Atomic Diffusion Models for Small Molecule Structure Elucidation from NMR Spectra
Authors: Ziyu Xiong
Yichi Zhang
Foyez Alauddin
Chu Xin Cheng
Joon Soo An
Mohammad R. Seyedsayamdost
Ellen D Zhong
Venue: NeurIPS 2025 poster ()
Keywords: Diffusion Models
NMR Spectroscopy
Natural Products
Machine Learning for Chemistry
Primary area: machine_learning_for_sciences
TL;DR: We propose an atomic diffusion model that can predict small molecule structures from 1D NMR spectra.

Abstract: Nuclear Magnetic Resonance (NMR) spectroscopy is a cornerstone technique for determining the structures of small molecules and is especially critical in the discovery of novel natural products and clinical therapeutics. Yet, interpreting NMR spectra remains a time-consuming, manual process requiring extensive domain expertise. We introduce ChefNMR (CHemical Elucidation From NMR), an end-to-end framework that directly predicts an unknown molecule's structure solely from its 1D NMR spectra and chemical formula. We frame structure elucidation as conditional generation from an atomic diffusion model built on a non-equivariant transformer architecture. To model the complex chemical groups found in natural products, we generated a dataset of simulated 1D NMR spectra for over 111,000 natural products. ChefNMR predicts the structures of challenging natural product compounds with an unsurpassed accuracy of over 65%. This work takes a significant step toward solving the grand challenge of automating small-molecule structure elucidation and highlights the potential of deep learning in accelerating molecular discovery.

Atomic Diffusion Models for Small Molecule Structure Elucidation from NMR Spectra
Ziyu Xiong
Princeton University
ziyux@princeton.com
Yichi Zhang
Foyez Alauddin Princeton University
Princeton University
zycddd@ppinnetto. edu
fa1073Galumni, wwwpceton.ncceeee edu
Chu Xin Cheng
Joon Soo An
California Institute of Technology ccheng20alumi caltech. edu
Princeton University
hanjjussoo@riineeon.edd
Mohammad R. Seyedsayamdost
Ellen D. Zhong
Princeton University mrseyed@princeton edu
Princeton University zhonge@princeton. edu
Abstract
Nuclear Magnetic Resonance (NMR) spectroscopy is cornerstone technique for determining the structures of small molecules and is especially critical the dis- covery of novel natural products and clinical therapeutics. Yet, interpreting NMR spectra remains consumin,,, manual process requiring extensive domain expertise. We introduce CHEFNMR (CHemical Elucidation From NMR), end- to-end framework that directly predicts an unknown molecule's 's structure solely from its ID NMR spectra and chemical formula. We frame structure elucidation conditional generation from an atomic diffusion model built on a non equivarriin transformer architecture. To model the complex chemical groups found in natural products, we generated a dataset simulated ID NMR spectra for over 1,000 natural products. CHEFNMR predicts the structures of challenging natural prod- uet compounds with an unsurpassed accuracy of over 65%. This work takes a significant step toward solving the grand challenge of automating structure elucidation and highlights the potential of deep learning in accelerating molecular discovery.
1 Introduction
The molecules that sustain life come several forms: large biopolymers such as DNA, RNA, and proteins described pathways and influence all aspects of biology. A category small molecules, known as secondary metabolites natural products, describes those that secreted into the environment where they serve myriad functions, such as signaling and chemical warfare. Because of these roles, natural products have delivered more than half of the FDA-approved small-molecule agents, including the majority of antibiotics and antitumor drugs in current clinical use, such as penicillin, taxol, and other blockbuster drugs such as lovastatin and semaglutide (48
genetic code, and small molecules. which form complex metabolic
68 58)
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Source Organism
1D NMR Spectroscopy
Novel Natural Products
J-caupling
THE NMR Spectrum
Chemical Shift
M NMR Spectrum
220
180
140
100
60
20
Chemical Shift (opm)
Erythromyyin
Figure 1: Natural products are small molecules secreted by natural sources such as plants, animals, and microorganisms (left). To identify an unknown molecule's structure, 1D NMR spectroscopy mea- sures peaks corresponding to each proton ('H) or carbon (1$C) atom (middle). The resulting chemical shifty (x-axis locations), peak intensities, and J-coupling (splitting patterns) encode information on chemical groups and connectivities, from which the molecular structure can be deduced (right).
The functions of small molecules are intrinsically linked their molecular structures, which govern their chemical and biological reactivity. Very recently, deep learning methods have revolutionized the prediction of a protein's 's 3D structure from its amino acid sequence encoded the genome [30 2]. Small molecules, by contrast, are neither directly genetically encoded nor repeating polymers. Structure clucidation therefore relics on de novo experimental methods for every new molecule, making the discovery of cellular metabolites, essential molecules, antibiotics, and other therapeutics
a slow and tedious process 8 48 [8].
