Atomic Diffusion Models for Small Molecule Structure Elucidation from NMR Spectra

Thank you for your thoughtful and extensive feedback. We are especially grateful for your recognition of the technical novelty, performance, and clarity of our paper. Below, we address your clarifications and concerns.

[Accuracy of synthetic data generation] MestreNova’s NMR prediction is a proprietary algorithm that uses an ensemble approach combining machine learning models with rule-based methods. While the exact implementation details and quantitative accuracy benchmarks are not publicly available, MestreNova is widely used in both academic and industrial settings and is considered a gold standard for NMR spectral prediction and analysis. Given the lack of large-scale experimental NMR datasets, we believe MestreNova provides sufficiently accurate training data for our task.

[Stereochemistry] We agree that including stereochemistry significantly increases the complexity of the structure elucidation problem, and we will highlight this complexity in our revisions. We initially did not include stereochemical information as 2D NMR spectra, degradation analysis, Marfey's analysis, or Mosher ester analysis are usually required to determine absolute configuration at chiral centers. To investigate the impact of stereochemistry, also suggested by reviewer 1WdQ, we train and evaluate NMRDiff3D-M on the USPTO, including stereochemistry as Alberts et al. [1]. Our model still consistently outperforms Alberts et al. with single 1H spectra or 1H and 13C spectra with sterechemistry information. We note that including stereochemistry indeed degrades the top-1 accuracy, but interestingly, our model can mostly predict the correct stereoisomer within the top-5 predictions.

[Generalization to chemically dissimilar structures] Thanks for your suggestion on providing similarity analysis between the train and test splits, as also suggested by reviewer 1WdQ. We compute the Scaffold similarity (Scaff) and fingerprint-based Tanimoto Similarity to a nearest neighbor (SNN) metrics [2] between the test set and training set. We denote $\sigma_\textrm{dataset}$ as the standard deviation of the atom coordinates in the dataset, and compute the absolute difference of std between the test set and training set, as shown in the table below. All metrics indicate that the training and test splits of all datasets are relatively similar.

We then evaluate all models on test subsets with scaffolds unseen during training, which are relatively chemically dissimilar to the training sets according to the metrics in the table above. NMRDiff3D still significantly outperforms baselines across these subsets, demonstrating its generalization ability.

[Minor questions or suggestions]

(L260) you should emphasize the big performance boost is already observed with NMRDiff3D-M. Authors can also change the naming to NMRDiff3D-S vs NMRDiff3D-L, as "M" naming hints at the existence of an "S" model, which is not the case.

Thank you for pointing this out. We agree that NMRDiff3D-M has already achieved a strong performance, and we will emphasize this in the revision to highlight the strength of the core design. We also appreciate the naming suggestion and will rename NMRDiff3D-M to NMRDiff3D-S for clarity.

(L279) The ablation study discussion can be revisited to add more nuance and emphasize the magnitude of the effects. For instance, not all ConvFormer components are equally important (some cause only a 1% drop in accuracy), and this can be highlighted. The comparison to the patch tokenizer can be moved to the main text from the appendix.

Thank you for the suggestion. Although we noted in L279 that components such as token count, positional/type encoding, and dropout are relatively important, we agree that this could be made clearer. We will revise the ablation study discussion to emphasize the magnitude of each component’s impact and move the comparison of spectra tokenizers to the main text if space allows.

Not a weakness, but a suggestion: authors can list their key contributions at the end of the intro, as this is typical in NeurIPS papers and helps the reader to follow the paper.

We thank the reviewer for the suggestion, and we will add a key contributions section at the end of the introduction in the camera ready version if space allows.

How long does it take to train one NMRDiff3D model?

For NMRDiff3D-M, it takes 12h to train on the SpectraBase dataset, 36h on the USPTO dataset, and 26h on the SpectraNP dataset with 4 A100 GPUs. For NMRDiff3D-L, it takes 20h to train on the SpectraBase dataset, 55h on the USPTO dataset, and 58h on the SpectraNP dataset with 4 A100 GPUs. A table of training and sampling time of our NMRDiff3D models on all datasets is found in the Appendix Table 5. In short, the training time increases with the model size, the dataset size, and the size of molecules.

Thank you again for your helpful feedback – we believe the revisions will directly address your concerns and improve the clarity and impact of the paper.

References:

[1] Alberts, Marvin, et al. "Unraveling molecular structure: A multimodal spectroscopic dataset for chemistry." Advances in Neural Information Processing Systems 37 (2024): 125780-125808.

[2] Polykovskiy, Daniil, et al. "Molecular sets (MOSES): a benchmarking platform for molecular generation models." Frontiers in pharmacology 11 (2020): 565644.

