REVIEW 3 major objections 5 minor 1 cited by
VEDA shows that variance-exploding diffusion with annealing generates 3D molecules that are chemically stable at 100 sampling steps, with median relaxation energy of 1.72 kcal/mol compared to 32.3 kcal/mol for its flow-based baseline.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
T0 review · deepseek-v4-flash
2026-08-03 22:57 UTC pith:DNRJXHRA
load-bearing objection Creditable engineering, but the headline ΔE_relax win over SemlaFlow is uninterpretable without a diversity/uniqueness check on GEOM-DRUGS. the 3 major comments →
VEDA: 3D Molecular Generation via Variance-Exploding Diffusion with Annealing
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The central claim is that the variance-exploding (VE) diffusion formulation, in which noise variance grows without bound, is a better fit for 3D molecular generation than variance-preserving diffusion or flow matching, once the coordinate-predicting equivariant network is preconditioned correctly. VEDA unifies continuous coordinates and discrete atom/bond types in one generative process, and during sampling it deliberately injects extra Gaussian noise (a 'churn' step with amplification factor gamma) that acts like Gaussian smoothing over the molecular potential energy surface, helping the trajectory escape local minima. The preconditioning correction subtracts alpha_t times the input from th
What carries the argument
The central mechanism is the preconditioned denoiser D_theta(x_t;t) = c_skip x_t + c_out (F_theta(c_in x_t;c_noise) - alpha_t c_in x_t), where alpha_t = sigma_d t/(sigma_d^2 + t^2) is the LMMSE coefficient that removes the identity component from the equivariant network's output. It is paired with a variance-exploding forward process x_t = x_0 + t epsilon with t drawn log-normally, an amplified noise-injection sampling step (churn) equivalent in expectation to smoothing the potential energy surface, and an arcsin-based sampler w(u) = (1-rho)u + (rho*2/pi)*arcsin(sqrt(u)) that concentrates steps near log-SNR = 0.
Load-bearing premise
The headline result assumes that median relaxation energy of 1.72 kcal/mol is not inflated by generating already-relaxed, low-diversity conformers, since no uniqueness or diversity metric is reported on GEOM-DRUGS for VEDA.
What would settle it
Compute the pairwise Tanimoto similarity (or scaffold uniqueness) of 5,000 VEDA-S generated molecules on GEOM-DRUGS. If the uniqueness rate is substantially below that of the flow-based baseline under the same protocol, or if after removing duplicate conformers the median relaxation energy rises toward the 32.3 kcal/mol baseline, the claim that VEDA achieves both efficiency and accuracy would be falsified.
If this is right
- Native 3D generative models can reach drug-relevant geometric quality without slow denoising samplers, if the diffusion schedule and preconditioning are matched to the architecture.
- The relaxation-energy metric under GFN2-xTB becomes a usable head-to-head benchmark for conformational quality, and VEDA's reported values set a new reference point.
- Bond-explicit generation reaches near-perfect validity and molecular stability at 50-100 steps, suggesting the annealed VE schedule also supports discrete bond formation.
- The arcsin scheduler's concentration of steps near log-SNR roughly equal to zero, which matches the log-normal training distribution, is a simple recipe that could transfer to other diffusion samplers.
Where Pith is reading between the lines
- If the LMMSE preconditioning truly decouples the network's identity bias, the same correction could transfer to other coordinate-predicting equivariant architectures (e.g., protein or material generators) for similar speed-accuracy gains, but the paper does not test this.
- The reported 20x relaxation-energy advantage rests on comparison with published baseline numbers; a fair head-to-head that re-evaluates the flow-based baseline under identical seeds and evaluation code would clarify how much of the gain is intrinsic.
- The annealing analogy suggests a testable scaling law: the optimal noise-amplification factor gamma should grow with molecular size or flexibility, which could be verified by reporting relaxation-energy breakdowns per molecule size.
- No diversity or uniqueness metric is reported on GEOM-DRUGS, so a plausible risk is that the extremely low relaxation energy reflects convergence to a narrow set of low-energy conformers, trading diversity for stability.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes VEDA, a variance-exploding diffusion framework for 3D molecular generation, with two variants (VEDA-E on an EGNN backbone, VEDA-S on a Semla backbone). The technical contributions are (i) a VE noise schedule with amplified noise injection during sampling, described as annealing-like stochastic smoothing; (ii) a preconditioning scheme that subtracts an LMMSE-derived coefficient α_t times the input from the equivariant network output; and (iii) an arcsin-based sampling scheduler that concentrates steps near log-SNR≈0. The main reported results are state-of-the-art validity/stability on QM9 and GEOM-DRUGS at 100 NFE, and a much lower median relaxation energy (ΔE_relax = 1.72 kcal/mol vs. 32.3 kcal/mol for SemlaFlow) under GFN2-xTB optimization. Ablations and a negative control on SemlaFlow are included to support the design choices.
