{"id":"902fc076-f144-4e76-977e-c4bc944c9f8b","arxiv_id":"2411.17196","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A flow-matching model conditioned on a data-derived 'approximate energy' generates protein ensembles matching MD simulations better than AlphaFlow and STR2STR on ATLAS.","lead":"P2DFlow is a generative model that learns to produce the full range of 3D shapes a protein adopts, using SE(3) flow matching trained on molecular dynamics simulations. It conditions generation on a data-derived 'approximate energy' and reports closer agreement with MD ground truth than AlphaFlow and STR2STR on the ATLAS benchmark.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'approximate energy' conditioner has no defined inference-time sampling procedure; using MD-derived energies at test would leak ground truth, and using a universal distribution would misguide generation for unseen proteins.","rationale":"I read the paper's central claim as: P2DFlow generates protein ensembles that match MD ground truth better than AlphaFlow and STR2STR, and this works for proteins without MD data. For that to hold, the 'approximate energy' conditioner must be obtainable at inference from the sequence alone, because that is the only input in a realistic use case (the abstract and conclusion emphasize no MD needed). The text defines approximate energy as a function of MD ensembles, but no inference-time recipe is given. The two natural readings both break the claim: using the test MD ensemble's energy distribution would be leakage, making the comparison to baselines unfair; using a non-specific distribution would mean the model is conditioned on the wrong quantity and the claimed fidelity (Table 1) is likely an artifact of training distribution overlap. The reader's weakest_assumption identifies the lack of procedure; I agree and sharpen it to the leakage/global-mismatch dichotomy. This does not require changing the verdict: the manuscript is currently not acceptable as is, but the flaw is potentially fixable by adding a sequence-based energy estimator or by re-evaluating with a carefully described sampling scheme. Hence CONDITIONAL remains appropriate (UNCHANGED).","tokens_in":9415,"tokens_out":5674,"duration_ms":51511,"concrete_test":"Run a controlled evaluation on the ATLAS test set, generating ensembles under three conditions: (a) approximate energy sampled from the target protein's ground-truth MD-derived distribution; (b) approximate energy sampled from a sequence-only estimator (e.g., a regressor predicting RG/RMSD density from the ESM-2 embedding, trained only on the training split); and (c) approximate energy drawn from a global distribution fit to training ensembles. Compare PWD J, RG J, RMWD and Weak/Transient Contacts metrics for each condition. If (a) substantially outperforms (b) and (c), the Table 1 gains depend on oracle conditioning; if (b) and (c) match (a), the paper must report the sequence-only estimator's parameters. Also report the actual sampling distribution used in the current experiments.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.2 defines 'approximate energy' per MD ensemble: project onto the RG/RMSD plane, compute Gaussian KDE density, and convert to energy via the Boltzmann equation. At inference (also Section 2.2 and Figure 2), the paper says only 'We then sample the approximate energy from Boltzmann Distribution' and keep it fixed during generation. For a test protein drawn from ATLAS, the target MD ensemble is available in principle, so the sampled distribution could be the ground-truth one. If so, the conditioner injects information about the target ensemble that AlphaFlow and STR2STR do not receive, making the Table 1 comparisons and the claim that P2DFlow works 'without MD simulations' unsupported. If instead a global or training-set Boltzmann distribution is used, there is no argument that its energies correspond to the unseen protein's conformational distribution; mismatch would push generation toward training-like energies and can explain both the fidelity gains on ATLAS and the failure to generalize. The manuscript provides no calibration procedure, no ablation on the sampling distribution, and no discussion of the train/inference discrepancy. This is the load-bearing premise of the central claim and it is unsecured.