REVIEW 4 major objections 6 minor 17 references
Revisiting Sampling Strategies for Molecular Generation
T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read The paper claims that switching to maximally stochastic sampling, StoMax, outperforms default DDPM and BFN samplers across four 3D molecular generation models, improving stability and validity on QM9 and GEOM-Drugs.
desk verdict Useful empirical result, but the 'consistently outperforms' claim is too strong and the sampler-validity question is unanswered. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing design is the one-parameter family of conditional reverse distributions $p_\lambda(x_{t-\Delta t}\mid x_t,x_0)=\mathcal{N}(\mu_{t-\Delta t}x_0+\gamma_t (x_t-\mu_t x_0)/\sigma_t,\ \lambda_t^2 I)$ with $\gamma_t^2+\lambda_t^2=\sigma_{t-\Delta t}^2$, together with the discrete update $x_{t-\Delta t}=\frac{\mu_{t-\Delta t}}{\mu_t}x_t+(\frac{\mu_{t-\Delta t}}{\mu_t}\sigma_t-\gamma_t)\sigma_t\nabla_x\log p_t(x_t)+\sqrt{2\sigma_t(\sigma_{t-\Delta t}-\gamma_t)}\,\epsilon$. Choices of $\gamma_t$ index the sampling method: the Markov forward process (DDPM and, as verified in the appendix, BFN) corresponds to $\gamma_t=\mu_t\sigma_{t-\Delta t}^2/(\mu_{t-\Delta t}\sigma_t)$, the deterministic DDIM limit to $\gamma_t=\sigma_{t-\Delta t}$, and StoMax to $\gamma_t=0$, which maximizes the variance under this parameterization and makes each reverse step conditionally independent of its predecessor given the clean data. The paper verifies that, for the DDPM schedule, StoMax with $\gamma_t=0$ also arises as the $\beta(t)\to\infty$ limit of the general reverse SDE, connecting it to Langevin-like dynamics.
What would settle it
A direct check is to run the StoMax update with $\gamma_t=0$ on a Gaussian target whose score function is known exactly: if the update is unbiased, the sample mean and covariance will match the target's as the step size shrinks, and any systematic offset would show that StoMax samples a different distribution. A molecule-level version of the same test is to increase the number of sampling steps by an order of magnitude and see whether the diversity drop in Table 1 persists; if it persists, the loss is a bias of the StoMax discretization rather than a natural property of the learned density.
Extended reading notes
Core claim
The paper establishes that, within the one-parameter family of reverse sampling updates derived from the general diffusion SDE, the maximally stochastic choice $\gamma_t = 0$ yields the best balance of quality and diversity for molecular generation. Concretely, replacing default samplers with StoMax improves molecule stability on QM9 from 82.0% to 87.9% for EDM and from 89.8% to 96.1% for UniGEM(EDM), and validity from 91.9% to 94.5% and 95.0% to 98.1% respectively; GeoBFN and UniGEM(BFN) also improve, with smaller but consistent gains. On GEOM-Drugs, StoMax lifts EDM validity from 92.6% to 99.7% and UniGEM(EDM) from 98.4% to 99.9%, and atom stability by roughly four to five points. The diversity metric V*U rises slightly for EDM-based models but falls for BFN-based ones, and interpolating between StoMax, DDPM, and DDIM shows stability and validity increasing monotonically with reverse-step stochasticity. The paper states plainly that a rigorous theory is still missing, and that in the continuous formulation StoMax corresponds to taking $\beta(t)\to\infty$, outside the bounded-$\beta$ condition under which the reverse SDE family provably shares the forward marginals.
Load-bearing premise
The load-bearing premise is that running the StoMax update still generates molecules from the distribution the model actually learned, even though StoMax's extreme noise level falls outside the range where the standard theory guarantees the reverse process matches that distribution.
Editorial extensions
If this is right
- Switching any of the four tested generators to StoMax improves atom stability, molecule stability, and validity on QM9 without retraining, so sampling design is a model-agnostic performance lever.
- On GEOM-Drugs StoMax brings validity close to 100% for EDM and UniGEM(EDM), suggesting gains grow on larger, more drug-like molecules.
- Interpolation results imply that within this family, more reverse-step stochasticity monotonically buys quality at a small uniqueness cost, and StoMax is the best operating point on the V*U trade-off.
