{"id":"462ddb2c-3504-4ee8-98df-ac562c9b3a3c","arxiv_id":"2412.04242","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"LMDM combines a latent equivariant autoencoder with local and global denoising networks plus a stochastic control variable, reporting improved metrics on QM9 and GEOM-Drug.","lead":"This paper introduces LMDM, a latent diffusion model that generates 3D molecules by adding and removing noise in a learned latent space instead of on atomic coordinates. The authors claim higher validity and diversity than EDM and GeoLDM, but the preprint lacks code, complete baseline values, and error bars.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sign error in Algorithm 2 line 9: z_{t-1} adds the predicted score/noise term instead of subtracting it, which would prevent denoising and invalidate the reported results unless the displayed algorithm is a typo.","rationale":"The reader correctly rejects the paper for incomplete evidence and missing code. I sharpen the concern to a specific internal inconsistency: the reverse sampling update in Algorithm 2 line 9 has the wrong sign relative to the training objective and the standard DDPM derivation in Appendix A. This is not a matter of outside consensus; it is an internal contradiction. If the plus sign is literal, the sampler diverges from the data manifold. If it is a typo, the paper does not describe the method that produced the numbers. Either way, the central empirical claim is not supported by the manuscript. The latent-radius calibration issue raised by the reader is also valid but secondary, since it affects only the local/global edge split rather than the core reverse process. I therefore agree with the REJECT verdict and recommend no change.","tokens_in":20048,"tokens_out":2444,"duration_ms":24529,"concrete_test":"Re-derive the reverse update from the published training objective: since s_theta learns grad log q(zt|z0) = -epsilon/sqrt(1-balpha_t), the reverse mean should be z_{t-1} = (1/sqrt(alpha_t)) [z_t - beta_t s_theta]. Compare this to Algorithm 2 line 9. Then run a minimum sanity check: a 10k-step DDPM on QM9 with the plus sign will typically fail to produce valid molecules; with the minus sign it will recover the Table 1 ballpark. If the authors supply code, run their sampling loop directly and check the sign of the score term.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's central claim is that LMDM outperforms EDM and GeoLDM on QM9 and GEOM-Drug. The decisive load-bearing issue is internal inconsistency in the reverse sampling update. Algorithm 2 line 9 sets z_{t-1} = (1/sqrt(1-beta_t)) [z_t + (beta_t/sqrt(1-balpha_t)) s_theta]. With alpha_t = 1 - beta_t, this has a plus sign before the score term. In the standard DDPM derivation (Appendix A, Eq. (19)), mu_theta = (1/sqrt(alpha_t)) [z_t - (beta_t/sqrt(1-balpha_t)) epsilon_theta]. The predicted noise must be subtracted; a plus sign moves the iterate away from the data manifold. The same training objective (Eq. (11), Algorithm 1 line 27) trains s_theta to match grad log q(zt|z0), which is proportional to -epsilon; so the consistent reverse step requires a minus sign. If the manuscript's formula is literal, the sampler cannot generate valid molecules; if it is a typo, the paper misdescribes its own method. Since no code or checkpoints are released, the reader cannot tell which. This is more load-bearing than the latent-radius calibration issue because it breaks the reverse process itself, not just the edge construction. The paper has other manuscript-quality problems (duplicated text, unfinished references, missing Table 1 entries), but the sign error is the single most decisive internal flaw. The abstract's claimed 4.8%/30.2% improvements and Table 1 numbers therefore lack a coherent algorithmic basis as presented.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes LMDM, a latent diffusion model for 3D molecule generation. A variational autoencoder with equivariant encoders/decoders maps molecular point clouds into latent variables, and a dual equivariant score network models local edges (within a 2 Å radius) and global edges separately, with the intent of capturing covalent and van der Waals interactions. A stochastic control variable is injected at every reverse step to promote diversity. The authors report unconditional generation results on QM9 and GEOM-Drug showing improvements over EDM and GeoLDM, and conditional generation results on QM9 for six properties.","tokens_in":20380,"tokens_out":9630,"duration_ms":86757,"significance":"If the reported gains hold, LMDM would be a useful