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes P2DFlow, a generative model based on SE(3) flow matching that aims to predict protein conformational ensembles from sequence. The method uses an ESMFold prediction with added Gaussian noise as a prior, and introduces an 'approximate energy' conditioning variable obtained by projecting MD ensembles onto the radius-of-gyration (RG)/RMSD plane, computing a Gaussian kernel density, and converting density to energy via the Boltzmann equation. The model is trained on the ATLAS MD dataset and evaluated on roughly 100 held-out ATLAS ensembles. The authors compare against AlphaFlow and STR2STR using validity, fidelity, and dynamics metrics, and report that P2DFlow outperforms both baselines on all metrics. They also present case studies on domain motions, PCA projections, weak and transient contacts, and RMSF profiles.","tokens_in":9699,"tokens_out":3547,"duration_ms":35086,"significance":"If the claims are substantiated, P2DFlow would be a valuable contribution: a fast, sequence-conditional generative model for protein ensembles could serve as a proxy for expensive MD simulations and would be broadly useful in structural biology and drug discovery. The paper introduces an interesting conditioning mechanism and the authors have released code. However, the current evidence is undermined by two load-bearing issues: the test-time sampling procedure for 'approximate energy' is not specified and may leak ground-truth MD information, and the baseline comparison is not controlled because AlphaFlow and STR2STR are used zero-shot rather than trained on the ATLAS training split. The absence of uncertainty quantification in the headline results further weakens the comparison. The core idea is defensible, but the manuscript needs additional experiments and analysis before the central claim can be accepted.","major_comments":[{"comment":"The 'approximate energy' conditioner is defined per MD ensemble as a function of the Gaussian KDE in the RG/RMSD plane, with density converted to energy via the Boltzmann equation. At inference, the text says only 'We then sample the approximate energy from Boltzmann Distribution' without specifying what distribution is used for a test protein. If the sampled energies are drawn from the target test protein's MD-derived distribution, then the model is conditioned with information about the ground-truth ensemble that AlphaFlow and STR2STR do not receive; this would make the Table 1 comparison unfair and directly contradict the claim that P2DFlow predicts ensembles 'without the need for expensive MD simulations.' If, instead, a training-set or global Boltzmann distribution is used, there is no argument that those energies correspond to an unseen protein's conformational distribution, and a mismatch could systematically misdirect generation. The manuscript provides no calibration procedure, no ablation of the sampling distribution, and no discussion of the train/inference discrepancy. This is the load-bearing premise of the central claim and it is unsecured.","section":"Section 2.2"},{"comment":"The baseline comparison is not controlled: P2DFlow is trained on ATLAS training ensembles, while AlphaFlow and STR2STR are evaluated using pretrained weights in a zero-shot manner. The paper states 'We use their pretrained weights offered at GitHub to sample ensembles on the test set' but does not fine-tune or train those baselines on the same ATLAS training split. Consequently, the reported improvements in Table 1 may reflect a training-domain advantage rather than an architectural or methodological advantage of P2DFlow. To support the claim that P2DFlow 'outperforms' these baselines, the authors should either train the baselines on the same ATLAS split with comparable compute, or clearly restrict the claim to the zero-shot setting and discuss the implications.","section":"Section 3.1 (Baseline)"},{"comment":"The central evaluation table reports only single point estimates for each metric, with no error bars, standard deviations, or significance tests across the approximately 100 test ensembles. Given the large variability expected across proteins, the claim that P2DFlow outperforms AlphaFlow and STR2STR on every metric is not statistically supported. Figure 3 provides histograms and fitted Gaussian curves, but these are also qualitative and lack per-protein paired comparisons. The authors should report per-protein distributions, confidence intervals, and paired significance tests (e.g., Wilcoxon signed-rank) for the main metrics.","section":"Table 1 and Figure 3"}],"minor_comments":[{"comment":"The loss in Eq. (6) is written with a 1/(1-t)^2 factor, but the text immediately after says this factor is replaced by 1/(1-min{t,0.9})^2 to prevent loss explosion. Please align the equation with the actual implementation.","section":"Section 2.1, Eq. (6)"},{"comment":"The phrase 'sample the approximate energy from Boltzmann Distribution' requires a temperature parameter and a specification of the energy function's normalization. The current description is not sufficient to reproduce the sampling