- The paper's Langevin connection suggests that treating sampling as annealing dynamics rather than denoising discretization could be the right lens for molecular generation; this is presented as a hypothesis, not a proof.
Reading between the lines
- A direct extension the paper does not test: if StoMax's benefit comes from its variance effect, the same update should improve other structured diffusion outputs, such as conformer ensembles or point clouds, where validity is hard to enforce.
- The formal gap at $\gamma_t=0$ suggests StoMax may sample from a mildly biased distribution whose bias happens to help valence and bond-counting metrics; a toy Gaussian experiment with an exact score would separate 'better sampling' from 'useful bias'.
- Because StoMax's variance acts like temperature, one testable extension is an adaptive schedule that starts near StoMax and anneals toward DDPM late in the trajectory, which might recover the lost uniqueness without sacrificing stability.
- If future theory identifies the effective stationary distribution of the StoMax update, the same calculation could prescribe an optimal noise level for each dataset, turning sampling design into a principled hyperparameter rather than a choice of extremes.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper revisits the choice of sampling strategy in diffusion-based 3D molecular generation. It works within the general reverse-SDE framework of Ni et al. (2025), derives a family of discrete samplers parameterized by γ_t in Eq. (7), and interprets DDPM/BFN default sampling as the Markov case, DDIM as the deterministic case, and the new 'StoMax' strategy (γ_t = 0) as the maximally stochastic case. The authors evaluate StoMax against default samplers for EDM, GeoBFN, UniGEM(EDM), and UniGEM(BFN) on QM9, and for EDM and UniGEM(EDM) on GEOM-Drugs, reporting improvements in atom stability, molecule stability, and validity, along with a diversity decrease that is described as minor. The paper concludes that StoMax consistently outperforms default sampling and motivates future theoretical work on the diversity-fidelity trade-off.
Significance. If the central claim were established, this would be a practically useful finding: a simple, almost parameter-free change to the sampling procedure that improves the quality of generated molecules across several models and datasets. The paper also provides a useful unifying derivation of DDPM, BFN, DDIM, and StoMax within one update rule, and the QM9 evaluation covers four model/sampler combinations at 1000 sampling steps. However, the significance is currently limited by two issues: StoMax is not shown to be a faithful sampler for the learned distribution, and the empirical record contradicts the word 'consistently' when diversity-aware metrics are included. The paper's own Section 4 concedes that a rigorous theoretical explanation is lacking.
major comments (4)
- [§2.3, §4, Eq. (3), Eq. (7)] StoMax is defined by γ_t = 0 in Eq. (7). In the continuous reverse SDE of Eq. (3), matching this discrete choice to the SDE requires β(t) ∝ 1/Δt, so β(t) → ∞, which is outside the bounded-β condition under which the reverse-process family shares the forward marginals. The exact discrete transition that preserves forward marginals samples x0* from p(x0|xt) and has conditional covariance σ_{t-Δt}^2 I + μ_{t-Δt}^2 Var(x0|xt); Eq. (7) replaces x0* by E[x0|xt] and drops that posterior-covariance term. Because the StoMax noise term √(2σ_t(σ_{t-Δt} - γ_t)) is O(1) rather than O(√Δt), the bias need not vanish as Δt → 0. Section 4 explicitly concedes that the rigorous theoretical explanation is lacking and that the discrete implementation differs from Langevin dynamics. The paper must either prove that the discrete StoMax update samples from the learned distribution (or is provably close to it), or explicitly reframe StoMax as an alternative generative procedure and remove the claim that it is a theoretically valid sampler within the family of Eq. (3).
- [Table 1] The abstract and Section 1 claim that StoMax 'consistently outperforms default sampling methods'. In Table 1, V×U drops for GeoBFN (92.7 to 91.9) and for UniGEM(BFN) (93.0 to 91.3), which are two of the four QM9 model/sampler combinations. Section 3.4 also uses U×V as the headline metric for the favorable trade-off, so these decreases directly contradict the unqualified wording of the central claim. The authors should either qualify the claim to the three quality metrics (atom stability, molecule stability, validity), explicitly acknowledge the V×U decreases in the abstract, or provide an aggregate justification for the word 'consistently'.
- [Table 2] The GEOM-Drugs results report only atom stability and validity, omitting molecule stability and all diversity-aware metrics such as V×U. As a result, the GEOM-Drugs experiments cannot support the global conclusions that StoMax consistently outperforms defaults or that the diversity trade-off is minor. The same metric suite as in Table 1 should be reported, or the GEOM-Drugs conclusions should be restricted to the two reported metrics.
