{"id":"3372d623-2d42-4d96-b0f8-07910d9aa9b6","arxiv_id":"2509.13916","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"A diffusion-based generative model (AMDEN) with energy-based Hamiltonian Monte Carlo refinement generates amorphous glass structures with targeted properties and low-energy relaxed states that standard denoising cannot reach.","lead":"The authors built a machine learning model, AMDEN, that generates atomic structures of glasses with desired properties such as stiffness, and they added a physics-inspired sampling step to reach relaxed low-energy states. It matters because inverse design could speed up discovery of amorphous materials for batteries, optics, and catalysis, though the current evidence comes from simulations.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim inherits unvalidated force-field ground truth; no DFT/experimental cross-check of structures or properties.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing concern: the classical force-field simulations are treated as ground truth for both structures and target properties. This is the most consequential gap because it affects every demonstration in the paper, not just a single figure. The internal evidence for AMDEN's generative capability is otherwise substantial: the systematic demonstration that standard denoising fails on relaxed structures and that HMC denoising recovers forward-trajectory noise energies and lowers physical potential energies is a real, internally coherent result. The inverse-design demonstrations on Li content, Young's modulus, shear modulus, and ring size are consistent with the model learning the training distribution. However, none of these results can be translated into a claim about real amorphous materials without an external cross-check of the force fields. The paper's own statements—that universal MLFFs are unreliable for melt-quench and that data quality is the biggest challenge—reinforce this concern. A DFT or experimental comparison on a modest subset of generated structures would be a decisive, feasible test. Since the reader already assigned a conditional verdict, my read does not change that verdict; it strengthens the rationale for requiring such a cross-check before acceptance.","tokens_in":18518,"tokens_out":12337,"duration_ms":156834,"concrete_test":"Select 15–20 generated MEG structures spanning the target modulus range, plus their requenched counterparts, and recompute Young's modulus and RDFs using a DFT-accurate surrogate (e.g., a universal ML force field benchmarked on oxides, or direct DFT for the smallest cells). Compare against the BMP-shrm values used for training/validation; if the mean modulus deviation exceeds ~15% or RDF peak positions shift by more than ~0.1 Å, the inverse design claim must be explicitly qualified as valid only within the training force field. A similar spot-check on SiO2 shear modulus/ring size against experimental or DFT data would further settle the concern.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim—that AMDEN inverse-designs amorphous materials with targeted properties—is load-bearing on the assumption that the classical MD melt-quench simulations used for training, conditioning, and validation are faithful proxies for real amorphous materials. Concretely, the MEG dataset is generated with the BMP-shrm potential, the amorphous Si datasets with Stillinger-Weber, and the SiO2 dataset with Tersoff-Munetoh (Methods IV A). All property labels (Young's modulus, shear modulus, ring size) and all structural references are computed with these same force fields. The requenching check in Fig. 2b uses the same BMP potential, so it only validates composition-to-modulus mapping within that potential, not against reality. The paper provides no DFT or experimental cross-check of bond lengths, ring statistics, or elastic moduli. The authors themselves note in the Introduction that universal ML force fields can be unreliable for high-energy melt-quench structures and that 'further validation is needed,' and in the Discussion that 'the biggest challenge' is a 'lack of high-quality training data.' If any of the three potentials misrepresents the relevant glass chemistry, AMDEN learns, conditions on, and validates against an incorrect target distribution, and the generated structures would not have the targeted properties in any real material. This is an external correctness risk, not an internal inconsistency, but it is directly load-bearing for the paper's stated goal of inverse design of amorphous materials.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces AMDEN, a diffusion-model framework for inverse design of amorphous materials. The model operates on atomic positions and element embeddings in a periodic cell, uses an equivariant graph neural network as the score backbone, and supports conditioning on macroscopic properties (Young's modulus, shear modulus) and structural features (average ring size). A 'ghost atom' mechanism is intended to control density during generation. The authors also propose an energy-based variant in which the score is obtained as the gradient of a learned noise energy E_theta, and they couple this with Hamiltonian Monte Carlo (HMC) refinement during denoising. Training and validation use three new classical-MD datasets: a multi-element glass (MEG) dataset with 11 elements, three amorphous silicon datasets with different thermal histories, and an amorphous SiO2 dataset with varied cell sizes. The paper reports that standard denoising fails to generate low-energy relaxed structures, that HMC denoising recovers energies and structures close to the training distributions, and that property-conditioned generation can adjust Young's modulus and Li content in the MEG system and shear modulus/ring size in SiO2 beyond the training range. The authors acknowledge several limitations, including the lack of high-quality training data and the reliance on classical force fields.","tokens_in":18854,"tokens_out":4036,"duration_ms":47247,"significance":"If