{"id":"7163db94-331d-4f8f-a471-a22783dbc092","arxiv_id":"2504.21092","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"ProT-GFDM swaps Brownian motion for fractional Brownian motion in a score-based diffusion model and reports small gains in density, coverage, and FID when generating 32-residue Cα distance maps.","lead":"This paper applies a fractional Brownian-motion diffusion model to generate protein backbone distance maps and reports small metric gains over a standard diffusion baseline. A generalist might read it to see whether replacing ordinary Brownian noise with fractional, memory-carrying noise helps generative models capture long-range structure in proteins.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline gains rest on a single run of the best of 12 post hoc FVP configurations; without seeds or error bars, the 7.19% density and 5.66% coverage differences are not distinguishable from run-to-run noise.","rationale":"I reviewed the full text. The central empirical claim rests on Table 4: one VP baseline run against one FVP run at H=0.8,K=3, with the winning configuration selected from 12 variants. The paper reports no seeds, no variance, no baseline tuning details, and no code or data. The mathematical framework is coherent in broad outline, following the GFDM construction with an augmented OU system, so the weakness is not the fractional-diffusion derivation itself. I agree with the reader that the load-bearing issue is statistical robustness rather than a fundamental mathematical flaw. The paper's own solver ablation (Tables 6-7) shows that pure sampling choices move density by up to 0.106 and FID by about 0.8, bracketing the claimed fractional-dynamics gain, so the attribution to replacing Brownian motion with MA-fBm needs a controlled multi-seed comparison. I also note a secondary internal inconsistency: in Eq. (17), for a Gaussian with covariance matrix Sigma_y^t, the score is -(Sigma_y^t)^{-1}Y, not -Sigma_y^t Y as written; this should be corrected or clarified because it affects the implemented augmented sampler if used as written. Because the reader already conditions acceptance on multi-seed evaluation and reporting of configuration selection, I recommend keeping the verdict conditional, i.e., UNCHANGED from the reader's assessment.","tokens_in":22598,"tokens_out":10629,"duration_ms":115092,"concrete_test":"Re-run Table 4 with 5-10 independent seeds per configuration under identical training budget, dataset, and U-Net, reporting per-seed density, coverage, and FID with a fixed k and the same 12,000 test samples. Then compute the paired difference between VP baseline and H=0.8,K=3 with a bootstrap 95% CI, and also correct for post hoc selection by recording the maximum FVP-vs-VP gap across all 12 configurations. If the CI includes zero or the selection-corrected max gap is not significant, the abstract's percentage gains are not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing evidence for the abstract's 'outperforms' claim is Table 4, which compares one VP-SDE baseline run with one FVP run at H=0.8, K=3. The paper reports no seeds, no standard deviations, and no baseline tuning history. The chosen configuration is the best of 12 FVP variants (H in {0.2,0.5,0.8}, K in {2,3}, linear/cosine), and the abstract's numbers are exactly the post hoc maximum on the test set; selection among 12 configurations inflates the expected gap even under a true null. In addition, the paper's own Tables 6-7 show that changing only the discretization/solver moves density from 1.118 to 1.224 and FID from 74.614 to 73.8, effects as large as or larger than the claimed 7.19%/1.01% gains, so the causal attribution to fractional dynamics is not isolated unless the VP baseline is re-run under the same solver and selection protocol.