contribution to 3D molecular generation: the latent-space approach with explicit local/global edge modeling is timely, and the two-stage training and the control variable are reasonable design choices. However, the manuscript as presented does not support the central claim. The sampling algorithm is internally inconsistent with the training objective, the baseline comparison table is incomplete, and the experimental evaluation lacks statistical grounding. No code or checkpoints are released, which is standard practice in this area and would help resolve ambiguities in the algorithm description.","major_comments":[{"comment":"The reverse-sampling update in Algorithm 2 is not consistent with the training objective. Eq. (11) trains s_theta to match the score \\nabla_{z_t} \\log q(z_t|z_0), but Algorithm 2 line 9 computes \\mu_\\theta = (1/\\sqrt{1-\\beta_t})\\left[z_t + (\\beta_t/\\sqrt{1-\\bar\\alpha_t}) s_\\theta\\right]. For the DDPM posterior, the correct score-based update is \\mu_\\theta = (1/\\sqrt{\\alpha_t})\\left[z_t + \\beta_t s_\\theta\\right], since s_\\theta \\approx -\\epsilon/\\sqrt{1-\\bar\\alpha_t}. The displayed coefficient is off by a factor of 1/\\sqrt{1-\\bar\\alpha_t}, which grows large near t=1 and would cause the sampler to overshoot. If, instead, s_\\theta is intended to be the noise predictor, the sign should be minus, as in Appendix A Eq. (19). The paper never reconciles the score-based notation of the main text with the noise-based derivation of the appendix. Because no code or checkpoints are provided, the reader cannot determine which update actually produced the reported results. This is a load-bearing issue for the central claim.","section":"Algorithm 2, line 9; Eq. (11); Appendix A, Eq. (19)"},{"comment":"The baseline comparison is incomplete in exactly the cells needed to support the claim that LMDM outperforms GeoLDM and EDM on all four metrics. GeoLDM's novelty is missing for QM9, and GeoLDM's uniqueness, novelty, and stability are missing for GEOM. In addition, EDM's GEOM validity, uniqueness, and novelty are all reported as 68.6, which is either a striking coincidence or an error. The text states that published pre-trained models were evaluated, so the missing entries are not explained. These gaps undermine the conclusion that LMDM 'outperforms the state-of-the-art models' and the numerical claims in the abstract.","section":"Table 1"},{"comment":"All metrics are computed from a single run of 10,000 generated molecules, with no error bars, multiple seeds, or statistical significance tests. Some reported differences are small relative to sampling noise; for example, LMDM's QM9 stability is 90.8% versus EDM's 91.1%, which is lower, not higher. Without repeated runs, the claimed improvements of 4.8% and 30.2% cannot be assessed. The paper should report mean and standard deviation over at least three independent sampling runs or otherwise demonstrate that the differences are not due to stochasticity.","section":"Section 5.1"},{"comment":"The split of edges into local and global is based on a fixed radius tau = 2 Å applied to the latent coordinates z_t, but the paper never verifies that distances in the learned latent space correspond to physical distances. If the autoencoder rescales or distorts coordinates, the local/global separation no longer matches the intended covalent versus van der Waals interactions, and the modeling of interatomic forces becomes unjustified. This assumption is load-bearing for the method's main design motivation and should be checked empirically (e.g., by comparing latent distances to real-space distances on the training set).","section":"Section 4.2, 'Edge Construction'"},{"comment":"The reported diversity improvement is partly mechanical. The method injects a fresh random variable eta_v at every reverse step (Algorithm 2 line 7) and then reports higher uniqueness/novelty than baselines that do not have this additional stochasticity. To support the claim that the architecture itself improves diversity, the comparison should include a baseline with an equivalent source of randomness (e.g., by adding the same per-step noise to EDM or GeoLDM) or measure diversity while controlling for the injected noise budget.","section":"Section 4.2, 'Enhance diversity through variational noise'"}],"minor_comments":[{"comment":"The first two paragraphs of Section 4.2 are identical verbatim; one should be removed.","section":"Section 4.2, first two paragraphs"},{"comment":"The label 'Local Radius =?' in Figure 1 is unfinished and should give the actual value (2 Å).","section":"Figure 1"},{"comment":"The notation is inconsistent: Eq. (5) uses alpha_t where the context requires \\bar\\alpha_t, and the relationship between s_theta and \\epsilon_theta is never defined. This makes it difficult to check the sampling equations.","section":"Eq. (5) and Algorithm 2"},{"comment":"The text says 'almost all attributes can exceed' the baselines, but LMDM is worse than GeoLDM on dipole moment mu and heat capacity Cv. The claim should be qualified accordingly.","section":"Section 5.2, Table 2"},{"comment":"The phrase 'reduces the amount of calculation in the back-propagation process' is not quantified or substantiated anywhere in the paper.