Nuclear Magnetic Resonance (NMR) spectroscopy is cornerstone technique for small molecule structure elucidation. This experimental method provides information regarding the connectivity and local environment of, typically, each proton ('H) and carbon (1)C) in a molecule, thus allowing the structure of a molecule to be deduced. However, the inverse problem inferring the chemical structure from these spectral measurements is challenging puzzle, which largely proceeds manually and requires significant time and expertise, even with computational assistance [8] Consequently, automating molecular structure elucidation directly from raw ID NMR spectra would significantly accelcrate progress in chemistry, biomedicine, and natural product drug discovery [56]
42
With the rise of deep learning approaches applied to molecules, diffusion generative models
20
59
32
have emerged as powerful tools for tasks such as small molecule generation 21
69
ligand-protenn docking [10] 577 and protein structure prediction [2] 73 and design 25 70
15
While early approaches emphasize 3D geometric symmetries via equivariant networks, recent trends suggest that non-equivariant transformers scale more effectively with model and data size and better
capture 3D structures with data augmentation 69 2
In this work, we tackle the challenging task of NMR structure elucidation for complex natural products. We introduce CHEFNMR (CHemical Elucidation From NMR), an end-to-end diffusion model designed to infer an unknown molecule's structure from its ID NMR spectra and chemical formula. CHEFNMR processes NMR spectra using a hybrid transformer with convolutional tokenizer designed to capture multiscale spectral features, which are then used to condition Diffusion Transformer [49] for 3D atomic structure generation. To scale the complex chemical groups found in natural products, we curate SpectraNP, large-scale dataset of synthetic ID NMR spectra for 11 111,181 complex natural products (up to 274 atoms), significantly expanding the chemical complexity of prior datasets (5101 atoms) 22 4 We compare CHEFNMR against chemical language model-based and graph-based formulations and demonstrate sfate-of-the accuracy across multiple synthetic and experimental benchmarks.

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2 Background
NMR spectroscopy is widely used analytical technique in chemistry for determining the structures of small molecules and biomolecules. A typical one-dimensional (ID) NMR experiment measures the response of all spin-active nuclei of given type, for example hydrogen (H or isotopic carbon (2) to radiofrequency pulses a strong magnetic field. The resulting spectrum consists of peaks from chemically distinct nuclei, where peak positions (i.c., chemical shifts), intensities, and fine splitting patterns (i.e., J-coupling) reflect local chemical environments and connectivities of the nuclei.
Formally, let the observed spectrum be a real-valued signal S()) R - R, where å denotes the chemical shift (in parts per million, ppm) along the x-axis. The signal can be modeled as sum over N resonance peaks corresponding to each spin-active nucleus:
N S()) = Σ 4 1(6; + c(6)
where A, is the intensity (amplitude) of the i-th peak, 8, is the chemical shift (peak center), and %/ is the linewidth (related relaxation) of the peak. L(ō: 6,, w) the normalized Lorentzian line shape:
74
L(6; m3
π [6
and e()) models additive noise (e.g., g., Gaussian white noise or baseline drift). J-coupling refers to the splitting of the signal for given nucleus into of multiple peaks when nearby atoms interact:
N
M, Au L(ō; 8ik, 7a) + e(0)
S(0)
where M, is the number of split components for the i-th nucleus, and 6g encodes the shifted peak positions. J-coupling occurs when other spin-active nuclei are within 2-4 edges in the molecular graph, and the signal splits into M, m++1 components assuming m interacting nuclei. See Figure for an example.
Together, these features encode rich information about the types of chemical groups present and their connectivities, enabling chemists to deduce the underlying molecular structure. For example, certain chemical groups produce peaks that appear at established range (e.g.. aromatic ring- protons are detected at 6.5-8 ppm), whose exact location depends on the amount of chemical shielding from nearby atoms in given molecule. These patterns, in addition to experimental noise due to the instrument, impurities, and solvent effects, make the inverse problem of deducing structure an extremely challenging task. NMR structure elucidation thus typically relies on additional information from 2D NMR experiments, prior information on the substructures present, or chemical formula from high-resolution mass spectrometry 7 combined with isotopic abundance and distribution patterns. In this work, we utilize the chemical formula as auxiliary input, as it is typically the most readily obtainable among common priors and effectively constrains the space of candidate molecular structures for complex natural products.
3 Method
In this section, we present CHEENMR, an end-to-end diffusion model for molecular structure elucidation from 1D NMR spectra and the chemical formula. Our approach consists of two key components: NMR-ConVFormer for spectral embedding (Section 3.1) and conditional diffusion model for 3D atomic coordinate generation (Section 3.2
In CHEFNMR, we represent molecule-spectrum pairs (A, X, where A E {0, Mx denotes the one-hot encoding of atom types for a molecule with atoms and dawn possible atom types, X E Nx3 represents the 3D atomic coordinates, and S = (SH, sc) contains the NMR spectra, specifically the 'H spectrum 8μ E Ie and the 13C spectrum sc E dede Our objective is to generate the 3D coordinates X conditioned on the atom types (i.e., chemical formula) and the spectra S by sampling from the conditional probability distribution p( X S).
3

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(a) NMR-ConvFormer
(b) ChefNMR Diffusion Transformer
Predicted Coordinates X
Embed
Layer Norm & Linear
Scale
Multihead
Pooling
15.0
Scale, Shift
Adaptive LN Linear
Layer Norm
x Transformer Encoder Block
N x DIT Block
Scale
Position Type Encoding
NMR Embed
MLP
Multi-head Self-Atbention
Conv Tokenizer
Conv Tokenizer
MLP
Scale, Shift
71.
Noise Level o
Layer Norm
Input Tokens
Conditions
NMR Spectrum
FC NMR Spectrum
Concat A
Overview of the CHEFNMR architecture. (a) IMR-ConVFormer processes 1D NMR spectra into a vector embedding using the convolutional tokemizer, transformer encoder, and multihead attention pooling (MAP). (b) Diffusion Transformer predicts clean 3D coordinates X, from atom tokens formed by concatenating noisy coordinates X, and atom types A, conditioned the spectral embedding and noise level via adaptive layer normalization [49]
Figure 2:
3.1 NMR-ConnFFormer: A Hybrid Convolutional Transformer for NMR spectral embedding
To effectively condition the generative process the NMR spectra S, propose NMR-Conv Former, an encoder designed to capture both local spectral features and global correlations within and between the 'H and 13C spectra, shown in Figure a). Unlike prior methods that rely solely ID convolutions [22 45 or transformers with simple e patching 66
Cee-ConyFormee
66]63, 63), MaRR-ConFForme uses a hybrid approach, combining convolutional tokenizer for local feature extraction and transformer encoder for modeling complex intra- and inter-spectral dependencies.