Thank you for your careful reading and thoughtful feedback. We appreciate your recognition of our model’s strong performance and agree that dataset similarity analysis, generalization experiments to unseen scaffolds, and systematic failure mode analysis would help clarify the scope of our approach and strengthen our manuscript. Below, we provide clarifications and new results addressing these points.

[Dataset similarity analysis] Thanks for your question on the similarity between the USPTO and SpectraNP datasets. We compute the Scaffold similarity (Scaff) and fingerprint-based Tanimoto Similarity to a nearest neighbor (SNN) metrics [1] between the test set and training set, as shown in the table below. The two metrics between the SpectraNP test set and the USPTO training set are significantly lower, indicating that the two datasets are relatively dissimilar.

[Generalization to unseen scaffolds] Thanks for your suggestion. We evaluated all models on test subsets with scaffolds unseen during training. As shown in the table, NMRDiff3D still significantly outperforms baselines across these subsets, demonstrating its generalization ability. Moreover, NMRDiff3D-L trained jointly on SpectraNP and USPTO achieves >5% accuracy gain over training on SpectraNP alone, indicating its ability to learn from scaffold-dissimilar datasets.

[Failure mode analysis] We agree that a systematic failure mode analysis of molecular structures can help understand our model’s generalization ability. We analyze the failure rate by the number of atoms, number of rings, largest ring size, and functional groups of our NMRDiff3D-L on the synthetic SpectraNP and Real-SpecTeach datasets, as shown in the tables below. On both datasets, the model fails more often on molecules with the most atoms or the largest number of rings due to less training data and increasing complexity of spectra and structures for larger molecules. However, the model is not systematically significantly failing in a specific category.

Table: Failure rate by total number of atoms on SpectraNP

Table: Failure rate by number of rings on SpectraNP

Table: Failure rate by largest ring size on SpectraNP

Table: Failure rate by functional group on SpectraNP

Table: Failure rate by total number of atoms on Real-SpecTeach

Table: Failure rate by number of rings on Real-SpecTeach

Table: Failure rate by largest ring size on Real-SpecTeach

Table: Failure rate by functional group on Real-SpecTeach

We also agree that it’s important to quantify the domain shift between synthetic and real spectra. Following [2], we computed the cosine similarity between synthetic and real spectra for all experimental datasets. The table below shows that the Real-SpecTeach is less noisy than our Real-5mer dataset, and the domain shift for 13C spectra is larger than for 1H spectra.

We also report the average cosine similarity of successful and failed predictions on the Real-SpecTeach. The table below shows that failed predictions have lower similarity between synthetic and real 1H spectra. We note that it’s non-trivial to develop systematic metrics to quantify the spectra domain shift, and it is a great suggestion for our future work.

[Include stereochemistry] We agree that including stereochemistry significantly increases the complexity of the structure elucidation problem, and we will highlight this complexity in our revisions. We initially did not include stereochemical information as 2D NMR spectra, degradation analysis, Marfey's analysis or Mosher ester analysis are usually required to determine absolute configuration at chiral centers. For a fair comparison with Alberts et al. [2], we trained and evaluated NMRDiff3D-M on the USPTO including stereochemistry as [2]. The table below shows that our model still consistently outperforms Alberts et al. with single 1H spectra or 1H and 13C spectra with stereochemistry information.

[Limited evaluation on experimental data] We thank the reviewer and Reviewer Jfo2 for suggesting additional experimental evaluations beyond our Real-5mer and Real-Spec-Teach datasets. We have now evaluated the zero-shot performance of our model on 23k experimental 13C spectra from the NMRShiftDB2 dataset [3] suggested by reviewer Jfo2, and our method obtains 49.51% top-1 accuracy and 56.08% top-5 accuracy.

Thank you again for your helpful feedback – we believe the revisions will directly address your concerns and improve the clarity and impact of the paper.

References:

[1] Polykovskiy, Daniil, et al. "Molecular sets (MOSES): a benchmarking platform for molecular generation models." Frontiers in pharmacology 11 (2020): 565644.

[2] Alberts, Marvin, et al. "Unraveling molecular structure: A multimodal spectroscopic dataset for chemistry." Advances in Neural Information Processing Systems 37 (2024): 125780-125808.

[3] Kuhn, Stefan, and Nils E. Schlörer. "Facilitating quality control for spectra assignments of small organic molecules: nmrshiftdb2–a free in‐house NMR database with integrated LIMS for academic service laboratories." Magnetic Resonance in Chemistry 53.8 (2015): 582-589.