- [§3.4, Figure 1] The interpolation experiment is performed only with UniGEM(EDM), so the statements that 'StoMax achieves the highest score on the U×V metric' and 'StoMax emerges as the most balanced and effective approach' are not general empirical results; they describe one model's interpolation curve. This is consistent with the V×U decreases for GeoBFN and UniGEM(BFN) in Table 1 and should be presented with that limitation.
minor comments (6)
- [§3.1, Metrics] The text 'the proportion of generated generated 3D structures' contains a duplicated word and should read 'generated 3D structures'.
- [§3.1 and Table 1] Section 3.1 refers to UniGEM(GeoBFN) but Table 1 labels the same variant UniGEM(BFN); please align the notation throughout.
- [Appendix A.2, Eq. (12)] The density f(x0) is used in the score derivation but is never defined; it should be written as p(x0) or q(x0) consistently with the rest of the paper.
- [Proposition A.1 and A.2] Proposition A.2 verifies only the BFN sampler; the corresponding explicit verification for the DDPM/Markov case is asserted in the text but not shown, so the claim that both default samplers belong to the Markov family would benefit from an explicit derivation or citation.
- [§3.4, Interpolation] The interpolation coefficients p′ and p″ are used in the formulas but are only described as being in [0,1]; please state which endpoint of each interpolation each value corresponds to.
- [§2.3, StoMax variance] The statement that the StoMax variance 'can be interpreted as a form of temperature control (Ni et al., 2025)' is vague; a precise relationship between the variance scale and a temperature parameter would be helpful.
Circularity Check
No significant circularity: StoMax is a defined sampling rule and the central empirical claim is an independent benchmark comparison, not a derived prediction.
full rationale
The paper's central claim is empirical: setting gamma_t=0 in Eq. 7 (StoMax) improves atom stability, molecule stability, and validity over default DDPM/BFN samplers on fixed pretrained models. This is not a fitted parameter called a prediction; gamma_t=0 is a pre-specified definition in Sec. 2.3, and the evaluation uses standard benchmarks (QM9, GEOM-Drugs) with standard metrics. The reverse-SDE family in Eq. 3 is cited from the authors' own prior work (Ni et al. 2025; Xue et al. 2024b, co-authored by Z.-M. Ma), but that framing is not load-bearing for the empirical result: StoMax is defined directly from Eq. 7, and Sec. 4 explicitly concedes that StoMax lacks a rigorous theoretical explanation and corresponds to beta(t)->infinity, outside the bounded-beta condition of the cited family. The paper therefore does not derive its conclusion from the self-citation; it tests a defined sampler against defaults. No predicted quantity is equivalent by construction to an input, and no self-citation forces the outcome. The score of 2 reflects only the presence of minor self-citations in the theoretical framing, not circularity.
Assumptions & free parameters
assumptions (4)
- standard math The reverse SDE in Eq. 3 with any non-negative bounded beta(t) yields the same marginals as the forward process.
- standard math The conditional distribution family in Eq. 5 (from Song et al. 2021a) covers all valid Gaussian reverse conditionals given the marginals.
- domain assumption The learned score (or noise predictor) is accurate enough for the sampling formulas to hold.
- ad hoc to paper The discrete StoMax update (gamma_t=0) remains a valid sampler for the model's distribution despite corresponding to beta(t) approaching infinity, outside the bounded-beta guarantee.
Cite this review
Pith. "Pith review of Revisiting Sampling Strategies for Molecular Generation." pith.science (2026). https://pith.science/paper/SVIE43CK
@misc{pith2026250617340,
author = {Pith},
title = {Pith review of: Revisiting Sampling Strategies for Molecular Generation},
year = {2026},
howpublished = {\url{https://pith.science/paper/SVIE43CK}},
note = {Machine review of arXiv:2506.17340}
}
read the original abstract
Sampling strategies in diffusion models are critical to molecular generation yet remain relatively underexplored. In this work, we investigate a broad spectrum of sampling methods beyond conventional defaults and reveal that sampling choice substantially affects molecular generation performance. In particular, we identify a maximally stochastic sampling (StoMax), a simple yet underexplored strategy, as consistently outperforming default sampling methods for generative models DDPM and BFN. Our findings highlight the pivotal role of sampling design and suggest promising directions for advancing molecular generation through principled and more expressive sampling approaches.