Convolutional Tokenizer. Each input spectrum ('H and 19C) is processed independently by convolutional tokenizer comprising two ID convolutional layers with ReLU and max-pooling, similar to [22]. This reduces sequence length while increasing channel dimensions, summarizing local patterns like peak intensity and splitting. The output is linearly projected to dimension Dencoder- yielding token sequences of shape (I', Dencoder).
Transformer Encoder. The token sequence, augmented with positional and type embeddings, is processed by standard transformer encoder comprising multi-head self self-attention and feed-forward networks with pre-layer norm and residuals. Self-attention captures patterns within each NMR spectrum and across different spectra, such as related peaks in H spectrum or matching signals from the same chemical group both HH and L&C spectra.
Multihead Attention Pooling (MAP). We use MAP 37
79 to obtain fixed-size spectral embed- ding. learnable [CLS] token prepended the encoder output sequence aggregates information via a final self-attention layer. The resulting [CLS] token state, after layer normalization and linear projection, serves the conditioning vector æs IR Drain for the diffusion model. Dropout is applied at multiple stages to mitigate overfitting, See Appendix D.2 for detailed hyperparameter settings.
3.2 Conditional 3D Atomic Diffusion Model
Training Objective. We adapt the EDM diffusion framework to conditional 3D molecular gen- eration (32. The model Dg is trained to predict clean 3D coordinates X, from noisy inputs X, X + where n ~ (N and the noise level is sampled from pre-defined

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distribution p(o). Given X 0, atom types A, and spectral embedding 2s. the model minimizes:
Ldiftusion -E
(s)
[OSE Xo. Xo) + Samooth Idu (Xo. Xo)
(4)
where Xo - Do(Xo: A. z5) are the predicted coordinates.
The MSE loss, LMSE = | - enforces global structure alignment. To ensure local geometric accuracy (e.g.. bond lengths), crucial for chemical validity and often poorly captured by MSE alone. we add smooth Local Distance Difference Test (LDDT) loss [33. adapted from AlphaFold3 [2].
X
The LDDT score is computed over all distinct atom pairs (i,
1 LDDT(Xo: Xo) N(N
Σ igj
Eij
where
Σ sigmoid((x
-dds digl). (5)
Here, dij 1 - 22112 and dij || æo.i l| the predicted and true distances, respectively. Thresholds tx (0.5, 1.0, 2.0, 4.0 Å} specify allowable deviations between predicted and true distances when evaluating prediction accuracy. The smooth LDDT loss is Lsmooth = 1 LDDT, encourages local geometric fidelity by penalizing pairwise deviations. The combined loss promotes both global alignment and local chemical validity.
Random Coordinate Augmentation. For each molecule, we generate h ground-truth conformers. During training, we randomly sample one conformer Xo and apply a random rigid transformation (translation and rotation) following (2] 29 40 This augmentation encourages Dg learn SE(3)-
invariant representations and mitigate overfitting, significantly improving performance.
Diffusion Transformer (DiT) Architecture. The network Dg is DiT [49] shown in Figure (b.). Input atom tokens are formed by concatenating noisy coordinates X, and atom types A, followed by an MLP projection. The noise level a is embedded using frequency encoding and MLP. This noise embedding is added to the spectral embedding 2s to form the conditioning vector, which is integrated into the DiT blocks via adaptive layer normalization LadaLN-Zero)
[49
Conditional Dropout and Classifier-Free Guidance. To improve robustness and flexibility in conditioning on different NMR spectra, we adopt classifier-free guidance (CFG) [19]. During training, the 'H NMR spectrum dropped with probability pa = 0.1, the 13C NMR spectrum is dropped with Pc = 0.1, and both are dropped simultaneously with Photh 0.1. At inference, conditional and unconditional predictions are combined via
Dø xx: A, =s) = (1 + w) Do a. A, zs) - w Do(X,; A),
where w w20 0 controls guidance scale. This enables generation conditioned on either or both spectra, improving versatility and performance. See Appendix A and D.2 for full training and sampling algorithms and hyperparameter settings.
4 Related Work
NMR Spectra Prediction. The forward task of predicting given molecule's NMR spectra is relatively established, facilitating data analysis and enabling the generation of simulatd datasets for structure elucidation of simple compounds via database retrieval. These spectra prediction methods range from precise, computationally intensive quantum-chemical simulations to more recent exploratory MI. approaches
39 44 Following established dataset curation practices [2 4. we create our SpectraNP dataset using the commercial software MestReNova [44)
6 28
13
35
31
16]
which combines closed-source ML and chemoinformattis algorithms.