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript applies the generative fractional diffusion model (GFDM) framework of [26] to generate 32-residue Cα distance maps. The forward dynamics replace Brownian motion with a Markov approximation of fractional Brownian motion governed by the Hurst index H and K Ornstein-Uhlenbeck processes; experiments vary H in {0.2, 0.5, 0.8}, K in {2, 3}, linear and cosine noise schedules, and several SDE/ODE solvers, comparing density, coverage, and FID against a single variance-preserving SDE (VP-SDE) baseline. The abstract claims a 7.19% density increase, a 5.66% coverage increase, and a 1.01% FID reduction relative to that baseline. Sections 2 through 4.3 restate the ScoreSDE and GFDM derivations from prior work; Section 5 contains the empirical study.","tokens_in":22807,"tokens_out":4951,"duration_ms":48423,"significance":"If the reported gains were reproducible and robust, the paper would demonstrate a useful application of fractional dynamics to protein backbone generation and would provide evidence that superdiffusive noise helps capture long-range dependencies in Cα distance maps. The theoretical framework is not new: Sections 4.1 through 4.3 closely follow [26], so the paper's own contribution is the empirical evaluation. No code, trained models, or seed-level results are provided, so the reproducibility of the headline claim cannot currently be assessed. The empirical comparison to a VP-SDE baseline is a reasonable first step, and the claims are falsifiable, but the evidence as reported is not yet sufficient to establish that ProT-GFDM 'outperforms conventional score-based models.'","major_comments":[{"comment":"The headline comparison rests on single-run measurements without seeds or error bars. The chosen configuration H=0.8, K=3 is the best of the 12 FVP variants evaluated on the test metrics, and no baseline tuning history is given. Under selection among 12 configurations, the expected gap from a baseline can inflate even under a true null hypothesis, so the reported 7.19% density gain and 5.66% coverage gain are not distinguishable from run-to-run noise as presented.","section":"Section 5, Table 4"},{"comment":"The claimed fractional-dynamics effect is not isolated from solver and schedule choices. Within the same fractional model at H=0.8, K=3, changing the solver from Euler-Maruyama to the PC sampler changes density from 1.118 to 1.224 (Table 6), which is a larger swing than the 7.19% gain attributed to fractional dynamics; RK45 at 1000 steps yields FID 73.8 (Table 7), below the headline 74.614. Additionally, Table 5 reports FID 73.452 for cosine H=0.2, K=3, contradicting the text following Table 4 that H=0.8, K=3 achieves the lowest FID. The causal attribution to H therefore requires re-running the VP baseline under the same solver, schedule, and selection protocol with repeated seeds.","section":"Section 5, Tables 6 and 7"},{"comment":"The conclusion that 'higher H generally improves density and coverage in both noise schedules' is contradicted by Table 5: for the cosine schedule, density at H=0.5 is lower than at H=0.2 for both K=2 (0.799 versus 0.960) and K=3 (0.832 versus 0.960). The statement that increasing K from 2 to 3 'does not significantly affect density' is also contradicted by Table 4 for the linear schedule at H=0.8 (density 1.0142 versus 1.118) and by Table 5 for the cosine schedule at H=0.5 (0.799 versus 0.832). The narrative should be revised to match the tabulated numbers.","section":"Section 6, Conclusion"},{"comment":"The evaluation is limited to distributional metrics on 32x32 Cα distance maps with a single VP-SDE baseline; no comparison is made with other protein generative models, and no structural validity check (e.g., reconstruction of 3D coordinates, Ramachandran statistics, or designability) is reported. As a result, the title-level claim of 'protein generation' is supported only indirectly. At minimum, the paper should either add such validation or soften the claims accordingly.","section":"Section 5, Evaluation metrics and dataset"}],"minor_comments":[{"comment":"The notation 'Y[K] t := (Y1 1,..., YK t )' appears to contain typos; the stacked vector should likely be (Y^1_t, ..., Y^K_t). The weights written as 'ηk t,...,η k t' are also ambiguous and should be defined more carefully.","section":"Section 4.3"},{"comment":"The text says 'Coverage is not normalized' and then immediately says 'Coverage is bounded between 0 and 1'; the formula in Table 3 is a normalized average of indicators, so this contradiction should be resolved.","section":"Section 5, Table 3 and surrounding text"},{"comment":"The paper introduces NFEs as a measure of computational cost but never reports NFE values in the solver comparison tables; reporting NFEs alongside the iteration counts would make the efficiency comparison meaningful.","section":"Section 5, Tables 6 and 7"},{"comment":"The dataset description does not mention redundancy reduction or sequence-identity splitting between training and test sets; homologous