Thank you for your careful reading and extensive feedback. We are especially grateful for your recognition of the technical novelty (“first diffusion-based model to use 1D NMR to generate 3D structure”), performance (“outperforms baselines often by very large amounts”), and potential impact ("would gain significant usage by the Natural Products community”). Below, we provide additional context on the dataset and modeling assumptions, and address your questions point by point.

[Clarifications on our SpectraNP dataset] Thank you for raising the important point on the complexity and scope of our SpectraNP dataset. We will revise our wording to clarify that SpectraNP is a large-scale, synthetic 1D NMR dataset specifically curated for machine learning on complex natural products. While the USPTO [1] dataset contains ~790k molecules, these molecules are limited to up to 35 heavy atoms, whereas ours contains molecules up to 130 heavy atoms. Detailed dataset statistics, including the number of data points, heavy atoms, total atoms, atom types, and solvent types, have been provided in Appendix Table 2. Although NP-MRD [2] includes ~200k predicted spectra and covers larger molecules, its synthetic spectra were generated by learning-based tools, not by MestreNova. For example, synthetic 1H spectra in NP-MRD are predicted by PROSPRE [3], an ML model that was trained on only 577 molecules and tested on ~60 molecules, lacking validation at a large scale. In contrast, we use MestreNova to generate synthetic spectra, which is widely considered a gold standard in the chemistry community and uses a combination of machine learning models with rule-based methods.

We appreciate the reviewer’s suggestion to expand SpectraNP using the COCONUT database [4]. We are actively pursuing this direction and have begun simulating additional spectra from COCONUT to further scale the dataset as part of ongoing work.

[MestreNova license] Thank you for raising this point. The MestreNova user agreement permits academic use of the software, and we note that the synthetic NMR spectra in the USPTO dataset [1] were also generated using MestreNova. We will investigate the release and license needed in compliance with any usage limitations.

[Known molecular formula from mass spectroscopy] Thank you for bringing up this point. We agree that molecular formula determination can be challenging for very large molecules and will make a note of this in the limitations. We note that, in practice, high-resolution mass spectrometry is commonly combined with isotopic abundance and distribution patterns to infer molecular formulas with high confidence. We will note this in our discussion.

[Minor questions]

Equations 1-3: I’m unclear how this enters into the modeling. Why aren’t you just entering the peak coordinates directly, since they are in the data?

The input to our model is the raw 10,000-dimensional NMR spectra vector, where each dimension corresponds to a chemical shift bin and its value represents peak intensity. We use the raw spectra rather than annotated peak coordinates because intensities carry important structural information. For example, in 1H NMR, the peak area reflects proton count. Additionally, using the raw spectra enables end-to-end learning without relying on peak-picking algorithms or external annotation. Further details are provided in Appendix Table 1.

Section 3.2: Can you clarify the output dimension of your diffusion transformer?

The diffusion transformer outputs predicted atom coordinates $\hat{\mathbf{X}}_0 \in \mathbb{R}^{N \times 3}$, where $N$ is the maximum number of atoms in the dataset, and 3 represents the 3D coordinates. For example, in SpectraNP, $N=274$, and molecules with fewer atoms are padded with zeros.

Line 134: Are these thresholds in the smooth LDDT loss annealed during training?

No, the thresholds in the smooth LDDT loss remain fixed during training.

Lines 143-144: You should include the scaling functions in the appendix so the paper is self-contained.

We have included the scaling functions in Appendix L29, and we are happy to clarify this in L143 of the main paper in our revisions.

Fig 4: Is NMRDiff3D-L covered by the curve for NMRDiff3D-M in the middle and right-hand graphs?

No. The middle and right-hand graphs in Figure 4 show the zero-shot performance of NMRDiff3D-M on Real-5mer-D2O and Real-5mer-DMSO datasets. Since NMRDiff3D-M achieves near 100% accuracy on these datasets, we did not train NMRDiff3D-L for computational efficiency. We will clarify this in Figure 4 in our revisions.

This is a tool that would gain significant usage by the Natural Products community if it were posted on the web with a user-friendly interface. Is there a plan to do that?

Yes, we plan to release a user-friendly web interface for NMRDiff3D and the SpectraNP dataset in future work.

Thank you again for your helpful feedback. We believe the revisions will address your concerns and improve the clarity and impact of the paper.

References:

[1] Alberts, Marvin, et al. "Unraveling molecular structure: A multimodal spectroscopic dataset for chemistry." Advances in Neural Information Processing Systems 37 (2024): 125780-125808.