NMR Structure Elucidation. Structure elucidation from NMR spectroscopy is challenging inverse problem, due to the complexity of spectra data and the vast chemical space [60] 17]. Traditional
computer-aides systems, while historically employed and useful, often suffer from computational inefficiencies [8]. Recent ML methods have tackled this challenge, but most simplify the problem by
predicting molecular substructures instead of full molecules 38
36
or by leveraging
richer inputs, such multimodal spectra beyond NMR 154
12
50
55
63 53 and database
33 In contrast, our method directly tackles the de nove elucidation of molecular structures using only raw ID NMR spectra and chemical formulae.
retrieval 78
5

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De Novo Structure Elucidation from 1D NMR Spectra. Recent work developing machine learning methods for de novo structure elucidation from ID NMR spectra focuses on structurally simple molecules, leveraging either chemical language models or graph-based models. Chemical language models 80 [2 3
generate SMILES strings [71], sequence-base molecular representation. For pairs and fine-tuned on 143k NMR spectra from SpectraBase [26). achieving 69.6% top-15 15 accuracy for molecules under 59 atoms. Alberts et al. B 4 employ transformers to predict SMILES from text-based ID NMR peak lists and chemical formulas, reporting 89.98% top-10 10 accuracy on the USPTO dataset [1 for molecules under 101 atoms. Graph-based models iteratively construct molecular graphs with GNNs, using methods like Markov decision processes or Monte Carlo tree search 27 23 61. However, these methods do not handle molecules with more than 64 atoms or large rings (>8 atoms), likely due to the limited availability of large-scale spectral datasets and the high computational cost of search-based algorithms for complex molecules. To the best of our knowledge, CHEENMR is the first method based on 3D atomic diffusion models for NMR structure elucidation that scales to complex natural products.
example, Hu et al. [22] use multitask transformer pre-trained on 3.1M substructure-molenn
3D Molecular Diffusson Models. Diffusion models have emerged as powerful tools for 3D molecular generation. E(3)-qquivariant GNNs [74 21 75 46 enforce geometric constraints, but non-equivariant transformers are increasingly favored for their scalability and performance in small molecule genera- tion 169 40 29 and protein structure prediction [2] [5] involving hundreds of thousands of atoms. Inspired by these recent trends, we apply a scalable DiT [49] to generate 3D atomic structures from NMR spectra, exploiting their scalability and expressivity by creating large synthetic NMR spectra dataset of natural products.
Experiments
5.1 Dataset Curation
Table Summary of dataset statistics.
Synthetic Datasets. We evaluate models on two public benchmarks, SpectraBase [22] and
Synthetic
# Molecules
# Atoms
USPTO 4. and our self-curated SpectraNP dataset.
SpectraBase
(22
141k
59]
SpectraBase contains simple molecules [22 26
USPTO 4
745k
[8, 101]
while USPTO features a broader range of molecules in chemical reactions [41]. SpectraNP com- bines data from NPAtlas [52] a database of small molecules from bacteria and fungi, with subset of NP-MRD 72 including various natural products.
SpectraNP
11lk
[4, 274]
Experimental
# Molecules # #Solvents
SpecTeach 665
238
2
NMRShiftDB2 33
23k
>7
Experimental Datasets. To evaluate the ability of models trained on synthetic data to generalize to experimental data, we curate two experimental datasets. Following [. we include the SpecTeach dataset 655 which contains 238 simple molecules for spectroscopy education. We also include NMRShiftDE2 34 a larger-seale dataset of 1&C NMR
spectra in various solvents, following [6] 28 These experimental datasets include impurities, solvents, and baseline noise (See Figure 5). enabling robustness testing for experimental variations.
Data Structure and Preprocessing. Each data entry is a tuple (SMILES, 1I1 NMR spectrum, C3c NMR spectrum, atom features). SMILES strings are canonicalized with stereochemistry removed, and synthetic spectra are simulated using MestreNova 44). Atom features include atom types A and 3D conformations X, generated using RDKit's ETKDGv3 algorithm M given the SMILES string.
To preprocess datasets, any duplicate SMILES are first removed. LH and I&C spectra are interpolated to 10.000-dimensional vectors following
22 4 and normalized by their highest peak intensity, except for SpectraBase [22 and experimental datasets, where 13C spectra are binned into 80 binary vectors. To validate 3D conformers, SMILES strings are reconstructed from atom types and 3D coordinates using RDKit's DetermineBonds function [ and molecules failing reconstruction are discarded. See Appendix C for dataset curation details.
5.2 Experimental Setup
Baselines. We compare CHRENMR against two existing chemical language models and introduce graph-based model to assess the impact of molecular representations the structure elucidation task.

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The chemical language models are: (1) Hu et al. 22 propose two-stage multitask transformer for predicting SMILES from ID NMR spectra. Their method pre-defines 957 substructures and pre-trains substructure-tee -onetturrrtt-----E-E---- SMILES model on 3.IM molecules, and then fine-tunes multitask transformer on 143k NMR spectra from SpectraBase. We retrain their PenstructurettoSMMIl..
model on the same 3.1M 1M dataset and fine-tune it on each synthetic benchmark. (2) Alberts et al. 4 develop transformer to predict stereochemical SMILES from text-based ID NMR peak lists and chemical formulae. Due to unavailable inference code and differences in input (peak lists raw spectra) and output (stereo vs. non-stereo SMILES), we report their published results on USPTO and SpecTeach.
To test an alternative graph- based representation, we also propose NMR-DiGress, model integrating the discrete graph diffusion model DiGress [66] with our WMMR-Conyorriit Molecular graphs are represented as atom types A and bond matrices E E {0, 1 xxdxax where N is the number of atoms and dhonn the number of bond types. DiGress adds noise each atom or bond independently via discrete Markov chains, and trains a graph transformer to reverse this process to generate molecular graphs. We adapt DiGress to condition on spectral features from UMR-ConvFormn and atom types A. generating only bond matrices. See Appendix B and D.I for full algorithms and detailed settings.
CHEENMR. We evaluate two variants: CHEENMR-S (134M parameters) and CHEENMR-L (462M parameters) with the same NMR-ConvFormer and different sizes of DiT. See Appendix D.2 for additional experimental details.