chains across splits could inflate all reported metrics and should be addressed or documented.","section":"Section 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is an application of an existing GFDM framework [26]; its novelty is empirical, and the empirical evidence is currently too fragile because of single runs, post hoc configuration selection, and the absence of baseline tuning details. I would not recommend rejection if the authors provide multi-seed results with error bars, correct the internal contradictions in Tables 4-7, and re-run the baseline under the same solver and selection protocol. Given the journal's q-bio scope, the paper would also be strengthened by releasing code and trained models."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nHere's my take on 2504.21092. The core theoretical machinery is not new: equations (9)-(19) are the GFDM framework of [26] restated with light notation changes, and the same group already applied fractional Lévy-Itô diffusion to protein generation in [25]. What is new is the specific application to 32-residue Cα distance maps and a systematic-looking scan over Hurst index, number of OU processes, noise schedule, and solver. The paper is clearly written and the math sections appear faithful to the prior work; I see no obvious derivation errors.\n\nThe problems are empirical. The abstract's claim that ProT-GFDM 'outperforms conventional score-based models' rests on Table 4, which compares one VP-SDE baseline run with one FVP run at H=0.8, K=3. No seeds, no standard deviations, no baseline tuning history. The chosen configuration is the best of 12 FVP variants (H in {0.2,0.5,0.8}, K in {2,3}, linear/cosine) — the abstract's numbers are the post hoc maximum on the test set. Selecting among 12 configurations inflates the expected gap even under a true null. Worse, Tables 6-7 show that changing the solver moves density from 1.118 to 1.224 and FID from 74.614 to 73.8, effects as large as or larger than the claimed 7.19%/1.01% gains, so the causal attribution to fractional dynamics is not isolated unless the VP baseline is re-run under the same solver and selection protocol.\n\nI also note the density/coverage metrics require a k value for nearest neighbors and the paper never reports it. No code or data are released. The authors do acknowledge that the cosine schedule does not consistently improve performance and that the schedule-sampler interaction is unclear, which is honest but further undercuts the single-number headline.\n\nWhere I think the reader's assessment is right: the central mathematical argument holds up; this is an application, not a circular derivation. Where I'd be slightly more charitable: the experimental design covers a wider range of configurations than the abstract suggests, and the underlying framework is legitimate. But as it stands, the evidence does not support 'outperforms' — it supports 'one configuration of a known method gives promising-looking numbers on a small test set.'\n\nWho is this for? Someone tracking fractional diffusion methods in generative modeling, or a protein-generative-modeling group wanting to see the approach applied to Cα distance maps. It deserves a serious referee — the topic is relevant and the flaws are fixable — but I would condition acceptance on multi-seed evaluation with error bars, pre-registered or held-out configuration selection, comparison with at least one modern protein generation baseline, and release of code, data identifiers, and the k value used in density and coverage.\n\nRecommendation: engage with it, but require the empirical fixes before believing the headline.","headline":"A competent application of an existing fractional diffusion framework to protein fragment distance maps, but the headline 'outperforms' claim rests on single-run comparisons with no error bars.","tokens_in":23352,"tokens_out":2272,"would_cite":false,"duration_ms":20505,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["60G22","60H10"],"pacs":[],"model":"deepseek-v4-flash","headline":"ProT-GFDM claims that swapping Brownian motion for a Markov approximation of fractional Brownian motion in a score-based diffusion model improves 32-residue protein backbone generation, raising density by 7.19% and coverage by 5.66%.","keywords":["fractional Brownian motion","score-based generative models","protein generation","alpha-carbon distance maps","Markov approximation