{"id":"ceccd1d0-5100-466d-99f1-0ee576348fde","arxiv_id":"2501.13514","paper_version":3,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"Di-Fusion is a single-stage, self-supervised diffusion denoiser for dMRI that maps between adjacent noisy volumes and adaptively terminates sampling, but its theoretical basis is questionable.","lead":"This paper introduces Di-Fusion, a self-supervised method that denoises diffusion MRI by training a diffusion model to map between adjacent noisy volumes. It reports strong empirical results, but the core assumption that adjacent volumes share the same clean signal is violated in real dMRI data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (9) does not inherit the Noise2Self guarantee: the input to Fθ is fused from the target slice x itself (Eq. 6), so Fθ can copy x rather than denoise, and the self-supervised denoising claim rests on a broken independence condition.","rationale":"The central claim is that Di-Fusion is a fully self-supervised dMRI denoiser, justified by Eq. (9) inheriting the Noise2Self guarantee. The single most load-bearing flaw is that the training input is constructed from the target slice itself: Eq. (6) defines x*_t as a linear interpolation between x and x′, and Eq. (9) feeds √ᾱt x*_t plus noise into Fθ. Because λ1 approaches 1 as t approaches 1, the network receives an almost direct copy of the target, so minimizing the loss against x can be achieved by copying the leaked component rather than by learning to denoise. This breaks the independence condition required for the Noise2Self/Noise2Noise equivalence, even under the idealized assumption that x and x′ are repeated noisy measurements of the same clean signal. The reader's weakest assumption focuses on the physical premise that adjacent dMRI volumes share the same clean signal; that concern is valid, but the target leakage is even more fundamental because it invalidates the derivation regardless of the domain. The paper does provide code, extensive experiments, and ablation studies, which are real strengths, but the theoretical guarantee is the load-bearing element of the central claim. The empirical results could be explained by identity shortcuts or contrast-adaptive smoothing rather than by principled self-supervised denoising. The proposed ablation test would settle whether the method depends on target leakage. Since this concern reinforces the reader's REJECT verdict, the recommended verdict remains unchanged.","tokens_in":32982,"tokens_out":5939,"duration_ms":54047,"concrete_test":"Run the same training pipeline with the Fusion process disabled (replace x*_t with x′ in Eq. (6), i.e., λ1 = 0, λ2 = 1) and compare SNR/CNR and downstream R2 metrics; if performance degrades markedly, the original objective exploited target leakage rather than a self-supervised denoising signal.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central theoretical claim is that minimizing the objective in Eq. (9) is equivalent, in expectation, to minimizing against the clean signal y, per Noise2Self/Noise2Noise. This equivalence requires the network input to be independent of the target given y; in Eq. (9) the input is √ᾱt (λ1 x + λ2 x′) + √(1−ᾱt) ξx−x′, and since λ1 → 1 as t → 1, the input contains an almost exact copy of x, the very slice used as the regression target. The loss is therefore minimized by copying the leaked target component from the input, and the expected-loss identity E||Fθ(x′) − x||^2 = E||Fθ(x′) − y||^2 + const no longer holds. This is not a domain-specific nuance: even if x and x′ were repeated acquisitions of the same clean y, Eq. (9) would not train a denoiser. The additional dMRI premise — adjacent volumes with different diffusion gradients do not share the same clean signal — further invalidates the Noise2Self basis on the real datasets, but the target leakage alone is sufficient to break the derivation. The empirical gains may reflect a learned identity shortcut, contrast-adaptive smoothing, or the adaptive termination selecting an intermediate output, but they do not substantiate the claimed self-supervised denoising guarantee.