Metrics. We evaluate models using: (1) Top-k matching accuracy, which checks whether the ground truth SMILES string exactly matched by any of the top-k predicted molecules. For non- language models, we reconstruct canonical, non-stereo SMILES from the predicted molecular graph (atom types and generated bond matrix) or 3D structure (atom types and generated 3D coordinates) using RDKit [II. (2) Top-k maximum Tanimoto similarity, which evaluates structural similarity between the ground truth and the most similar molecule in the top-k predictions, using the Tanimoto similarity of Morgan fingerprints (length 2048, radius 2) [].
6 Results
This section presents the quantitative and qualitative results across benchmarks. Section 6.1 shows CHEENMR'S 's state-of-the-an performance synthetic datasets, and Section 6.22 demonstratsss robust zero-shot generalization on experimental datasets. Section 66.3 presents ablation studies on the contributions of the diffusion training process and the NMR-Conv spectra embedder.
6.1 Performance on Synthetic Spectra
Sable the performance on synthetic 'H and L3C NMR spectra. CHEENMR significantly surpasses all baselines in matching accuracy and maximum Tanimoto similarity across datasets. The
Table 2: Performance on synthetic 'H and 13C NMR spectra, reported as the mean + standard deviation over three independent sampling runs. Acc%: accuracy; Sim: Tanimoto similarity. reported results. N/A: not applicable.
Top-1
Top-5
Top-10
Dataset
Model
Acc%
Sim f
Acc% f
Sim f
Acc% f
Sim
Hu NMR-DiGress
45.24
0.6864.001
0.815 62.37
67.384.05
0.847+.001
43.56.2.30
0.625.1.02
62.47
0.779 002
68.394.35
0.817+.001
SpectraBase
CHEENMR-S
69.15:1.08 0.807:1002
82.09
0.904 000
85.301.04
0.922+.000
CHEENMR-L L
72.04:1.02
0.833:1.000
85.24
0.923
88.201.07
0.940:1.000
Hu et al.
38.02#:02
0.6744.001
55.85
0.810 1810= 000
61.764.03
0.845+.000
Alberts al."
73.38
N/A
87.94
N/A
89,98+.16
N/A
USPTO
MMR-DiGress
22.51+.13 0.5044.00 000
41.26#.12
0.708
48.87+.11
0.761
CHEENMR-S
81.16.1.08
0.902.1.000
91.03
0.9641..00 1.000
92.90.1.05
0.973 1.000
CHEENMR-L
81.57 11009
0.912.1.000
91.09
0.9651.00
93.01
1.973
Hu et al.
19.26:t.10
0,585+.001
34.00=.19
0.736 001
39,87+.02
0.774+.000
NMR DiGress 2.12+114
0.260=+001
6.31
0.432#.001
9.17+.11
0.485+.000
SpectraNP
CHEENMR-S
40.37
0.583
59.08
0.791 0.00
64.374.0R
0.834
CHEENMR-L.
40.154.29
0.631 -.04
59.83
0.8224.002 .002
65.74.1.9
0.860

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(a)
(b) Target Structure
Predicted Structures
Target Structure
Predicted Structures
0.794
0.657
0.718
Figure 3: Examples of CHEFNMR'S 's predictions on the synthetic SpectraNP dataset. (a) Correctly predicted diverse and complex natural products top-1 predictions. (b) Incorrect top-2 predictions ranked by Tanimoto similarity remain chemically valid and structurally similar to the ground truth.
advantage is most pronounced on the challenging SpectraNP dataset, where CHEENMR achieves 40% top-1 accuracy compared to 19% for Hu et al. and only 2% for NMR-DiGress.
Performance scales with both model and dataset size. CHEFNMR-S outperforms baselines by large margins across all datasets, and CHEFNMR-L further improves accuracy. Larger datasets also yield better results, with the highest performance observed on USPTO (745k data), followed by SpectraBase (141k data) and SpectraMP (111k data). This suggests expanding SpectraNP could further enhance performance in elucidating complex natural products.
Figure 3 provides qualitative examples of CHEENMR'S performance on SpectraNP. CHEENMR accurately predicts diverse and complex natural product structures in its top-1 predictions (Figure We additionally show incorrect predictions (Figure b)), and find that many of the generated structures remain chemically valid and similar to the ground truth. Additional qualitative examples are provided Appendix F.4
SpecTeach
NMRShRDD62
80
80
20
1.0
0.8
Shileng
0.4
02
Predictons
Predicions
Alberts
NMR-DIGRE
CheINMR-S
ChaNNMR-L
Figure 4: Zero-shot performance on experimental NMR spectra, shown as the mean + standard deviation over three independent sampling runs. Models are trained on USPTO. Evaluation on HH and 13C spectra for SpecTeach, and on 1&C spectra for MMRShfftDB2. ": reported results.

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(a)
TH NMR
NMR
Correct Prediction
(b)
CC NMR
Correct Prediction
CDCCs
CD,0D
JDMOO
CyDe
Figure 5: Examples of correct structures in CHEFNMR's top-1 predictions on experimental (a)
SpecTeach and (b) XMRShiftDB2 datasets respectively, with solvent peaks marked in red.
6.2 Zero-shot Performance on Experimental Spectra
Figure reports the zero-shot performance on experimental 'H and 1$ NMR speetra. CHEENMR achieves 56% top-1 accuracy SpecTeach and 21% on NMRShi
significantly outperforming Hu et al. [22] and AMR-DiGrees which generalize poorly to both experimental benchmarks. Figure shows that CHEFNMR can generate the correct structures in its top-1 predictions despite substantial experimental variations, such as solvent effect and impurities.
