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arxiv: 2604.15459 · v1 · submitted 2026-04-16 · 📡 eess.IV · cs.AI· cs.CV

RelativeFlow: Taming Medical Image Denoising Learning with Noisy Reference

Yuxin Liu , Yiqing Dong , Wenxue Yu , Zhan Wu , Rongjun Ge , Yang Chen , Yuting He This is my paper

Pith reviewed 2026-05-10 09:13 UTC · model grok-4.3

classification 📡 eess.IV cs.AIcs.CV
keywords medical image denoisingflow matchingnoisy referencesconsistent transportsimulation-based velocity fieldCT denoisingMR denoising
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The pith

RelativeFlow decomposes medical image denoising into relative flows between noisy versions to reach a unified high-quality target.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

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.

Core claim

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.

What carries the argument

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.

If this is right

  • 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.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • 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.

Load-bearing premise

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.

What would settle it

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.

Figures

Figures reproduced from arXiv: 2604.15459 by Rongjun Ge, Wenxue Yu, Yang Chen, Yiqing Dong, Yuting He, Yuxin Liu, Zhan Wu.

Figure 1
Figure 1. Figure 1: Noisy reference problem: Varying reference quality across categories causes medical image denoising models to learn category-specific mappings, limiting denoising performance. ity level ( [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Motivation: Composing relative denoising flows from arbitrary noisy references into an absolute denoising flow trans￾ports images with different quality levels to a unified high-quality level, breaking reference bias. reference-biased learning, where each acquisition condition is mapped to its own reference quality level when the model converges [1, 30]. As a result, the model capability is fun￾damentally … view at source ↗
Figure 3
Figure 3. Figure 3: Overview of RelativeFlow framework: Our method learns relative flows from noisy references at varying quality levels through Consistent Transport (CoT) and Simulation-based Veloc￾ity Field (SVF), enabling unified denoising across different quality levels. Our RelativeFlow framework addresses the noisy refer￾ence problem via two key innovations: Consistent Trans￾port (CoT, Sec. 3.2) that enables relative fl… view at source ↗
Figure 4
Figure 4. Figure 4: Relative flows are components of absolute flow. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relative flows progressively compose absolute flow. [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative comparison: Our RelativeFlow delivers visually superior denoising on a) CT and b) MR images, recovering fine anatomical structures with clearly discernible textures that even surpass those visible in the noisy references. The figure shows visual results for CT (display window [-160, 240] HU) and MR denoising compared against 10 SimSDL, SSL, and SimSGL baseline methods. SSIM, and by relative red… view at source ↗
Figure 7
Figure 7. Figure 7: Trajectory analysis: Comparison of transport trajectories learned by DDIM, Flow Matching, and RelativeFlow, training with noisy references (blurred Gaussians) and predicting for clean labels (sharp circular distributions). Our method introduces the ring pattern earlier and generates results closer to clean targets. importance of progressive refinement in flow-based denois￾ing. 4.3. Trajectory Analysis We c… view at source ↗
Figure 8
Figure 8. Figure 8: Visual comparison of training and testing data quality distributions for CT (left) and MR (right) datasets. [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Denoising process visualization for multiple quality levels. Left: three CT examples. Right: three MR examples. Each row shows the denoising trajectory with five images: noisy input, three intermediate steps, and the reference. Yellow boxes indicate ROI with zoomed-in views. RelativeFlow achieves consistent high-quality outputs across different noise levels and modalities [PITH_FULL_IMAGE:figures/full_fig… view at source ↗
read the original abstract

Medical image denoising (MID) lacks absolutely clean images for supervision, leading to a noisy reference problem that fundamentally limits denoising performance. Existing simulated-supervised discriminative learning (SimSDL) and simulated-supervised generative learning (SimSGL) treat noisy references as clean targets, causing suboptimal convergence or reference-biased learning, while self-supervised learning (SSL) imposes restrictive noise assumptions that are seldom satisfied in realistic MID scenarios. We propose \textbf{RelativeFlow}, a flow matching framework that learns from heterogeneous noisy references and drives inputs from arbitrary quality levels toward a unified high-quality target. RelativeFlow reformulates flow matching by decomposing the absolute noise-to-clean mapping into relative noisier-to-noisy mappings, and realizes this formulation through two key components: 1) consistent transport (CoT), a displacement map that constrains relative flows to be components of and progressively compose a unified absolute flow, and 2) simulation-based velocity field (SVF), which constructs a learnable velocity field using modality-specific degradation operators to support different medical imaging modalities. Extensive experiments on Computed Tomography (CT) and Magnetic Resonance (MR) denoising demonstrate that RelativeFlow significantly outperforms existing methods, taming MID with noisy references.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

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.

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 (3)
  1. [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.
  2. [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.
  3. [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.
minor comments (2)
  1. [Abstract] 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.
  2. [Abstract] 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.

Simulated Author's Rebuttal

3 responses · 0 unresolved

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.

read point-by-point responses

  1. Referee: [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.

    Authors: 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: yes

  2. Referee: [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.

    Authors: 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: yes

  3. Referee: [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.

    Authors: 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: partial

Circularity Check

0 steps flagged

No significant circularity in RelativeFlow derivation

full rationale

The abstract and available description present RelativeFlow as a proposed reformulation of flow matching that introduces CoT and SVF as new components to handle noisy references. No equations or steps are shown that reduce the claimed unified absolute flow or performance gains to a fitted parameter, self-citation chain, or definitional tautology. The decomposition is presented as a modeling choice rather than derived from prior results by the same authors in a load-bearing way. The framework is self-contained against external benchmarks like CT/MR experiments, with no evidence of the central claim collapsing to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The central claim rests on the unproven composition property of relative flows and on the adequacy of modality-specific simulated degradations; no free parameters are explicitly named in the abstract.

axioms (2)
  • domain assumption Relative noisier-to-noisy mappings can be constrained by a displacement map to compose into a single absolute noise-to-clean flow.
    Invoked as the basis for the Consistent Transport component.
  • domain assumption Modality-specific degradation operators can be used to construct a learnable velocity field that supports arbitrary medical imaging modalities.
    Basis for the Simulation-based Velocity Field component.
invented entities (2)
  • Consistent Transport (CoT) no independent evidence
    purpose: Displacement map that forces relative flows to be components of and progressively compose a unified absolute flow.
    New construct introduced to realize the relative-mapping reformulation.
  • Simulation-based Velocity Field (SVF) no independent evidence
    purpose: Learnable velocity field built from modality-specific degradation operators.
    New construct to handle different medical imaging modalities.

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discussion (0)

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