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Di-Fusion, a single-stage self-supervised dMRI denoising method based on a diffusion model. The forward process uses a 'Fusion' interpolation between the target slice x and its neighboring volume slice x', and replaces Gaussian noise with a spatially shuffled difference volume ('Di-' process). Training minimizes Eq. (9) over the last Tc diffusion steps, and sampling uses a deterministic Run-Walk schedule with an adaptive termination threshold C_SNR. Experiments on Stanford HARDI, Sherbrooke 3-Shell, PPMI, and simulated fastMRI data report improved SNR/CNR, microstructure model R2, tractography quality, and PSNR/SSIM relative to several baselines, and the authors claim a Noise2Self-style guarantee for the training objective.","tokens_in":33219,"tokens_out":7749,"duration_ms":69828,"significance":"If the theoretical basis were valid, the method would be significant for clinical dMRI because it needs no clean data, no explicit noise-model training, and offers controllable iterative refinement with demonstrated downstream benefits. Strengths of the manuscript include released code, ablations of the main components, and simulated experiments evaluated against held-out ground truth, so the reported numbers are not circular. However, the central Noise2Self derivation is invalid: Eq. (9) feeds the regression target x into the network input, and the dMRI premise that adjacent volumes share the same clean signal fails. The empirical results may still indicate a useful learned mapping, but they do not establish the paper's core claim of a self-supervised denoising guarantee.","major_comments":[{"comment":"The objective in Eq. (9) does not inherit the Noise2Self guarantee because the network input contains the regression target x. The input is sqrt(ᾱ_t)(λ_t^1 x + λ_t^2 x') + sqrt(1−ᾱ_t) ξ_{x−x'}, and for small t the coefficient λ_t^1 approaches 1, so the input is nearly x. Noise2Self J-invariance requires the output for a pixel to be independent of the input at that pixel; here the whole target image is available as an input, so the network can minimize Eq. (9) by copying x, and the identity E||F_θ(input)−x||^2 = E||F_θ(input)−y||^2 + const no longer holds. This failure is independent of the dMRI premise and is sufficient to break the claimed self-supervised denoising derivation.","section":"Section 3.2, Eq. (9)"},{"comment":"The assumption that x = X_{*,*,i,j} and x' = X_{*,*,i,j−1} are 'independent corrupted measurements of the clean ground truth y' is false for dMRI: adjacent volumes are acquired with different diffusion gradient directions, so their underlying diffusion-weighted signals differ. Noise2Noise and Noise2Self require pairs that share the same clean target y. On the real HARDI, Sherbrooke, and PPMI datasets, the training objective therefore minimizes toward a different diffusion-weighted signal rather than toward a common clean volume, which is a second, independent failure of the theoretical basis.","section":"Section 3, first paragraph, and Eq. (8)"},{"comment":"The 'Di-' process is effectively absent from the reverse sampling update: Eq. (10) contains the term (σ_t · η) ξ_{x−x'}, and the experiments set η = 0. The shuffled noise ξ appears only in the initial x_Tc and during training. Thus the statements that the Di- process characterizes real-world noise during the iterative refinement (Q2 and Q5) overstate its role; the refinement steps themselves are deterministic. This is a consistency issue between the method description and the actual sampling procedure.","section":"Section 3.3, Eq. (10), and Algorithm 2"}],"minor_comments":[{"comment":"Equation (1) is stated as an equality of argmin without explicitly listing the required conditions on x, x', and y; please state the independence and identical-clean-target assumptions explicitly, since the paper later relies on them.","section":"Section 2.1, Eq. (1)"},{"comment":"The symbols β1 and β2 are used both for the noise-schedule terms in Section 2.2 and for the brain-mask thresholds in Appendix D.1 (β1 = −0.93, β2 = −0.95); the main text also uses ρ1 and ρ2 for the same thresholds. Please rename to avoid confusion.","section":"Eq. (12), Appendix D.1"},{"comment":"The sentence 'we first consider x and x′ as J = {x, x′}' conflates Noise2Self's pixel-partition J-invariance with a pair of whole images; please clarify the intended partition and how it is implemented in the network.","section":"Section 3.2, first paragraph"}],"recommendation":"reject","confidential_remarks":"The