the claims are substantiated, this would be a useful contribution to generative modeling of amorphous materials, an area where diffusion models are less mature than for crystals and molecules. The paper's strengths are the introduction of multiple new MD datasets, the explicit requenching validation for the composition-to-modulus mapping, the forward-noising ground-truth check for the noise-energy evaluation, and the interesting proposal to use HMC on the learned noise energy to counteract the rugged potential-energy-landscape problem. The 'structure-only' control of shear modulus and ring size, and the idea of generating 'forbidden glasses,' are conceptually valuable. However, the quantitative evidence is currently incomplete: key figures lack error bars and correlation metrics, main plots exclude a disclosed subset of samples, there is no comparison against published baselines, and the entire framework inherits the accuracy of the classical force fields with no independent DFT or experimental cross-check. The paper also does not yet provide code or trained models, so reproducibility cannot be assessed.","major_comments":[{"comment":"The main plots in Fig. 4 include only perfectly charge-balanced samples, while unbalanced samples are relegated to Supp. Fig. S3. The text reports mean absolute charge errors (0.0025 e and 0.0096 e per atom) but does not report the fraction of generated samples excluded, nor the R²/MAE for the correlations, nor error bars. Because the central claim is that AMDEN adjusts shear modulus and ring size purely through structure, this selection could bias the apparent correlation. Please report the yield of charge-balanced samples, the metrics for all generated samples, and the metrics with and without the charge-balance filter.","section":"§II E, Fig. 4"},{"comment":"The inverse-design result for the MEG dataset is described qualitatively as 'decent correlation' and 'within few percent' Li content, but no quantitative metrics (R², MAE, standard error) or error bars are given. The requenching comparison uses the same BMP potential as the training data, so it validates composition-to-modulus mapping only within that potential. Moreover, no comparison is made to existing generative models for amorphous materials, such as the diffusion model of Yang & Schwalbe-Koda (2025) or earlier GAN/VAE approaches. Please add numerical error metrics, confidence intervals, and a baseline comparison so the reader can assess whether AMDEN improves over the state of the art.","section":"§II B, Fig. 2"},{"comment":"The HMC refinement is validated against forward noising trajectories of the same model and against potential energies computed with the same Stillinger-Weber potential used for training. This is a self-consistency check, not an independent validation. More importantly, the comparison between standard denoising and HMC denoising is confounded by compute budget: standard denoising uses n=200 steps, while HMC denoising uses n=2000 steps and sets wcond=0. The reported improvement may come from the larger number of diffusion steps, the absence of CFG, or the HMC sampling itself. Please include an ablation with standard denoising at 2000 steps, and report HMC acceptance rates and wall-clock cost. A comparison to a short MD relaxation (as used in prior work) would also clarify the contribution of HMC.","section":"§II D and §IV B 4"},{"comment":"The entire pipeline—training data, property labels, and validation—is based on classical force fields (BMP-shrm for MEG, Stillinger-Weber for a-Si, Tersoff-Munetoh for SiO2). The paper itself notes that universal ML force fields can be unreliable for high-energy melt-quench structures and that 'the biggest challenge' is a lack of high-quality training data, yet the title and abstract claim inverse design of amorphous materials without qualification. No DFT or experimental cross-check is provided for any generated structure, RDF, ring statistic, or elastic modulus. This is an external-correctness risk. Please either add DFT validation of a representative subset of generated samples (e.g., RDFs and elastic moduli for a few MEG and SiO2 structures) or explicitly reframe the claims as 'in silico inverse design within the accuracy of the chosen force fields.'","section":"§IV A and Discussion"},{"comment":"The ghost atom mechanism is described as enabling density control, but the paper never quantitatively evaluates whether the target density is achieved. No results show achieved versus target density, and it is unclear how the ghost fraction interacts with property conditioning. Since density is a physically important variable, particularly for shear modulus, please report the achieved densities for the generated MEG and SiO2 samples, or state explicitly if density was not controlled in those experiments.","section":"§II A and Fig. 1"}],"minor_comments":[{"comment":"The figure has panels a–f, but the text refers to panel 'e' for noise energy and panel 'd' for potential energies; the caption and in-text references should be checked for consistency. Also, the RDF panels in a and c have the same x-axis and y-axis labels but different data; consider adding legends and clarifying the line styles.","section":"Fig. 3"},{"comment":"The learnable scale factor γ is said to balance position-based and atomic energies, but no initialization, regularization, or final value is given. Please provide these details, since the magnitude of γ directly affects the score and the HMC dynamics.","section":"Eq. (21)"},{"comment":"The Metropolis–Hastings acceptance criterion is written in terms of total energy E_tot, which includes momenta. It would be helpful to state explicitly that momenta are refreshed after each acceptance/rejection and that only positions are updated, and to clarify whether element embeddings are also updated during HMC.","section":"Eq. (24)"},{"comment":"After Eq. (19), the text states 'kB × T = 1' but does not define the separate values of kB and T. Since these are arbitrary normalization constants, a single constant would be clearer and would avoid confusion with the physical Boltzmann constant.","section":"§IV B 4"},{"comment":"The paper states that source code and training data 'will be made available upon final publication.' For a computational methods paper, it would be preferable to provide at least trained model checkpoints and dataset statistics in a repository or supplement during the review process, to enable independent verification of the central claims.","section":"Data Availability"},{"comment":"Several references are preprints or lack page numbers (e.g., [35], [17], [20], [33]). If final versions are available, they should be updated; otherwise, the preprint status should be explicitly noted.