of fBm","Hurst index","diffusion SDE","protein backbone modeling"],"falsifier":"Re-run the baseline and ProT-GFDM ($H=0.8$, $K=3$) on the same data split with multiple random seeds and report the distributions of density, coverage, and FID; the central claim fails if the 7.19% density and 5.66% coverage advantages collapse into overlapping error bars or reverse.","tokens_in":22373,"feed_emoji":"🧬","tokens_out":14246,"duration_ms":133485,"temperature":0.7,"pith_summary":"The paper argues that the stochastic process driving a score-based diffusion model does not have to be Brownian motion. It substitutes a Markov approximation of fractional Brownian motion—noise with positively correlated increments when the Hurst index $H$ exceeds $1/2$—so the forward process can carry long-range dependencies through protein structures. Tested on 32-residue alpha-carbon distance maps, the model reports a 7.19% gain in density (fidelity), a 5.66% gain in coverage (diversity), and a 1.01% improvement in the Fréchet inception distance over a standard score-based baseline. If the comparison holds, fractional driving noise becomes a practical lever for structure generation rather than a mathematical curiosity.","feed_headline":"Fractional noise beats Brownian motion in protein diffusion generation","feed_subtitle":"The paper reports a 7.19% density gain and a 5.66% coverage gain on 32-residue protein backbone maps.","key_machinery":"The central object is MA-fBm, the Markov approximation of fractional Brownian motion: a weighted sum of $K$ Ornstein–Uhlenbeck processes with geometrically spaced mean-reversion speeds, with weights chosen to minimize the $L^2$ approximation error to true fractional Brownian motion. It replaces the Brownian driver in the forward SDE, injecting long-range dependence controlled by the Hurst index $H$ while keeping the system finite-dimensional and Markovian, so the reverse-time SDE and probability-flow ODE remain tractable. The score is learned on the augmented state $(X, Y^1, \\dots, Y^K)$ by augmented score matching.","core_discovery":"The paper's central claim is that a fractional diffusion model built on a Markov approximation of fractional Brownian motion (MA-fBm) generates protein backbone structures better than a conventional Brownian-driven diffusion model. On 32-residue $\\alpha$-carbon ($C_\\alpha$) distance maps with $H=0.8$ and $K=3$ Ornstein–Uhlenbeck terms, ProT-GFDM reports density 1.118 versus 1.043 for the variance-preserving SDE baseline, coverage 0.934 versus 0.884, and Fréchet inception distance 74.614 versus 75.368. The paper also claims that the choice of noise schedule and solver changes the trade-off: the cosine schedule reaches its best FID (73.452) at low $H$ with $K=3$, the linear schedule gives the highest density and coverage at $H=0.8$, and among samplers the predictor-corrector SDE and the adaptive RK45 ODE give the best quality at 1,000 steps.","pith_inferences":["If the reported gains reproduce across independent training runs, fractional driving noise should transfer to other structured outputs with long-range correlations, such as RNA backbones or small-molecule conformer ensembles, though the paper tests only 32-residue protein fragments.","The paper fixes $H$ at 0.2, 0.5, and 0.8, but a data-driven estimate of the Hurst index from each training set could outperform either preset and make the method adaptive.","The noise-schedule crossover suggests that $H$, $K$, the schedule, and the solver interact; a joint selection rule for these four choices may yield larger gains than any single best setting reported."],"forward_implications":["With a linear noise schedule, $H=0.8$ and $K=3$ is the best configuration tested, so superdiffusive noise is the setting to copy for similar protein tasks.","The cosine schedule changes the picture: it reaches a lower FID at $H=0.2$ and $K=3$ than any linear-schedule run, so the best Hurst index depends on the noise schedule.","Solver choice matters as much as the driving noise: predictor-corrector sampling at 1,000 steps gives the best SDE results, and adaptive RK45 at 1,000 steps gives the best ODE results.","Raising $K$ from 2 to 3 and doubling solver steps from 1,000 to 2,000 produce only marginal or inconsistent gains, so the fractional model's advantage does not depend on extra compute."],"supporting_citations":[{"why":"Defines the score-based SDE framework and probability-flow ODE