procedure.","section":"Section 2.2"},{"comment":"The generation process is described as 'autoregressive sampling,' but the method solves an ODE via Euler integration and does not appear to be autoregressive in the usual sense. Please clarify or reword.","section":"Section 2.1"},{"comment":"The text mentions a 'box plot distribution' that 'further corroborates this observation,' but Figure 3 only shows histograms. Please either add the box plot or remove the reference.","section":"Section 3.2.1"},{"comment":"The paper states that ~100 ensembles were randomly chosen from ATLAS excluding the training set, but it does not specify how many distinct proteins this corresponds to or how the training/test split was defined. Please report the exact split and ensure there is no sequence-level leakage.","section":"Section 3.1"}],"recommendation":"major_revision","confidential_remarks":"The 'approximate energy' leakage issue is the most serious concern; if the authors cannot provide a test-time sampling procedure that does not rely on the target MD ensemble, the central claim of the paper should be substantially reframed. The baseline training discrepancy and lack of statistical testing are also important. The paper is not ready for publication in its current form, but the issues are potentially addressable with additional experiments and analysis. The code release is a positive factor."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the only really new ingredient here is the 'approximate energy' conditioner, and it appears to help, but the test-time procedure for that conditioner is vague in a way that could undermine the main comparison. The flaws are fixable, though, and the paper deserves a serious referee.\n\nWhat's new: 'approximate energy' is a per-ensemble quantity — project MD frames onto the RG/RMSD plane, KDE the density, convert to energy via Boltzmann. Conditioning the flow on that scalar is not in the cited literature, and the ablation shows it improves fidelity beyond the ESMFold-with-noise prior. That prior choice is a sensible, incremental improvement over Gaussian/harmonic priors, and the comparison with AlphaFlow and STR2STR on ATLAS is useful. Code is available.\n\nNow the soft spots, in proportion. The load-bearing one is the inference-time sampling of approximate energy. Section 2.2 says only 'sample from Boltzmann Distribution' and keep it fixed. For a protein in the ATLAS test set, the target MD ensemble is available in principle, so one reading is that the model is told which region of RG/RMSD space to aim for — information the baselines never receive. If instead the authors intend a universal or training-set Boltzmann distribution, there is no argument that its energies match an unseen protein's conformational distribution, and no calibration procedure. This is exactly the train/inference discrepancy the stress-test flags, and I agree it is unresolved. No ablation on the sampling distribution is reported.\n\nThe evaluation is also underpowered: no error bars or significance tests, and AlphaFlow and STR2STR are run zero-shot rather than trained on the target dataset. The 'outperforms' claim is provisional. The domain-motion case studies are illustrative but anecdotal; the PCA plots are qualitative.\n\nWho is this for: people working on learned surrogates for MD ensemble generation, who will want to read the conditioning mechanism carefully. I would send it to peer review, but I would push for major revision: specify and justify the inference-time approximate-energy sampler, and rebuild the comparison so all methods are on equal footing. If those two things are fixed, this becomes a solid methods paper.","headline":"The approximate-energy conditioner is a genuine new idea and clearly helps in the ablation, but the inference-time sampling procedure for it is underspecified, which leaves the headline comparison against zero-shot baselines open to an information-leakage critique.","tokens_in":10154,"tokens_out":2447,"would_cite":false,"duration_ms":25279,"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":"P2DFlow claims that SE(3) flow matching with an 'approximate energy' condition generates protein ensembles that resemble MD ground truth more closely than two baselines.","keywords":["protein ensembles","flow matching","SE(3) equivariance","conformational dynamics","molecular dynamics surrogate","ESMFold prior","approximate energy","equivariant graph neural network"],"falsifier":"An ablation that replaces the Boltzmann-sampled 'approximate energy' with a fixed median value, evaluated on the same ATLAS test set: if the fidelity metrics (PWD/RG Jensen-Shannon divergences, weak/transient contact Jaccard similarities) do not degrade, the