model can train on pairs of real noisy medical images instead of needing clean targets. It names two pieces for this: Consistent Transport to force the relative paths to add up to one absolute flow, and Simulation-based Velocity Field to build modality-specific velocity fields from degradation operators. That directly targets the practical limit in CT and MR where clean ground truth is unavailable, and it correctly flags why SimSDL, SimSGL, and standard SSL fall short.","headline":"RelativeFlow reframes flow matching for noisy-reference medical denoising via relative mappings and CoT/SVF, but the abstract gives no evidence that the composition actually works or that the gains are real.","tokens_in":2322,"tokens_out":196,"would_cite":false,"duration_ms":25133,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"RelativeFlow decomposes medical image denoising into relative flows between noisy versions to reach a unified high-quality target.","keywords":["medical image denoising","flow matching","noisy references","consistent transport","simulation-based velocity field","CT denoising","MR denoising"],"falsifier":"Apply the trained model to a held-out test set that does contain known clean ground-truth images and check whether the denoised outputs match those ground truths more closely than outputs from prior methods, or verify whether the sequence of relative flow steps actually reaches the expected quality level when composed.","tokens_in":2608,"feed_emoji":"🖼️","tokens_out":786,"duration_ms":57207,"temperature":0.7,"pith_summary":"Medical image denoising struggles because truly clean reference images are almost never available for training, so prior approaches either misuse noisy references as targets or impose noise assumptions that rarely hold in practice. RelativeFlow instead uses flow matching to break the overall task into a chain of smaller relative mappings that move from noisier images to less noisy ones. A consistent transport step ensures these partial flows add together into one coherent improvement path, while a simulation-based velocity field supplies the direction of movement using the known degradation behavior of each imaging modality. The result is a model that can start from inputs of any quality level and push them toward the same high-quality endpoint using only the noisy references that are already on hand.","feed_headline":"RelativeFlow denoises medical images using only noisy references","feed_subtitle":"Decomposing the task into relative noisy-to-noisy steps composes into one unified high-quality target without clean supervision.","key_machinery":"Consistent transport (CoT), a displacement map that forces relative noisier-to-noisy flows to compose into one unified absolute flow, together with a simulation-based velocity field (SVF) built from modality-specific degradation operators to define the direction and speed of each step.","core_discovery":"RelativeFlow reformulates flow matching by decomposing the absolute noise-to-clean mapping into relative noisier-to-noisy mappings, realized through consistent transport (CoT) that constrains the relative flows to compose progressively into a unified absolute flow and through a simulation-based velocity field (SVF) constructed from modality-specific degradation operators. This enables the framework to learn from heterogeneous noisy references and drive inputs from arbitrary quality levels toward a single high-quality target, outperforming existing simulated-supervised and self-supervised methods on CT and MR denoising tasks.","pith_inferences":["If the composition of relative flows holds, the same decomposition idea could be tested on denoising tasks outside medicine where only noisy references exist, such as astronomical imaging or sensor data.","Adapting the simulation-based velocity field to additional modalities would allow the method to scale to new imaging types without collecting fresh clean datasets.","The flow perspective suggests that other generative models could be redesigned to treat noisy references as intermediate states rather than fixed targets."],"forward_implications":["The method can train directly on whatever noisy references exist without treating them as clean targets, avoiding both suboptimal convergence and reference bias.","A single model can improve images that start at widely different quality levels because all paths are driven toward the same unified high-quality endpoint.","Modality-specific degradation operators in the velocity field allow the same framework to handle CT and MR data without separate retraining pipelines.","By avoiding restrictive assumptions about noise statistics, the approach applies to realistic clinical acquisitions where noise distributions are unknown or mixed."],"fun_headline_variants":["RelativeFlow decomposes noise-to-clean into relative noisier mappings","RelativeFlow constrains relative flows via consistent transport","Simulation-based fields support modality-specific medical denoising","Decomposed mappings drive inputs to unified high-quality targets"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The assumption that relative mappings between noisy images can be constrained so they reliably add up to one overall mapping toward a clean image, and that the velocity field constructed from degradation operators will work across scan types without additional adjustments.","fun_headline_variants_meta":{"raw":{"variants":["RelativeFlow decomposes noise-to-clean into relative noisier mappings","RelativeFlow constrains relative flows via consistent transport","Simulation-based fields support modality-specific medical denoising","Decomposed mappings drive inputs to unified high-quality targets"]},"model":"grok-4.3","cost_usd":0.009904,"raw_usage":{"total_tokens":4332,"prompt_tokens":687,"num_sources_used":0,"completion_tokens":52,"cost_in_usd_ticks":99040500,"prompt_tokens_details":{"text_tokens":687,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3593,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":687,"tokens_out":52,"duration_ms":46530,"temperature":1.0,"reasoning_tokens":3593,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-10T09:13:22.865271+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Apply the trained model to a held-out test set that does contain known clean ground-truth images and check whether the denoised outputs match those ground truths more closely than outputs from prior methods, or verify whether the sequence of relative flow steps actually reaches the expected quality level when composed.","supporting_citations":[],"review_version":1}