reader's stress-test concern lands: Eq. (9) is not a Noise2Self objective because the input contains the target slice, and the same-clean-y premise is false for adjacent dMRI volumes. These are load-bearing errors for the paper's central claim, not local presentation issues. A reframing that drops the Noise2Self guarantee and presents Di-Fusion purely as an empirical mapping, with correspondingly weaker claims, would require substantial new justification and evidence, so I recommend rejection rather than major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Take a look at this paper if you want to see how far empirical work can outrun its theory. Di-Fusion is a single-stage diffusion-based denoiser for dMRI that trains a U-Net to map from one noisy volume to an adjacent volume, using a \"Fusion\" interpolation to define intermediate states, a \"Di-\" noise term derived from the difference volume, and adaptive termination during sampling. The authors also introduce Run-Walk accelerated sampling. The experiments are extensive: they compare against several baselines on three real dMRI datasets, plus simulated fastMRI data, and report PSNR/SSIM, microstructure fitting R², tractography fiber bundle coherence, and SNR/CNR. The code is available, and the ablations show each component contributes. That is real, reproducible work, and the improvement over DDM2 on downstream metrics looks solid.\n\nThe problem is the central theoretical claim. Equation (9) is presented as inheriting the Noise2Self guarantee: minimizing ||x - Fθ(√ᾱ_t x*_t + √(1-ᾱ_t)ξ, t)||² should be equivalent to minimizing against the clean y, because x and x' are independent corrupted measurements of the same y. Two things break this. First, the input to Fθ is x*_t = λ_t1 x + λ_t2 x', and for t near 1, λ_t1 → 1, so the input contains an almost exact copy of the target x itself. The network can simply copy the leaked component, and the Noise2Self independence condition — input independent of target given y — is violated. Second, in real dMRI, adjacent volumes with different diffusion gradients do not share the same clean signal. The paper's own definition, \"x' = X_{*,*,i,j-1}\" and \"x = X_{*,*,i,j}\", means different diffusion directions, so the clean underlying images differ. The premise \"independent corrupted measurements of the clean ground truth y\" is physically false. Even if you fixed the premise by using repeated same-direction acquisitions, the target leakage alone is sufficient to invalidate the derivation.\n\nWhere does that leave the method? It may still work as a practical denoiser, perhaps as a form of learned contrast-adaptive smoothing or conditional generation, but the paper provides no theoretical justification for calling it a principled self-supervised denoiser. The empirical gains on real data could be from the diffusion prior and iterative refinement, not from a Noise2Self guarantee. The simulated experiments, where ground truth is available, do show PSNR/SSIM gains, which is evidence the network learns something useful, but those experiments do not test the real-dMRI premise.\n\nThis paper deserves a serious referee, because the engineering is competent and the empirical work is thorough. But it needs major revision: either fix the theory (e.g., by using only x' as input, or redesigning the loss), or reframe the contribution without the Noise2Self claim. As it stands, I would not cite it for the self-supervised guarantee; I might cite it as an example of an overclaimed method.\n\nMy recommendation: engage with it, but send it back for major revision with a clear explanation of the broken Eq. (9). A corrected version could be a useful contribution to the dMRI preprocessing literature.","headline":"Well-engineered dMRI denoising with a broken Noise2Self argument: Eq. (9) leaks the target into the network input, and adjacent volumes do not share a clean signal.","tokens_in":33830,"tokens_out":4245,"would_cite":false,"duration_ms":36261,"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":"Di-Fusion claims that a single neighboring noisy dMRI volume can supervise a diffusion-model denoiser, achieving state-of-the-art downstream results without clean data or a separate noise model.","keywords":["diffusion MRI denoising","self-supervised