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is a serious contribution to a timely topic, and the authors are transparent about many limitations. My main concern is not the internal logic but the gap between the strength of the claims ('inverse design of amorphous materials with targeted properties') and the quantitative evidence provided. The lack of error bars, R²/MAE, baseline comparisons, and the selective inclusion of charge-balanced samples in Fig. 4 are fixable with additional analysis. The force-field ground-truth concern is inherent to the simulation-based approach, but the authors should either add DFT spot-checks or soften the generality of their claims. The HMC ablation is important because the current comparison conflates the HMC algorithm with longer sampling and different guidance settings. I recommend major revision rather than rejection, as the core ideas and datasets are valuable and the load-bearing issues appear addressable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a solid, honest methods paper, and the most useful part is the systematic failure analysis of standard denoising on relaxed amorphous structures. The HMC-refinement variant is a genuine modification over prior diffusion work on glasses, and the ghost-atom mechanism for density control is simple and effective. The paper's own discussion concedes the training-data problem, which is the right thing to do, and it should be read as proof-of-concept for the generative machinery rather than as a direct path to experimental inverse design.\n\nWhat's new and good: the energy-based score—where the network predicts a scalar noise energy and the score comes from backprop—combined with HMC steps during reverse diffusion is a real contribution. The demonstration that standard denoising fails to reproduce annealed a-Si structures and that HMC fixes both the energy and the RDFs is convincing. The MEG, a-Si, and SiO2 datasets are useful resources, assuming they become public. The inverse design on Young's modulus and Li content is suggestive; the requenching check is a nice independent validation within the same force field.\n\nSoft spots: Fig. 4 only shows charge-balanced samples, which overstates the design capability; the main text needs the MAE or R2 for all samples, and a justification for the exclusion. There are no error bars anywhere, and no quantitative comparison against existing generative models for amorphous materials (e.g., ref 35). The extrapolation claims—larger cells, properties beyond the training range—rest on a few samples and should be softened. The bigger issue is the force-field ground truth: all training and validation uses BMP, Stillinger-Weber, and Tersoff-Munetoh potentials, and the requench check uses the same potential, so it validates the model's ability to match the force-field's composition-property mapping, not reality. The authors acknowledge this and call for better data, which is fine, but the framing sometimes overreaches.\n\nThe paper deserves a serious referee. The core claims about generation quality and HMC refinement are internally supported, and the limitations are mostly disclosed. A referee should push for full data and code release, error bars and goodness-of-fit statistics, inclusion of unbalanced samples, and at least one baseline comparison. A DFT cross-check on a handful of generated structures would also go a long way toward addressing the force-field concern.","headline":"A serious methods paper with two genuinely new ideas—HMC-refined energy-based denoising and ghost-atom density control—but the claims are only validated within classical force-field MD, so treat the inverse-design results as proof-of-concept, not as a recipe for real glasses.","tokens_in":19387,"tokens_out":1891,"would_cite":true,"duration_ms":23524,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["61.43.-j","62.20.de","02.70.Ns"],"model":"deepseek-v4-flash","headline":"This paper claims that a diffusion model trained on simulated amorphous structures can generate new glassy atomic configurations conditioned on target properties, and that adding Hamiltonian Monte Carlo refinement to the denoising step is w","keywords":["inverse design","amorphous materials","diffusion model","Hamiltonian Monte Carlo","glass","generative model","equivariant graph neural network","melt-quench simulation"],"falsifier":"Relax AMDEN-generated structures for a fixed composition with a quantum-mechanical (e.g., density functional theory) relaxation and compare energies and pair distribution functions to the same treatment of melt-quench reference structures; if the generated samples systematically relax to different energies or moduli, the claim that HMC denoising reaches the correct low-energy basin fails. Alternatively, train on a small atomic cluster whose ground-state structure is independently known and check whether HMC denoising finds that known minimum.","tokens_in":18352,"feed_emoji":"⚛️","tokens_out":4499,"duration_ms":51556,"temperature":0.7,"pith_summary":"The paper introduces AMDEN, a diffusion model that generates atomic structures of amorphous materials conditioned on target properties such as Young's modulus, lithium content, shear modulus, and ring size. Its central