conditioning dimension is not carrying the claimed work.","tokens_in":1704,"feed_emoji":"🧬","tokens_out":2552,"duration_ms":75499,"temperature":0.7,"pith_summary":"This paper claims that protein conformational ensembles can be generated by a flow-matching model that starts from perturbed ESMFold predictions and is conditioned on a scalar 'approximate energy' derived from the ensemble's density in the radius-of-gyration/RMSD plane. On roughly a hundred test proteins from the ATLAS MD dataset, the generated ensembles are closer to the ground-truth MD distributions than two current generative baselines across validity, fidelity, and contact-dynamics metrics. The method also samples both open and closed states of two well-studied multi-state proteins and reproduces residue flexibility profiles. If the result holds, P2DFlow is a fast proxy for molecular dynamics simulations of backbone ensembles.","feed_headline":"P2DFlow outmatches two baselines at protein ensemble generation","feed_subtitle":"Conditioning on an 'approximate energy' lets it reproduce open-closed transitions and weak residue contacts from MD.","key_machinery":"The machinery is SE(3) flow matching on rigid frames: the backbone of each residue is represented as a frame (rotation plus translation) in SE(3), interpolated along optimal-transport straight paths on rotations (geodesics) and translations, with the vector field learned by an equivariant network built from Invariant Point Attention and E(n)-equivariant graph neural network layers. The 'approximate energy' is a scalar condition computed from a 2D Gaussian kernel density over radius-of-gyration and RMSD, converted to an energy through the Boltzmann equation; this scalar is fed to the network to distinguish intermediate states. A strong prior, ESMFold predictions with Gaussian coordinate perturbation, provides the flow with a physically reasonable starting geometry, and a Kabsch pre-alignment plus a center-of-mass subtraction enforce equivariance. An auxiliary loss on reconstructed atom coordinates and distance matrices helps the model recover all-atom geometry.","core_discovery":"The central claim is that the distribution of protein backbone conformations from MD can be learned as a flow from a strong structural prior, ESMFold predictions with coordinate noise, to the ensemble distribution, provided the target state is labeled by an 'approximate energy'. The 'approximate energy' is obtained by projecting an MD ensemble onto a 2D plane spanned by radius of gyration and RMSD to the crystal structure, estimating the Gaussian kernel density, and converting it via the Boltzmann relation. At inference the model draws this scalar from a Boltzmann distribution and keeps it fixed as a condition while integrating the SE(3) flow. The discovery, as the authors state it, is that this extra dimension prevents the model from generating non-existent intermediate states and lets a single model reproduce observable dynamics such as weak and transient contacts, open/closed transitions, and per-residue fluctuations more accurately than the baselines.","pith_inferences":["The 'approximate energy' is defined per MD ensemble, so applying P2DFlow to a protein without MD data would require estimating the Boltzmann distribution over RG/RMSD from sequence or a single structure; the paper gives no such calibration, which limits zero-shot use.","The conditioning mechanism is testable: one could sample energies at the extremes of the training distribution and check whether the generated structures occupy the corresponding RG/RMSD regions, and whether the marginal density matches the kernel density used to define the energies.","Because the prior comes from ESMFold, the model inherits ESMFold's bias toward the predicted static structure, which is visible in the bias toward one state; this suggests ensemble coverage could be improved at the prior level, not only by autoregressive resampling.","The backbone-only design leaves side-chain conformations out; adding torsion prediction or explicit side-chain frames would be a natural extension, but the paper does not address it."],"forward_implications":["On the ATLAS test set, P2DFlow's sampled structures pass steric, bond, and Ramachandran sanity checks more often than the baselines, with steric validity at 94.1% versus 72.5% and 66.7%.","The generated ensembles have lower Jensen-Shannon divergence to MD for pairwise distances and radius of gyration, and a much lower 2-Wasserstein distance (15.2 versus 33.6 and 78.2), meaning the whole distribution, not just the average, is closer to MD.","Weak and transient contact Jaccard similarities are higher (0.710 and 0.422), indicating that the model recovers residue pairs that