learning","Noise2Self","denoising diffusion models","tractography","microstructure modeling","adaptive sampling"],"falsifier":"Acquire two sets of dMRI volumes: one with repeated identical diffusion-gradient acquisitions (true independent measurements of the same $y$) and one with adjacent different-gradient volumes as used in the paper, then train Di-Fusion with Eq. (9) on each. If the same-gradient pair performs markedly better, or if the different-gradient pair's denoised output is visibly biased toward the target gradient, then the shared-clean-signal assumption is the active ingredient and the Noise2Self justification is the part that matters.","tokens_in":32696,"feed_emoji":"🧠","tokens_out":5296,"duration_ms":46872,"temperature":0.7,"pith_summary":"Di-Fusion is a fully self-supervised method for denoising diffusion MRI volumes. It maps one noisy diffusion-weighted slice, $x'$, onto its neighboring slice $x$ through a $T$-step diffusion chain, and argues that because both are independent noisy readings of shared tissue signal, minimizing the squared error against $x$ also minimizes error against the clean underlying image. To keep the chain stable it introduces a Fusion process that linearly interpolates between $x'$ and $x$ at every step, and a \"Di-\" process that replaces Gaussian noise with spatially shuffled measured differences. Training only the last $T_c$ diffusion steps suppresses the generative diversity that causes hallucinations. The paper reports that this single-stage pipeline outperforms prior self-supervised methods on tractography, microstructure fitting, and simulated denoising benchmarks.","feed_headline":"One noisy neighbor volume trains a self-supervised dMRI denoiser","feed_subtitle":"Di-Fusion maps one diffusion-weighted volume to the next and still beats prior methods on tractography and microstructure fits.","key_machinery":"The load-bearing object is the simplified training objective of Eq. (9), a Noise2Self-style noisy-target loss that makes a diffusion model learn denoising from one neighboring noisy volume. The Fusion interpolation of Eq. (6), $x_t^* = \\lambda_t^1 x + \\lambda_t^2 x'$, aligns the forward trajectory with the target slice and avoids drift; the \"Di-\" noise of Eq. (8), $\\xi_{x-x'} = \\mathrm{mess}((x-x') - \\mu_{x-x'})$, supplies a non-Gaussian, empirically grounded noise distribution for both forward and reverse processes; and the adaptive termination rule of Section 3.3, comparing $d_x = \\|x - x_{\\mathrm{out}}\\|_2 \\cdot b_x$ against $C_{\\mathrm{SNR}}$, makes the refinement iterative and controllable.","core_discovery":"The central claim is that the simplified training loss in Eq. (9) inherits the Noise2Self guarantee: with $x$ and $x'$ independent corrupted measurements of the same clean volume, minimizing $\\mathbb{E}\\|x - F_\\theta(\\sqrt{\\bar\\alpha_t}\\,x_t^* + \\sqrt{1-\\bar\\alpha_t}\\,\\xi_{x-x'}, t)\\|^2$ equals minimizing the same loss against the clean signal $y$ up to a constant. The paper develops this in three moves. First, the Fusion process defines $x_t^* = \\lambda_t^1 x + \\lambda_t^2 x'$, so the forward trajectory is an interpolation toward the target rather than a pure noising of $x'$, preventing cumulative drift. Second, the \"Di-\" process sets $\\xi_{x-x'} = \\mathrm{mess}((x-x') - \\mu_{x-x'})$, a zero-mean spatially shuffled version of the measured noise difference, which retains noise variance and better matches real dMRI noise than a Gaussian. Third, training only the latter diffusion steps ($t \\le T_c$) restricts the model to conditional generation and reduces hallucinations. At sampling, Run-Walk accelerated sampling and an adaptive threshold $C_{\\mathrm{SNR}}$ let each slice terminate early, giving fast and controllable denoising.","pith_inferences":["The paper's Noise2Self justification is not literally satisfied by adjacent volumes with different diffusion gradients, since those volumes encode different diffusion-weighted signals; the empirical success may indicate that the diffusion prior and the redundancy of brain structure carry much of the load.","The \"Di-\" process is effectively an empirical noise sampler, and one could test whether injecting this shuffled-difference noise improves other self-supervised denoisers that currently assume Gaussian noise.","Training