claim is that standard denoising cannot reach the low-energy relaxed structures typical of slow-cooled glasses, so the authors add an energy-based score function refined with Hamiltonian Monte Carlo steps during generation. The work also provides three amorphous datasets (multi-element glass, amorphous silicon with three thermal histories, and amorphous silica) to train and test the method. If the claims hold, inverse design of glasses becomes possible at the atomic level, including structures that standard melt-quench simulations cannot produce.","feed_headline":"Diffusion model generates glasses with targeted stiffness","feed_subtitle":"Energy-aware denoising reaches relaxed structures that ordinary diffusion misses.","key_machinery":"The central object is AMDEN's score-based diffusion process over atomic positions and element embeddings, with an equivariant graph neural network as the score function. The novel piece is the energy-based variant: instead of predicting noise directly, the network outputs a scalar 'noise energy' per atom; the score is its gradient, and Hamiltonian Monte Carlo steps on that energy are inserted between denoising iterations. This lets the generator equilibrate on the learned distribution and cross barriers that standard denoising cannot, which is what enables relaxed low-energy structures. A 'ghost atom' class controls atomic density without breaking equivariance.","core_discovery":"AMDEN learns the distribution of amorphous atomistic structures from classical molecular dynamics melt-quench simulations using a score-based diffusion process with an equivariant graph neural network. It generates atomic positions and element types, and a 'ghost atom' mechanism lets it adjust density. The paper's key finding is that the standard denoising trajectory reproduces melt-like structures well but fails to produce annealed low-energy structures; a variant that predicts a scalar 'noise energy' and interleaves Hamiltonian Monte Carlo steps during denoising recovers the low-energy structures, with radial distribution functions and potential energies close to training data. On the mult","pith_inferences":["If the same HMC-refinement scheme were applied to models trained on quantum-mechanical or experimental data, it might correct some of the classical force-field bias; the paper does not test this.","The failure of standard denoising on glassy landscapes suggests a general limitation of diffusion models on rough energy landscapes, not just a flaw of this architecture; the authors hint at this through a spin-glass analogy.","The fixed-cell diffusion process, combined with ghost-atom density control, could be extended to variable cell volumes or open-boundary conditions to target pressure-dependent properties, though the paper does not explore that.","Ring-size conditioning on small training cells may allow targeted generation of medium-range order features, enabling systematic study of structure-property relationships in disordered materials beyond current simulation workflows."],"forward_implications":["AMDEN can adjust the Young's modulus of generated multi-element glasses while keeping lithium content within a few percent of the targeted value.","Requenched compositions from AMDEN match target moduli better than the raw generated structures, indicating that structural inaccuracy is the dominant source of error.","Standard denoising cannot generate low-energy relaxed amorphous structures; energy-based HMC refinement recovers energy and structure matching the training data for slow-cooled samples.","On fixed-composition silica, conditioning on shear modulus and average ring size produces samples beyond the training range at larger cell sizes, enabling structure-only property control.","The approach opens the route to generating 'forbidden glasses' whose structural features cannot be obtained by traditional melt-quench procedures."],"fun_headline_variants":["Energy-aware diffusion generates low-energy glass structures","Diffusion plus Monte Carlo designs amorphous materials with targeted traits","Diffusion model overcomes limit to yield relaxed glass states","AMD: inverse design of amorphous materials via energy refinement","Energy-aware denoising reaches structures standard diffusion misses"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The training data come from classical force-field melt-quench simulations, so if those potentials misrepresent the real atomic structures or elastic properties of glasses, everything AMDEN learns and validates is offset from reality.","fun_headline_variants_meta":{"raw":{"variants":["Energy-aware diffusion generates low-energy glass structures","Diffusion plus Monte Carlo designs amorphous materials with targeted traits","Diffusion model overcomes limit to yield relaxed glass states","AMD: inverse design of amorphous materials via energy refinement","Energy-aware denoising reaches structures standard diffusion misses"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000555,"raw_usage":{"total_tokens":2468,"prompt_tokens":721,"completion_tokens":1747,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":465,"completion_tokens_details":{"reasoning_tokens":1671}},"tokens_in":465,"tokens_out":1747,"duration_ms":15734,"temperature":1.0,"reasoning_tokens":1671,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T16:27:23.779004+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Relax AMDEN-generated structures for a fixed composition with a quantum-mechanical (e.g., density functional theory) relaxation and compare energies and pair distribution functions to the same treatment of melt-quench reference structures; if the generated samples systematically relax to different energies or moduli, the claim that HMC denoising reaches the correct low-energy basin fails. Alternatively, train on a small atomic cluster whose ground-state structure is independently known and check whether HMC denoising finds that known minimum.","supporting_citations":[],"review_version":1}