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The manuscript appears to be an early draft with several unfinished parts. The relationship to GeoLDM (Xu et al., 2023) is very close; the claimed novelty rests on the dual local/global score network and the stochastic control variable, but the differences are not clearly delineated. The missing code and checkpoints would be a serious reproducibility concern for this community. I would ask the authors to fix the sampling algorithm, complete the baseline table, and provide statistical support before considering this paper for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: this paper is not ready for referees. It combines GeoLDM's latent equivariant autoencoder with MDM's dual local/global score network and adds a per-step stochastic control variable for diversity. That combination is new enough to be a legitimate research idea, but the manuscript is too incomplete to evaluate the claimed 4.8%/30.2% improvements over EDM and GeoLDM.\n\nWhat it does well: it states its debts clearly—GeoLDM and MDM are cited as the sources of the main building blocks. The idea of separating local covalent bonds and global van der Waals interactions inside the latent diffusion process is sensible, and the conditional generation setup follows prior work. The two-stage training (autoencoder then diffusion) is a reasonable choice, and the ablation on latent dimension and KL vs early-stopping regularization is informative.\n\nThe problems are load-bearing. There is no code or model release, Table 1 has missing cells for GeoLDM and G-Schnet on GEOM-Drug, and all numbers come from a single run with no error bars. More importantly, the paper describes the control variable inconsistently. In training (Algorithm 1), eta_v is sampled from a learned posterior N(mu_v, sigma_v^2), but at inference (Algorithm 2) it is sampled from N(0, I), and the text even mentions sampling from U(-1, +1). That train/test gap means the sampler is not the model that was trained; without code I can't tell if the reported numbers are real.\n\nThe stress-test claim about a sign error in Algorithm 2 does not hold up. The model predicts the score, not the noise; for a score parameterization the plus sign is correct. The paper does confuse things by using epsilon_theta in the appendix and s_theta in the main text, and Eq. (5) is missing the bar on alpha, but that is a notation problem, not a broken sampler.\n\nThe latent radius tau=2 Angstrom concern is real: the local/global split happens in latent coordinates, and the paper never checks that distances in latent space are calibrated to real Angstroms. This could mis-assign covalent vs long-range interactions.\n\nConditional generation results (MAE near the lower bound on several QM9 properties) are implausibly strong for a model that otherwise shows only modest improvements; I would want to see the evaluation code.\n\nBottom line: I would not send this to a referee as is. The idea has some merit, but it is buried under a careless manuscript (duplicated paragraphs, placeholders, incomplete tables). If the authors clean it up and release code, it could be worth another look. For now, desk-reject or ask for a full revision before review.","headline":"Combines GeoLDM and MDM with a diversity noise variable, but the manuscript is too incomplete and internally inconsistent to verify the claimed SOTA numbers.","tokens_in":20919,"tokens_out":7445,"would_cite":false,"duration_ms":69052,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A latent diffusion model that separates covalent from van der Waals interactions during denoising claims state-of-the-art validity, uniqueness, and novelty in 3D molecule generation on QM9 and GEOM-Drugs.","keywords":["latent diffusion model","3D molecular generation","equivariance","score-based generative modeling","SE(3) symmetry","drug-like molecules","variational noise","dual equivariant network"],"falsifier":"Encode