Figures
Reference graph
Works this paper leans on
-
[1]
and Gomez-Bombarelli, R
Axelrod, S. and Gomez-Bombarelli, R. Geom, energy-annotated molecular conformations for property prediction and molecular generation. Scientific Data, 9 0 (1): 0 185, 2022
2022
-
[2]
Analytic-dpm: an analytic estimate of the optimal reverse variance in diffusion probabilistic models
Bao, F., Li, C., Zhu, J., and Zhang, B. Analytic-dpm: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. International conference on learning representations, 2022
work page 2022
-
[3]
Unigem: A unified approach to generation and property prediction for molecules
Feng, S., Ni, Y., Lu, Y., Ma, Z.-M., Ma, W.-Y., and Lan, Y. Unigem: A unified approach to generation and property prediction for molecules. International conference on learning representations, 2025
work page 2025
-
[4]
K., Atkinson, T., and Gomez, F
Graves, A., Srivastava, R. K., Atkinson, T., and Gomez, F. Bayesian flow networks. arXiv preprint arXiv:2308.07037, 2023
arXiv 2023
-
[5]
Denoising diffusion probabilistic models
Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33: 0 6840--6851, 2020
2020
-
[6]
G., Vignac, C., and Welling, M
Hoogeboom, E., Satorras, V. G., Vignac, C., and Welling, M. Equivariant diffusion for molecule generation in 3d. In International conference on machine learning, pp.\ 8867--8887. PMLR, 2022
2022
-
[7]
Straight-line diffusion model for efficient 3d molecular generation
Ni, Y., Feng, S., Chi, H., Zheng, B., Gao, H.-a., Ma, W.-Y., Ma, Z.-M., and Lan, Y. Straight-line diffusion model for efficient 3d molecular generation. arXiv preprint arXiv:2503.02918, 2025
arXiv 2025
-
[8]
O., Rupp, M., and Von Lilienfeld, O
Ramakrishnan, R., Dral, P. O., Rupp, M., and Von Lilienfeld, O. A. Quantum chemistry structures and properties of 134 kilo molecules. Scientific data, 1 0 (1): 0 1--7, 2014
2014
Show all 17 references
-
[9]
C., and Reymond, J.-L
Ruddigkeit, L., Van Deursen, R., Blum, L. C., and Reymond, J.-L. Enumeration of 166 billion organic small molecules in the chemical universe database gdb-17. Journal of chemical information and modeling, 52 0 (11): 0 2864--2875, 2012
2012
-
[10]
and Hyv \"a rinen, A
Saremi, S. and Hyv \"a rinen, A. Neural empirical bayes. Journal of Machine Learning Research, 20 0 (181): 0 1--23, 2019
2019
-
[11]
Denoising diffusion implicit models
Song, J., Meng, C., and Ermon, S. Denoising diffusion implicit models. 2021 a . URL https://openreview.net/forum?id=St1giarCHLP
2021
-
[12]
and Ermon, S
Song, Y. and Ermon, S. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems, 32, 2019
2019
-
[13]
P., Kumar, A., Ermon, S., and Poole, B
Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021 b . URL https://openreview.net/forum?id=PxTIG12RRHS
2021
-
[14]
Unified generative modeling of 3d molecules with bayesian flow networks
Song, Y., Gong, J., Zhou, H., Zheng, M., Liu, J., and Ma, W.-Y. Unified generative modeling of 3d molecules with bayesian flow networks. In The Twelfth International Conference on Learning Representations, 2023
2023
-
[15]
Unifying bayesian flow networks and diffusion models through stochastic differential equations
Xue, K., Zhou, Y., Nie, S., Min, X., Zhang, X., ZHOU, J., and Li, C. Unifying bayesian flow networks and diffusion models through stochastic differential equations. In Forty-first International Conference on Machine Learning, 2024 a . URL https://openreview.net/forum?id=1jHiq640y1
2024
-
[16]
Sa-solver: Stochastic adams solver for fast sampling of diffusion models
Xue, S., Yi, M., Luo, W., Zhang, S., Sun, J., Li, Z., and Ma, Z.-M. Sa-solver: Stochastic adams solver for fast sampling of diffusion models. Advances in Neural Information Processing Systems, 36, 2024 b
2024
-
[17]
write newline
" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...
Reviewed August 6, 2026 · model on record in the stance chip above.
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