6.3 Ablation Studies
Table 3: Ablation results (Top-1 Acc% Sim). Configuration
We perform extensive ablation studies assess the contributions of key components in diffusion train- ing and the NMR-ConyFormer the SpectraBase dataset. Each row in Table 3 corresponds to a vari-
Acc@ 1% t Sim @ 1
Base (CHEFNMR-S)
69.15
0.807
Diffusion Training Ablation
with one component removed or modified from
Coord Augmentation
49.75
0.651
the base setting. Coordinate augmentation improves accuracy by 20%, indicating learning symmetries is crucial. Within the OMR-ConvFormme, convo-
Smooth LDDT Loss
68.31
0.798
MMRR-CnnFormmer Ablation
lutional tokenizer, MAP pooling, and dropout are
Conv Tokenizer
61.78
0.756
Token Count Reduction
66.28
0.789
relatively important. Detailed settings and additional
Transformer Block
68.12
0.797
ablations, including separate contributions of H and
MAP Pooling
62.97
0.758
C&C spectra, are provided in Appendix
Dropout
65.48
0.777
7 Conclusion
In this work, we address the challenge of determining structures for complex natural products directly from raw ID NMR spectra and chemical formulas. We introduce CHEENMR, an end-to-end diffusion model that combines hybrid convolutional transformer for spectral encoding with Diffusion Transformer for 3D molecular structure generation. To encompass the chemical diversity present in natural products, we curate SpectraNP, a large-scale dataset of synthetic ID NMR spectra for natural products. Our approach achieves state-of-the-a accuracy on synthetic and experimental benchmarks, with ablation studies validating the importance of key design components.
Several limitations highlight promising directions for future work. Expanding the training set to include experimental spectra and more natural products could further improve model performance. Additional information, such as 2D NMR spectra, could be incorporated to resolve stereochemistry. Furthermore, adding confidence module could help chemists better assess the reliability of predicted structures. Overall, automating NMR-based structure elucidation has the potential to significantly accelerate molecular discovery. Careful validation and responsible deployment will be essential to ensure safe and impactful use real-world applications.

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Acknowledgements
The authors acknowledge the of computing resources Princeton Research Computing. consortium of groups led by the Princeton Institute for Computational Science and Engineering (PICSciE) and Office of Information Technology's Research Computing. The Zhong lab is grateful for support from the Princeton Catalysis Initiative, Princeton School of Engineering and Applied Sciences, Chan Zuckerberg Imaging Institute, Janssen Pharmaceuticals, and Generate Biomedicines. The Seyedsayamdos! lab is grateful for support from the Princeton Catalysis Initiative and a Princeton SEAS grant. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. The authors also thank the silhouette of Actinomyces used Figure Preateed created by Matt Crook and licensed under CC BY-SA 3.0 Unported.
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A Details of Conditional 3D Atomic Diffusion Model
In this section, provide full training and sampling algorithms for the conditional 3D atomic diffusion model described in Section 3.2 of the main paper.
Training Procedure. The complete training procedure is outlined in Algorithm [ The smooth LDDT loss is detailed Algorithm 2 adapted from AlphaFold3 [2). Unlike the original, which computes the smooth LDDT loss within certain radius for proteins (2), we compute it of all atom pairs for small molecules, as small molecules are more compact in 3D space than proteins.
Algorithm 1 Diffusion Training.
procedure TRFINDIFPUSION(D,, atom types A, ground truth conformers {X
NMR spectra (811 sc), noise schedule (Pimam: Pud) (-1.2, 1.3), standard deviation atom coordinates daw
kmml
2: S + (#n, 0), (0, sc). or (0, 0) with probability 0.1 each
> Randomly drop spectra
3:
MMR-CONVFORMMRH
D. Encede spectra Select target conformer
4: sample Uniform( (L...., )): Xo X
Xo X. X
> Center coordinates
6: sample R ~ (0) t ~~ NO0 I); Xo RXD +
> Random rigid transformation
7: sample In ~ ~NN (P mean: Puu): J + 0. Jdau
> Sample noise scale
8: sample NN0,00 00 o2 I); Xo f- Xa 1
Add Gaussian noise
9: X t (x xs)
D Predict clean coordinates
10: minimize Laitussonn \(o) [[o)] X
Xoll2 Lancon Xo)
11:
end procedure
Algorithm 2 Smooth LDDT Loss.
procedure AMOOTHLDDDLLLS((ppaaidddd coordinates Xo. ground- coordinates [0.5, 2.0, 4.0))
Xo, thresholds
du 6 || ă lla
3: dij + |.0. 20.5
Compute pairwise distances
4:
Adj - Id:- dıy
D Distance differences
5:
6ij 1 1 sigmoid(ta Adg)
Preserved scores
LDDT < (ess)
b Mean score, excluding self-pairs > Smooth LDDT loss
7: Lanooth Iddit + 1 LDDT
8: return Lsmooth
9:
end procedure
Preconditioning. To stabilize training across different noise levels, we precondition the denoising network Dg following EDM [32]:
Do(X zs) (xkip()),, (o
Cnoise (aniise(o)),a A,
where Fo is the core neural network performing the actual computation. The scaling functions Cskip, Cout: Cun Cuoise, and the loss weight X(r) are defined as EDM 32)
danta
Odata
Co)ip(o) 0² + data
(our(a) = v data +
(8)
Guoise (a) In(o), ((o) 0² + data
(o)
oa + + data
- )
Here, data represents the standard deviation of atom coordinates in the dataset (see Appendix Table
Conditional Dropout and Classifier-Fres Guidance. To improve robustness and flexibility in conditioning on NMR spectra, we adopt classifier-free guidance (CFG) [19] During training, the 'H NMR spectrum is replaced with zeros with probability PH 0.1, the C NMR spectrum is dropped with Pc = 0.1, and both are dropped simultaneously with Pooth = 0.1 (see Algorithm D). At inference, conditional and unconditional predictions are combined via
Dø (X,:o, 0, A, zs) = (1 + w) Do(X,;o, a A, zs) - w D (xxio A),
(10)
where w 2 0 controls guidance scale. This enables generation conditioned on either or both spectra, improving versatility and performance. In this paper, set {1, 1.5, 2} depending datasets.