Significance. If the central relaxation-energy claim survives scrutiny, this is a substantial advance: it suggests that flow-level sampling efficiency (100 NFE) can be combined with denoising-level geometric accuracy, and it offers a concrete preconditioning recipe for SE(3)-equivariant coordinate-predicting networks. The paper is methodologically careful in several respects: the component ablation in Table 3 isolates the effects of preconditioning and noise injection; Table 6 includes a negative control on SemlaFlow with added noise; and Table 7 provides 5-subset confidence intervals for VEDA-S. The code is released and the theoretical derivations are presented explicitly. However, the significance is conditional on resolving the diversity/mode-collapse concern on GEOM-DRUGS and on correcting the theoretical justification of the preconditioning step.
major comments (3)
- [Appendix B, Tables 2 and 5] The headline claim of median ΔE_relax = 1.72 vs. 32.3 kcal/mol for SemlaFlow (Table 2) is only interpretable as evidence of conformational accuracy if VEDA-S generates diverse, representative molecules. No uniqueness or internal diversity metric is reported on GEOM-DRUGS. Table 5 shows VEDA-S generated molecules have lower MMFF energy (43.0 kcal/mol) and strain (12.7 kcal/mol) than the GEOM-DRUGS training data (50.3 and 15.9 kcal/mol), which is the signature one would expect if the model collapses onto a low-energy, low-diversity subset. Under the Nikitin et al. protocol, low ΔE_relax and post-optimization RMSD reward already-relaxed structures, so this gap could inflate the 90% improvement. Please report uniqueness and diversity metrics on GEOM-DRUGS (e.g., fraction of unique valid molecules, pairwise Tanimoto dissimilarity, distributions of heavy-atom counts/molecular weight) for VEDA-
- [Methodology, Eqs. (5)-(9) and Appendix I] The derivation of α_t does not support the stated role in the preconditioning scheme. Eq. (7)-(9) show that α_t is the LMMSE predictor of the noise component σ_d ε from x_t, but F_target in Eq. (5) is not that noise; it is a coordinate-space residual involving both x_0 and ε. Moreover, the identity-like component of F_θ that the subtraction is meant to remove contributes c_out·c_in·x_t = α_t·x_t after c_out multiplication (since c_out·c_in = α_t under the Karras et al. definitions). Subtracting α_t·c_in·x_t inside the parentheses subtracts only α_t²·x_t after c_out multiplication, not the full identity component. Thus the theoretical claim that α_t optimally corrects the network's identity bias is not established. Please correct the derivation, or explicitly reframe the subtraction as a heuristic whose empirical benefit is demonstrated by the ablation.
- [Table 2 vs. Table 7, Appendix B] The evaluation conditions are not consistent across methods. Table 2 states 'For each model, 5000 molecules were evaluated,' but Table 7 says 'All other methods are evaluated on 1,000 generated samples' while VEDA-S uses 5000. Published baseline numbers are not re-evaluated under identical sample sizes or filtering protocols. Since the comparison against SemlaFlow and other baselines is central to the paper's claims, please either re-run all baselines under the same sample size and conditions, or clearly state the discrepancy and quantify its effect, e.g., by giving bootstrap confidence intervals for the baselines. Without this, the state-of-the-art comparisons may be confounded by sample-size differences.
minor comments (5)
- [Table 4 and Figure 4] The noise injection amplification γ is a key hyperparameter in Figure 4 (selected γ=0.4) but does not appear in the hyperparameter table (Table 4). Please list γ for both datasets and both model variants.
- [References] The reference list contains a duplicate: 'Song et al. 2023a' and 'Song et al. 2023b' refer to the same Equivariant Flow Matching paper. Also, the footnote in the introduction has a formatting artifact ('SemlaFlowa' with a missing space before the citation).
- [Appendix J] The heading says 'Derivation for the Smoothed Potential Energy Equivalence' but the text uses 'deviation' (typo). Also, the Gaussian-smoothing claim is stated in the main text as 'equivalent in expectation to Gaussian smoothing on the molecular potential energy surface'; the appendix derives this for a single 3D coordinate but the connection to the multi-atom molecular energy surface and to the specific noise schedule (√(γ²+2γ·t_i)) is not shown. Please clarify the scope of the equivalence.
- [Eq. (31) and Appendix G] In the detailed-balance term, the notation δ(j,x_0) is used where the discrete data variable was earlier denoted z_0. This is confusing: x_0 was defined as continuous coordinates. Please use z_0 consistently in the discrete derivation.
- [Methodology, Eq. (7)-(8)] The simplification from Eq. (7) to Eq. (8) drops c_in and the denominator without explanation. It works because c_in = 1/√(σ_d²+t²) under Karras et al., but this should be stated explicitly for readability.