only the latter diffusion steps appears to be a transferable recipe for reducing hallucinations in conditional diffusion restoration beyond dMRI.","The global $C_{\\mathrm{SNR}}$ threshold could be calibrated per slice or per region instead of per volume, potentially improving edge-slice performance."],"forward_implications":["Denoising dMRI needs only one neighboring volume rather than a large set of diffusion directions, so the method could apply to clinical scans with very few volumes.","No clean ground truth and no separately trained noise model are required, simplifying the pipeline to a single training stage.","The $C_{\\mathrm{SNR}}$ threshold gives a user-controlled trade-off: lower values preserve anatomical detail, higher values remove more noise at the cost of some detail.","Improved downstream performance follows directly: higher $R^2$ on DTI and CSD microstructure fits, fewer spurious tractography streamlines, and better SNR/CNR on in-vivo data.","Simulated fastMRI experiments suggest the approach may extend to self-supervised denoising of other MRI contrasts, not only diffusion-weighted images."],"supporting_citations":[{"why":"Supplies the J-invariance / Noise2Self guarantee that makes minimizing a noisy-target loss equivalent to minimizing against the clean signal, the theoretical basis for Eq. (9).","marker":"Batson & Royer, 2019"},{"why":"Establishes the Noise2Noise paired-measurement equivalence used as the starting point of the self-supervised training objective.","marker":"Lehtinen et al., 2018"},{"why":"Provides the DDPM forward and reverse Markov chain, noise schedule, and sampling machinery that Di-Fusion modifies with the Fusion and \"Di-\" processes.","marker":"Ho et al., 2020"},{"why":"Supplies the deterministic DDIM sampling special case that the Run-Walk accelerated sampling builds on.","marker":"Song et al., 2020a"},{"why":"Introduces DDM2, the prior state-of-the-art self-supervised dMRI denoising method, and the spatial shuffling operation that the \"Di-\" process adapts.","marker":"Xiang et al., 2023"},{"why":"Provides Patch2Self, the main self-supervised dMRI baseline, and the downstream evaluation protocol for microstructure fitting and tractography.","marker":"Fadnavis et al., 2020a"},{"why":"Supplies the U-Net architecture modifications used to implement the denoising function $F_\\theta$.","marker":"Saharia et al., 2022b"}],"fun_headline_variants":["Noise your neighbor: self-supervised dMRI denoiser","Di-Fusion: one noisy volume teaches a denoiser","Denoise dMRI with a noisy sibling","No clean data? Use noisy pairs for dMRI denoising","Self-supervised diffusion denoising for dMRI, no clean data"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Adjacent diffusion volumes $x$ and $x'$ are independent noisy measurements of the same clean signal $y$, so their difference carries only noise; on real dMRI scans adjacent volumes use different diffusion gradients and therefore encode different signals.","fun_headline_variants_meta":{"raw":{"variants":["Noise your neighbor: self-supervised dMRI denoiser","Di-Fusion: one noisy volume teaches a denoiser","Denoise dMRI with a noisy sibling","No clean data? Use noisy pairs for dMRI denoising","Self-supervised diffusion denoising for dMRI, no clean data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001213,"raw_usage":{"total_tokens":5014,"prompt_tokens":986,"completion_tokens":4028,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":602,"completion_tokens_details":{"reasoning_tokens":3952}},"tokens_in":602,"tokens_out":4028,"duration_ms":27752,"temperature":1.0,"reasoning_tokens":3952,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T15:53:25.777640+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Acquire two sets of dMRI volumes: one with repeated identical diffusion-gradient acquisitions (true independent measurements of the same $y$) and one with adjacent different-gradient volumes as used in the paper, then train Di-Fusion with Eq. (9) on each. If the same-gradient pair performs markedly better, or if the different-gradient pair's denoised output is visibly biased toward the target gradient, then the shared-clean-signal assumption is the active ingredient and the Noise2Self justification is the part that matters.","supporting_citations":[],"review_version":1}