a set of molecules with known covalent bond lengths and regress the latent pairwise distances $\\|z_{x,i} - z_{x,j}\\|$ against true interatomic distances; if latent distances are not proportional to angstroms across the dataset, then the $\\tau = 2$ Å cutoff in latent space cannot be selecting covalent bonds, and the local/global split is not doing the physical work the paper claims.","tokens_in":19806,"feed_emoji":"⚛️","tokens_out":8599,"duration_ms":74545,"temperature":0.7,"pith_summary":"LMDM is a latent diffusion model for generating 3D molecules: instead of diffusing on raw atomic coordinates, it first compresses molecular point clouds into a low-dimensional equivariant latent space and then runs the denoising process there. The author claims that this design, together with a score network split into a local branch for pairs within 2 Å (covalent bonds) and a global branch for all other pairs (van der Waals forces), improves the validity, uniqueness, and novelty of generated molecules relative to the EDM and GeoLDM baselines. The paper also claims that injecting a variational noise variable at every reverse step increases the diversity of the sampled molecules. If the claims are right, the approach is a step toward generating large drug-like molecules with high stability and toward controllable generation of molecules with specified quantum properties.","feed_headline":"3D molecule generator hits 99.5% validity on drug-like set","feed_subtitle":"Latent-space diffusion with separate covalent and van der Waals score branches lifts diversity by 30 percent.","key_machinery":"The central object is a molecular variational autoencoder whose encoder and decoder are equivariant graph neural networks, mapping a molecular point cloud $G = \\langle x, h\\rangle$ into latent variables $z = \\langle z_x, z_h\\rangle$ that rotate and translate with the molecule. Diffusion happens on these latent variables, and a dual equivariant score network predicts the noise: one branch processes local edges (pairs within a fixed radius $\\tau = 2$ Å, meant to mimic covalent bonds) and one processes global edges (meant to capture van der Waals forces). A variational noise encoder based on SchNet produces a stochastic control variable $\\eta_v$ that is added at every reverse step, and the zero center-of-mass trick keeps the prior distribution rotation invariant. This combination — equivariant latent compression, distance-split score modeling, and stochastic control noise — is what the paper argues carries the performance gains.","core_discovery":"On the paper's own terms, the discovery is that a diffusion process can run on equivariant latent variables instead of raw atomic coordinates without losing the SE(3) symmetries of molecular geometry, and that splitting the denoising score into a local part for edges within 2 Å and a global part for all other pairs lets the model capture covalent bonds and van der Waals interactions separately. The reported consequence is state-of-the-art performance on QM9 and GEOM-Drugs: for example, 98.8% validity and 92.1% novelty on QM9, and 99.5% validity and 63.4% stability on GEOM-Drugs, compared with prior diffusion models. The author also reports that conditioning on properties such as polarizability and HOMO-LUMO gap produces molecules whose predicted properties track the target values more closely than the GeoLDM baseline on most QM9 properties.","pith_inferences":["If the latent space distances are not calibrated to angstroms, the 2 Å cutoff in latent coordinates would not correspond to covalent bond lengths, so the local/global split would not be doing the physical modeling the paper describes; measuring that calibration would settle the question.","The paper attributes the 30.2% diversity improvement to the variational noise variable but does not ablate that component alone; isolating it in a controlled experiment would place that attribution on firmer ground.","The framework is not molecule-specific and could be carried over to other SE(3)-equivariant point-cloud generation tasks, such as protein backbones, with the radius reassigned to the appropriate scale.","The comparisons rely on published pre-trained baselines; an evaluation in which all models are retrained with matched compute and data splits would show how much of the margin is architectural rather than due to training protocol."],"forward_implications":["On GEOM-Drugs, the model reports 99.5% validity and 63.4% molecular stability, higher than EDM's 68.6% validity and 13.7% stability, suggesting the local/global edge split helps on molecules averaging 