[2] Wishart, David S., et al. "The natural products magnetic resonance database (NP-mrd) for 2025." Nucleic Acids Research 53.D1 (2025): D700-D708.

[3] Sajed, Tanvir, et al. "Accurate prediction of 1H NMR chemical shifts of small molecules using machine learning." Metabolites 14.5 (2024): 290.

[4] Venkata Chandrasekhar, Kohulan Rajan, Sri Ram Sagar Kanakam, Nisha Sharma, Viktor Weißenborn, Jonas Schaub, Christoph Steinbeck, COCONUT 2.0: a comprehensive overhaul and curation of the collection of open natural products database, Nucleic Acids Research, 2024; gkae1063

We thank the reviewer for their thoughtful review and feedback. We appreciate the reviewer for recognizing the high impact of our work in chemistry, novel modeling approach (similar to reviewers 5f4b and bfwb), and extensive ablations, with reviewer bfwb agreeing that "experimental pipelines are well thought out and executed." Below, we address your questions and concerns point by point.

[Train on only 1H or 13C spectra] We agree with your point that our model should, in principle, work well when only applied to 1H or 13C NMR spectra. We have analyzed the impact of training on 1H and/or 13C spectra in Appendix E.3 and Appendix Figure 2. We found that while the model has performed well with a single spectrum type, the combination of 1H and 13C spectra provides complementary information that further improves performance in general. We chose to focus on the combined setting to demonstrate the full potential of our approach.

To benchmark our model against baselines on a single type of spectrum, we evaluate all models on the SpectraBase dataset as shown in Table 1. Our model still consistently and significantly outperforms the baselines with only $^1$H or ${}^{13}$C spectra.

Table 1: Performance on SpectraBase dataset using $^1$H or ${}^{13}$C spectra.

[Additional experimental benchmarks] Thank you for the suggestion for benchmarking on the NMRShiftDB2 dataset [3] used by [1] and [2]. We have evaluated the zero-shot performance of our model on the 23k experimental 13C spectra from NMRShiftDB2, and our method obtains 49.51% top-1 accuracy and 56.08% top-5 accuracy. In comparison, [1] reports <1% top-5 accuracy on a subset of 2k molecules, and [2] reports 55.9% top-1 accuracy and 58.6% top-5 accuracy on a subset of simpler molecules with only C, H, O, and N elements and fewer than 64 atoms. We further note that [2] requires additional information on the number of adjacent hydrogens bonded to each carbon.

Thank you for pointing out reference [4], which has also been evaluated on the van Bramer dataset (referred to as “Real-SpecTeach” in our manuscript). [4] is a sequence-based approach that reports 53.16% top-1 accuracy with 13C spectra, and 31.58% top-1 accuracy with 1H spectra. In comparison, our NMRDiff3D-L achieves 66.86% top-1 accuracy with 13C spectra and 62.26% top-1 accuracy with 1H spectra. We note that they evaluate on a subset of the dataset (171 molecules) while we use all 239. Finally, [4] was released on ChemRxiv after the NeurIPS 2025 submission deadline, and their model is not yet fully open-sourced, however we will include a head-to-head benchmark against this method in our revisions.

Thank you again for your helpful feedback. We believe the revisions will directly address your concerns and improve the clarity and impact of the paper.

References:

[1] Sridharan, Bhuvanesh, et al. "Deep reinforcement learning for molecular inverse problem of nuclear magnetic resonance spectra to molecular structure." The Journal of Physical Chemistry Letters 13.22 (2022): 4924-4933.

[2] Jonas, Eric. "Deep imitation learning for molecular inverse problems." Advances in neural information processing systems 32 (2019).

[3] Kuhn, Stefan, and Nils E. Schlörer. "Facilitating quality control for spectra assignments of small organic molecules: nmrshiftdb2–a free in‐house NMR database with integrated LIMS for academic service laboratories." Magnetic Resonance in Chemistry 53.8 (2015): 582-589.

[4] Alberts, Marvin, Nina Hartrampf, and Teodoro Laino. "Automated Structure Elucidation at Human-Level Accuracy via a Multimodal Multitask Language Model." (2025).

Thank you for your thoughtful review and feedback. We appreciate your recognition of the novelty of our approach (“novel diffusion-based approach”), the novelty of our problem (“a very interesting/relevant problem that not a lot of people focus”), and the clarity of our paper (“The paper is well written and is of sufficient quality for NeurIPS”). Below, we address your questions and concerns point by point.