Circularity Check
No significant circularity: the derivation of the preconditioning coefficient is a closed-form LMMSE calculation, the scheduler is an empirically ablated design choice, and the headline relaxation-energy claim is an external benchmark result rather than a quantity fitted by construction.
full rationale
I walked the paper's claimed derivation chain and found no step that reduces by construction to its own inputs. The main theoretical contribution, the LMMSE preconditioning coefficient α_t, is derived in Eqs. (6)-(9) and Appendix I by minimizing E[||σ_d ε - α x_t||^2] under explicit assumptions (zero-mean data, x_0 independent of ε, Var(x_0)=σ_d^2, Var(ε)=1). The closed form α_t = σ_d t/(σ_d^2 + t^2) is not fitted to the evaluation metric and does not presuppose the claimed downstream improvement in molecular stability. The arcsin scheduler is motivated by an observed match between critical sampling steps and the log-normal training noise distribution, but it is not a prediction derived from that match; its benefit is supported by ablations and sensitivity analyses (Figure 4, Table 3), so this is a design choice, not a self-validating derivation. The central quantitative claim, median ΔE_relax of 1.72 vs 32.3 kcal/mol on GEOM-DRUGS, comes from the external Nikitin et al. (2025) GFN2-xTB protocol; VEDA's sampling does not use xTB energies as inputs, so the low relaxation energy is an empirical outcome rather than a fitted quantity renamed as a prediction. The paper's one self-citation (Zhang et al. 2025) is used only to motivate the research gap and is not load-bearing for any derivation. The concern that low ∆E_relax could be inflated by mode collapse or low diversity is a validity/evaluation concern about the benchmark, not a circularity of the derivation; it does not exhibit the specific definitional reduction required for a circularity flag. Overall, the derivation chain is self-contained and the score is 0.
Axiom & Free-Parameter Ledger
free parameters (7)
- arcsin scheduler factor ρ =
2.5 (QM9 and GEOM-DRUGS)
- noise injection amplification γ =
0.4 (GEOM-DRUGS)
- categorical noise level / DFM detailed-balance noise η =
1.0
- sampling temperature τ =
0.9 (VEDA-S on QM9), 1.0 otherwise
- loss weights (λx, λa, λb, λc) =
e.g., (1.0, 0.2, 0.5, 1.0) and (1.0, 0.2, 1.0, 1.0)
- noise range T_min, T_max =
0.001, 80
- prediction mode for preconditioning =
Constant (α=1) on QM9; Adaptive (LMMSE α_t) on GEOM-DRUGS
axioms (6)
- standard math Adding Gaussian noise to coordinates is equivalent in expectation to evaluating a Gaussian-smoothed potential energy surface (Appendix J).
- domain assumption SE(3)-equivariant networks with residual connections carry a strong identity-like mapping bias whose linear part is removable by subtracting α_t·x_t.
- ad hoc to paper The LMMSE coefficient α_t = σ_d·t/(σ_d²+t²) is the right correction for that bias.
- domain assumption Median ΔE_relax and post-optimization RMSD under GFN2-xTB faithfully measure conformational quality and are comparable across methods under the Nikitin protocol.
- domain assumption For VEDA-E, post-hoc bond inference from coordinates yields chemically valid molecules.
- standard math Zero-mean data and independence of x_0 and ε for the LMMSE derivation (Appendix I).
read the original abstract
Diffusion models show promise for 3D molecular generation, but face a fundamental trade-off between sampling efficiency and conformational accuracy. While flow-based models are fast, they often produce geometrically inaccurate structures, as they have difficulty capturing the multimodal distributions of molecular conformations. In contrast, denoising diffusion models are more accurate but suffer from slow sampling, a limitation attributed to sub-optimal integration between diffusion dynamics and SE(3)-equivariant architectures. To address this, we propose VEDA, a unified SE(3)-equivariant framework that combines variance-exploding diffusion with annealing to efficiently generate conformationally accurate 3D molecular structures. Specifically, our key technical contributions include: (1) a VE schedule that enables noise injection functionally analogous to simulated annealing, improving 3D accuracy and reducing relaxation energy; (2) a novel preconditioning scheme that reconciles the coordinate-predicting nature of SE(3)-equivariant networks with a residual-based diffusion objective, and (3) a new arcsin-based scheduler that concentrates sampling in critical intervals of the logarithmic signal-to-noise ratio. On the QM9 and GEOM-DRUGS datasets, VEDA matches the sampling efficiency of flow-based models, achieving state-of-the-art valency stability and validity with only 100 sampling steps. More importantly, VEDA's generated structures are remarkably stable, as measured by their relaxation energy during GFN2-xTB optimization. The median energy change is only 1.72 kcal/mol, significantly lower than the 32.3 kcal/mol from its architectural baseline, SemlaFlow. Our framework demonstrates that principled integration of VE diffusion with SE(3)-equivariant architectures can achieve both high chemical accuracy and computational efficiency.
Figures
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Reference graph
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