that the model generalizes and that supplies the baseline family.","marker":"[21]"},{"why":"Introduces the DDPM/variance-preserving formulation used as the Brownian baseline and the linear noise schedule.","marker":"[22]"},{"why":"Supplies the generative fractional diffusion model and the Markov approximation of fBm that ProT-GFDM adapts to proteins.","marker":"[26]"},{"why":"Establishes the affine representation of fractional processes that underlies the Markov approximation.","marker":"[27]"},{"why":"Provides the practical scheme for choosing approximation coefficients and for estimating the Hurst index.","marker":"[28]"},{"why":"Introduces the cosine noise schedule tested as an alternative to linear scheduling.","marker":"[29]"},{"why":"Gives the reverse-time diffusion equation result that justifies the reverse SDE and probability-flow ODE machinery.","marker":"[30]"},{"why":"Establishes the alpha-carbon pairwise distance map as a rotation- and translation-invariant protein representation for generative models.","marker":"[47]"}],"fun_headline_variants":["Fractional diffusion outdoes Brownian in protein generation","Superdiffusive model improves protein backbone density by 7%","Fractional diffusion: 7.19% density boost for protein maps","Long-range protein dependencies captured by fractional diffusion","Fractional diffusion boosts protein coverage by 5.66%"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The comparison rests on the assumption that the standard score-based baseline was run under equivalent conditions and that the reported metric gaps are not random run-to-run noise, since the paper reports no seeds, error bars, or baseline tuning details.","fun_headline_variants_meta":{"raw":{"variants":["Fractional diffusion outdoes Brownian in protein generation","Superdiffusive model improves protein backbone density by 7%","Fractional diffusion: 7.19% density boost for protein maps","Long-range protein dependencies captured by fractional diffusion","Fractional diffusion boosts protein coverage by 5.66%"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00146,"raw_usage":{"total_tokens":5870,"prompt_tokens":932,"completion_tokens":4938,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":548,"completion_tokens_details":{"reasoning_tokens":4856}},"tokens_in":548,"tokens_out":4938,"duration_ms":36762,"temperature":1.0,"reasoning_tokens":4856,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:13:56.725516+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the baseline and ProT-GFDM ($H=0.8$, $K=3$) on the same data split with multiple random seeds and report the distributions of density, coverage, and FID; the central claim fails if the 7.19% density and 5.66% coverage advantages collapse into overlapping error bars or reverse.","supporting_citations":[{"cited_title":"Score-based gen- erative modeling through stochastic differential equations","cited_arxiv_id":null,"evidence_quote":"Defines the score-based SDE framework and probability-flow ODE that the model generalizes and that supplies the baseline family."},{"cited_title":"Denoising diffusion probabilistic models","cited_arxiv_id":null,"evidence_quote":"Introduces the DDPM/variance-preserving formulation used as the Brownian baseline and the linear noise schedule."},{"cited_title":"Affine representations of fractional processes with appli- cations in mathematical finance","cited_arxiv_id":null,"evidence_quote":"Establishes the affine representation of fractional processes that underlies the Markov approximation."},{"cited_title":"Variational inference for SDEs driven by fractional noise","cited_arxiv_id":null,"evidence_quote":"Provides the practical scheme for choosing approximation coefficients and for estimating the Hurst index."},{"cited_title":"Improved denoising diffusion probabilistic models","cited_arxiv_id":null,"evidence_quote":"Introduces the cosine noise schedule tested as an alternative to linear scheduling."},{"cited_title":"Reverse-time diffusion equation models","cited_arxiv_id":null,"evidence_quote":"Gives the reverse-time diffusion equation result that justifies the reverse SDE and probability-flow ODE machinery."},{"cited_title":"Generative modeling for protein structures","cited_arxiv_id":null,"evidence_quote":"Establishes the alpha-carbon pairwise distance map as a rotation- and translation-invariant protein representation for generative models."}],"review_version":1}