[Clarifications on technical contributions] As recognized by reviewers 5F4B and BFWB, our method is “the first approach that uses diffusion to predict 3D coordinates from 1D NMR spectra and chemical formula.” While this model builds on diffusion transformers, the novelty lies in applying them to the challenging and underexplored task of structure elucidation from 1D NMR spectra. To do so, we introduce a hybrid convolutional-transformer encoder for 1H and 13C spectra and adapt a non-equivariant diffusion transformer to condition on spectral and formula embeddings for complex natural products. To the best of our knowledge, we are also the first to include a smooth LDDT loss term in the diffusion objective for small molecule generation to improve the local structural fidelity. We will revise the introduction to clarify and highlight these contributions.

[Weak baselines] We emphasize that the baselines may appear weak because the task of structure elucidation from 1D NMR spectra is intrinsically challenging and remains largely underexplored. Part of our contribution is to establish stronger modeling approaches for this new and difficult task.

[Equivariance] We agree that equivariant models are valuable in low-data regimes. However, we note that datasets on the order of 100k-1M do not necessarily require equivariance for strong performance in 3D atomic generation. For example, MCF [1] shows that a non-equivariant transformer outperforms equivariant baselines for the molecular conformation generation task on GEOM-QM9 (130k) and GEOM-DRUGS (304k) [2]. Recently, a non-equivariant version of Proteina [3] for protein backbone generation was shown to outperform equivariant baselines on Foldseek-AFDB (588k).

[RMSD 3D metric] Thank you for the suggestion. We report the top-k Average Minimum RMSD (AMR) of heavy atoms in the table below. We initially did not compute RMSD as there is no baseline of comparison for other non-3D methods, and RMSD is not a size-independent metric, which limits its interpretability, but we find that the AMR on each dataset is reasonable considering the complexity of the dataset. We will add this metric to the appendix of our manuscript.

[Generalization across atom types and solvents] Our model is trained on a diverse set of natural products with a wide range of atom types (C, H, O, N, S, P, F, Cl, Br, I) in the CDCl3 solvent, as shown in Appendix Table 2. To assess generalization across different atom types or local environments, we compute the top-10 accuracy of our NMRDiff3D-L by functional group on the SpectraNP test set. As shown in the table below, our model performs consistently across different functional groups.

Additionally, we note that our model trained on the 5mer dataset with CDCl3 solvent can achieve nearly 100% accuracy on the Real-5mer dataset with D2O and DMSO solvents (Figure 4), suggesting its potential to generalize to unseen solvents. However, we acknowledge that performance will not necessarily hold for solvents with different polarities, and will expand the limitations section to reflect this.

Table: Top-10 accuracy by functional group on the SpectraNP test set.

[Limitations of existing graph methods] Apologies for the confusion. Graph-based methods are not inherently limited to 64 atoms; however, the existing graph methods [4, 5, 6], based on Markov decision processes, beam search, or Monte Carlo tree search, mentioned in the related work section, address molecular graphs with no more than 64 atoms. This may be due to a lack of large-scale spectra datasets for larger molecules or the computational complexity of search-based methods when applied to larger molecules. We will revise the manuscript to clarify this point.

[Evaluation and practical adoption] Thank you for your comments about evaluation. There are currently no widely adopted methods that can reliably predict structures from 1D NMR spectra, which was the motivation for this work. The main approach used in the community is manual structure elucidation by expert chemists, which is time-consuming and labor-intensive. We believe our NMRDiff3D model can be used to suggest candidate structures that chemists can then verify, significantly reducing the time and effort involved. While it's hard to define a universal accuracy threshold for full adoption, we believe our current performance is already useful in real application settings.

Thank you again for your careful reading. We believe these clarifications and planned revisions will substantially strengthen the paper.

References:

[1] Wang, Yuyang, et al. "Swallowing the bitter pill: Simplified scalable conformer generation." arXiv preprint arXiv:2311.17932 (2023).

[2] Axelrod, Simon, and Rafael Gomez-Bombarelli. "GEOM, energy-annotated molecular conformations for property prediction and molecular generation." Scientific Data 9.1 (2022): 185.

[3] Geffner, Tomas, et al. "Proteina: Scaling flow-based protein structure generative models." arXiv preprint arXiv:2503.00710 (2025).

[4] Jonas, Eric. "Deep imitation learning for molecular inverse problems." Advances in neural information processing systems 32 (2019).

[5] Huang, Zhaorui, et al. "A framework for automated structure elucidation from routine NMR spectra." Chemical Science 12.46 (2021): 15329-15338.

[6] Sridharan, Bhuvanesh, et al. "Deep reinforcement learning for molecular inverse problem of nuclear magnetic resonance spectra to molecular structure." The Journal of Physical Chemistry Letters 13.22 (2022): 4924-4933.