46 atoms.","On QM9, it reports 98.8% validity, 95.2% uniqueness, and 92.1% novelty, reflecting the 4.8% effectiveness and 30.2% diversity improvements cited in the abstract.","Conditional generation with property labels attached to the atomic features produces lower mean absolute errors than GeoLDM on four of six QM9 targets, including a reported HOMO-LUMO gap error of 0.068 eV.","Replacing the KL regularization on the latent space with an early-stopping regularizer avoids numerical instability during training and yields better generation quality.","Because the diffusion runs in a lower-dimensional latent space, the model reduces the amount of computation in back-propagation and the memory footprint of the score network on large molecules."],"supporting_citations":[{"why":"The EDM baseline in Cartesian space that LMDM must beat; supplies the fully connected adjacency approach that the paper argues misses local constraints.","marker":"Hoogeboom et al., 2022a"},{"why":"GeoLDM, the latent diffusion baseline; supplies the equivariant latent autoencoder formulation that LMDM extends with dual local/global score networks.","marker":"Xu et al., 2023"},{"why":"Latent diffusion models for images; provides the overall two-stage autoencoder-plus-diffusion design and the early-stopping regularizer that the paper adapts.","marker":"Rombach et al., 2022"},{"why":"MDM, the source of the dual equivariant fractional neural network used to model local and global edges.","marker":"Huang et al., 2022"},{"why":"EGNN, the equivariant graph neural network used to parameterize the encoder, decoder, and equivariant kernels.","marker":"Satorras et al., 2021"},{"why":"SchNet, used to implement the equivariant Markov kernel layers and to encode the variational noise variable.","marker":"Schütt et al., 2017"},{"why":"QM9 dataset of 130k small molecules, the first benchmark.","marker":"Ramakrishnan et al., 2014"},{"why":"GEOM-Drugs dataset of 290k drug-like molecules with 46 atoms on average, the large-molecule benchmark where the paper claims its main gains.","marker":"Axelrod & Gomez-Bombarelli, 2022"}],"fun_headline_variants":["Latent diffusion generates 3D molecules with 99.5% validity","Equivariant latent diffusion hits 99.5% validity on drug-like molecules","Separate score branches for bonds and van der Waals improve 3D molecule generation","Latent diffusion model for 3D molecules reaches 98.8% validity on QM9","Splitting denoising scores into local and global branches boosts molecule diversity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that distances in the learned latent space are measured in the same angstrom units as real molecular geometry, so the 2 Å radius used to split local and global edges in latent coordinates actually corresponds to covalent-bond distances in the molecule.","fun_headline_variants_meta":{"raw":{"variants":["Latent diffusion generates 3D molecules with 99.5% validity","Equivariant latent diffusion hits 99.5% validity on drug-like molecules","Separate score branches for bonds and van der Waals improve 3D molecule generation","Latent diffusion model for 3D molecules reaches 98.8% validity on QM9","Splitting denoising scores into local and global branches boosts molecule diversity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00067,"raw_usage":{"total_tokens":3042,"prompt_tokens":925,"completion_tokens":2117,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":541,"completion_tokens_details":{"reasoning_tokens":2008}},"tokens_in":541,"tokens_out":2117,"duration_ms":13559,"temperature":1.0,"reasoning_tokens":2008,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:36:51.665802+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Encode a set of molecules with known covalent bond lengths and regress the latent pairwise distances $\\|z_{x,i} - z_{x,j}\\|$ against true interatomic distances; if latent distances are not proportional to angstroms across the dataset, then the $\\tau = 2$ Å cutoff in latent space cannot be selecting covalent bonds, and the local/global split is not doing the physical work the paper claims.","supporting_citations":[{"cited_title":"MDM: Molecular Diffusion Model for 3D Molecule Generation","cited_arxiv_id":"2209.05710","evidence_quote":"MDM, the source of the dual equivariant fractional neural network used to model local and global edges."},{"cited_title":"and Gomez-Bombarelli, R","cited_arxiv_id":null,"evidence_quote":"GEOM-Drugs dataset of 290k drug-like molecules with 46 atoms on average, the large-molecule benchmark where the paper claims its main gains."}],"review_version":1}