16

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Algorithm 3 Diffusion Sampling using Stochastic Heun's is 2nd order Method.
procedure SAMPLEDIFFUSION(D) (Xa:o, A, zs). atom type NMR spectra embedding zs, noise 0.8, "Ymin 1.0, w guidance scale)
level schedule (N) sample Xo (0, oō 1)
3: for E (0, ........... N - 1 do
4:
7= 70 if 0; > T clsc (1
5:
6 + + 7
b Temporarily increase noise level à;
6:
sample O. 1)
X;
V o.
Add new noise to move from to O; Evaluate d.X /do at ds
8:
d: (X. Dī (X;;ú, A, 25)
X,41 X; (0.41 o.)di
D Take Buler step from o; to 0:41
10:
o * then
11:
d; - (14+1 Dÿ (x++;
b Apply 2dd order correction
12:
X,11 + X. + (0+t1 - 8.) 2d))
13:
end
end for
15:
return X end procedure
16:
Sampling Procedure. The reverse diffusion process begins with X ~ (O, m I) and iteratively denoises to obtain Xx. This process is governed by the stochastic differential equation (SDE) [2]
dx VV (ogp((;:0 A, zs) do - 3(o))
A, do + 2 dw,
probubility
Langevin diflussion SDE
(11)
where V log X; a A =s)
(Dg (Da(x.ioo A, zs) tion (24). is the noise level, and dw is the Wiener process. The term B(r) determines the rate at which existing noise replaced by new noise.
x)/o² is the conditional score func-
During inference, the noise level schedule (O....... is defined as EDM 32
m Tmaxx 2)) ON
OK<N
max
(12)
where 0max 80, min 0.0004, p 7, and N 50 is the number of diffusion steps. The sampling process is performed by solving the SDE using the stochastic Heun's 's 2nd method [32), outlined in Algorithm
B Details of NMR-DiGress
As introduced in Section 5.2 of the main paper, NMR-DiGress graph-based baseline model integrating the discrete graph diffusion model DiGress [66] with our EMR-ConvForme for molecular structure elucidation from ID NMR spectra and the chemical formula. this section, we provide detailed description of the training and sampling procedures of NMR-DiGress.
In NMR-DiGress, molecule-spectrune pairs are represented (G,8), where (A, is the molecular graph. The atom types A E {0, N and bond types E {0, N.N represent the graph, with being the number of heavy atoms (excluding hydrogens), and datom and dyond being the total number of atom and bond types, respectively. Bond types include no bond, single bond, double bond, triple bond, and aromatic bond.
The objective of (i.e., chemical formula) and the spectra S by sampling from the conditional probability distribution p(E) E A, S). Key differences from the original DiGress are: (1) Atom types are already known NMR- -iR--sG so only bond matrices are predicted. (2) Spectra embeddings zs from NMR- FormFrrmer added as graph-level features during training and sampling.
is to generate the bond types E conditioned on the atom types A
17

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Algorithm 4 NMR-DiGress Training.
1: procedure TRAIN NMR-DiGaEsS/mobcula graph g = (A, E). NMR spectra embedding zs)
2: sample [[
Sample a diffusion time from the uniform distribution
3: sample E² ~ EQ'
> Add noise to the bond matrix
4:
G + A, E²)
5:
- f(9
Structural features computed from the graph
8 oo 2g, ks)
Predict the bond matrix
7: minimize Ef e)
D. Cross-entropy loss
end procedure
Algorithm 5 NMR-DiGress Sampling.
1: procedure SAMPLE MAR-DIGRESs(NMR spectra embedding zs, atom types A, marginal distribution of bond types m, number of diffusion steps 7)
2: sample E" ~ m
> Independently sample cach initial bond from the marginal distribution
3: G" f (A, E
4: for T,... ......1 do
zg 6 f(g',t)
Structural features computed from the graph
6:
be (0 2g, zs)
Predict the bond matrix
7:
p
1-1 gt) x- Σ. ((6 ea = =e, ())) G
D Posterior distribution of each bond
8:
II. po
po(e 1-1 (9t)
> Reverse process
9:
end for
return g
11: end procedure
Training Procedure. The training procedure of NMR-DiGress is adapted from DiGress [66]. Noise added to each bond independently via discrete Markov chains, and a neural network is trained to reverse this process generate bond matrices.
Specifically, to add noise graph, we define discrete Markov process {E")T> starting from the bond matrix E E:
(E"
E Q'
(13)
where Q' is the transition matrix from step to t. From the properties of the Markov chain, the distribution of E' given E is:
q E E = EQ',
(14)
where Q' = Q? Q.. Following DiGress, we use the noise schedule:
a'= 5'1mmmm
(15)
where a² = cos (0.5m (t/T+ +) -1 and s a small hyperparameter. Here, m the marginal distribution of bond types the training dataset and m is the transpose of m. This choice of noise schedule ensures that each bond in Er is converged to the prior noisy distribution (i.e., the marginal distribution bond types m.)