dissociate or associate under thermal fluctuation.","P2DFlow can populate both open and closed states of D-ribose binding protein and adenylate kinase, and an autoregressive resampling scheme with the farthest sample as a new prior expands conformational coverage.","Used as a proxy for MD, the model generates backbone ensembles in a fraction of the cost, potentially enabling ensemble-based analysis of protein function at scale."],"supporting_citations":[{"why":"Supplies the ATLAS MD simulations used for training and the roughly one hundred test ensembles used for evaluation.","marker":"[22]"},{"why":"Provides AlphaFlow, the flow-matching baseline with a harmonic prior that P2DFlow is compared against.","marker":"[21]"},{"why":"Provides STR2STR, the score-based diffusion baseline used for comparison.","marker":"[4]"},{"why":"Supplies ESMFold, whose prediction plus coordinate perturbation forms the specialized prior distribution.","marker":"[6]"},{"why":"Supplies the SE(3) flow matching details and operational settings, including frame representation and Euler integration.","marker":"[30]"},{"why":"Establishes the flow-matching objective that the model trains on.","marker":"[23]"},{"why":"Supplies the AlphaFold frame representation and the Invariant Point Attention module used in the equivariant block.","marker":"[5]"},{"why":"Supplies the E(n)-equivariant graph neural network module used to encode spatial features.","marker":"[34]"}],"fun_headline_variants":["SE(3) flow matching with energy condition yields realistic protein ensembles","P2DFlow: energy-guided flow generation of protein conformational ensembles","Outperforming baselines: P2DFlow reproduces protein dynamics from MD","Approximate energy as prior improves SE(3) flow for protein ensembles","Protein ensemble generation via SE(3) flow matching and Boltzmann prior"],"cache_read_input_tokens":12416,"weakest_assumption_plain":"The load-bearing premise is that the sampler's 'approximate energy' distribution, drawn from a Boltzmann distribution at inference, is the right conditioning for a new protein; since that energy is derived from an MD ensemble's geometry-density map, a protein without MD data has no defined way to set it.","fun_headline_variants_meta":{"raw":{"variants":["SE(3) flow matching with energy condition yields realistic protein ensembles","P2DFlow: energy-guided flow generation of protein conformational ensembles","Outperforming baselines: P2DFlow reproduces protein dynamics from MD","Approximate energy as prior improves SE(3) flow for protein ensembles","Protein ensemble generation via SE(3) flow matching and Boltzmann prior"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000288,"raw_usage":{"total_tokens":1671,"prompt_tokens":906,"completion_tokens":765,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":522,"completion_tokens_details":{"reasoning_tokens":670}},"tokens_in":522,"tokens_out":765,"duration_ms":7202,"temperature":1.0,"reasoning_tokens":670,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:23:52.629517+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"An ablation that replaces the Boltzmann-sampled 'approximate energy' with a fixed median value, evaluated on the same ATLAS test set: if the fidelity metrics (PWD/RG Jensen-Shannon divergences, weak/transient contact Jaccard similarities) do not degrade, the conditioning dimension is not carrying the claimed work.","supporting_citations":[{"cited_title":"-C.; Galochkina, T., ATLAS: protein flexibility description from atomistic molecular dynamics simulations","cited_arxiv_id":null,"evidence_quote":"Supplies the ATLAS MD simulations used for training and the roughly one hundred test ensembles used for evaluation."},{"cited_title":"The Twelfth International Conference on Learning Representations 2024","cited_arxiv_id":null,"evidence_quote":"Provides STR2STR, the score-based diffusion baseline used for comparison."},{"cited_title":"Science 2023, 379 (6637), 1123-1130","cited_arxiv_id":null,"evidence_quote":"Supplies ESMFold, whose prediction plus coordinate perturbation forms the specialized prior distribution."},{"cited_title":"T., Ben -Hamu, H., Nickel, M.; Le, M., Flow matching for generative modeling","cited_arxiv_id":null,"evidence_quote":"Establishes the flow-matching objective that the model trains on."},{"cited_title":"Nature 2021, 596 (7873), 583-589","cited_arxiv_id":null,"evidence_quote":"Supplies the AlphaFold frame representation and the Invariant Point Attention module used in the equivariant block."},{"cited_title":"G., Hoogeboom, E.; Welling, M","cited_arxiv_id":null,"evidence_quote":"Supplies the E(n)-equivariant graph neural network module used to encode spatial features."}],"review_version":1}