500 is the number of diffusion steps,
To predict the original bond matrix E from the noisy graph n = (A, E₁), we train a neural network de (g', zg. zs), where zg is extra features derived from G DiGress and zs is the NMR spectra embedding from NMR- LARR-ConFFormer We use the same graph transformer architecture as in DiGress for de 66 The complete training algorithm is shown in Algorithm 4
Sampling Procedure. We extend DiGress 666 by conditioning on atom types and spectra embeddings zs- Each bond in ET is independently sampled from the marginal distribution to form the noisy graph GT = A, E For each timestep t, we compute extra features 2ş = f(" f), predict bond probabilities j (g Zg, 2s), and derive the posterior for each bond ezy:
polet
1-1 g') = Eeeet | = e, ctty pf
(16)
where e can be chosed from dhomt bond types. Then each bond in g- is independently sampled according to this posterior. After T steps, the denoised molecular graph go generated. The complete algorithm is given in Algorithm 5
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C Details of Dataset Curation
In this section, we provide details on the dataset curation process, including the data structure, preprocessing pipeline, and summary of the statistics for each dataset.
C.1 Dataset Structure and Preprocessing
Each data entry is represented as tuple (SMILES, 'H NMR spectrum. C NMR spectrum, atom features). The SMILES string is a sequence of characters representing molecule 771 Each SMILES string is canonicalized, with stereochemistry such as chiral centers and double bond configurations removed. Only molecules containing the elements C, H, O. N, S, P. F, CI, Br, and I are retained. Duplicate entries are removed to ensure one unique SMILES per molecule.
The NMR spectra are stored as vectors, and details of the preprocessing steps are provided in Appendix C.2 Atom features include atom types A and ground-truth conformers X, which are generated using RDKit's s ETKDGv3 algorithm [ from the SMILES string. To validate the generated 3D conformations, SMILES strings are reconstructed from the atom types and 3D coordinates using RDKit's s DetermineBonds function [.] Molecules that fail reconstruction are discarded. Explicit hydrogens are included to ensure accurate SMILES reconstruction, as required by DetermineBonds.
C.2 NMR Spectrum Preprocessing
Synthetic Spectra Simulation. Synthetic spectra are generated from SMILES using MestreNova [44], with deuterated chloroform (CDCI,) the solvent. Default simulation settings applied: 'H spectra (-2 ppm to 12 ppm, 32k points, 500. 12 Hz frequency, 0.75 Hz line width) and 1'C spectra (-20 ppm to 230 ppm, 128k points, 125.03 MHz frequency, 1.5 Hz line width, proton decoupled).
Experimental Spectra Collection. SpecTeach [65] experimental raw spectra are in .mnova file format, with default NMR processing steps preserved, including group delay correction, apodiza- tion in the time domain, and phase and baseline corrections in the frequency domain if exist. NMRShiftDB2 (34) has C NMR spectra chemical shift lists.
Spectra Preprocessing. To standardize spectra from different datasets, which vary in chemical shift ranges, resolutions, and intensity scales, we adopt the formats in 4 [22] and the preprocessing
method [22]. 'H NMR spectra are linearly interpolated ppm, and C NMR spectra are interpolated to 10,000 points in the range [-20, 230] ppm. Spectra outside these ranges are truncated, while shorter spectra are zero-paddedd. Intensities are normalized
10,000 points in the range [-2, 10
by dividing by the maximum intensity. For SpectraBase dataset [22] and experimental datasets, C NMR spectra are preprocessed into 80 binary vectors spanning (3.42, 231.3) ppm.
To ensure compatibility with baseline models (i.e., Hu et al. 122 and NMR-DiGress), we also preprocess 'H NMR spectra into 28,000 points within the range 2-2, 12) ppm and I&C NMR spectra
into 80 binary vectors spanning (3.42, 231.3) ppm where applicable. Appendix Table provides detailed preprocessing formats for each model and dataset.
Table 4: Standardized formats for preprocessed NMR spectra, specifying spectrum dimensions, chemical shift ranges, and intensity ranges.
NMR Spectrum
Dimension Chemical Shift (ppm)
Intensity
CHEFNMR
*H (Default)
10,000
[-2, 10]
S
CºC (USPTO, SpectraNP)
10,000
[-20, 230] (3.42, 231.3)
< 1
18C (SpectraBase, SpecTeach, JMRShiftDB2)
80
{0, 1}
Hu et al. 22
'H (Default)
28,000
[-2, 12] (3.42, 231.3)
< 1 {0, 1} $
13C (Default)
80
"H (USPTO)
10,000
[-2, 10]
NMR-DiGress
HH (Default)
10,000
[-2, 10] (3.42, 231.3)
< {0, 1}
C (Default)
80
19

---

Table 5: Summary of dataset statistics with the number of data points, heavy atoms (excluding hydrogens), atoms (including hydrogens), atom types, and solvent types reported.
Dataset
# Data
Heavy Atoms
Atoms
Atom Type
Solvent
Synthetic Datasets
SpectraBase
141,489
[2, 19]
[3.
H,C.H,O.N.
CDCL; CDCIs CDCI3
USPTO
744,602
[5, 35]
18. 101] (C, O. P.F. Br. D
SpectraNP 111,181
[3, 130]
[4, C.C.H.
Experimental Datasets
SpecTeach 238
[2]
[5.
CL.
CDCls, DMSO
NMRShif tDDS
23,457
[3]
[3. HO C. Br.
>7 solvents
C.3 Dataset Statisties
This section provides detailed preprocessing steps and dataset statistics (Appendix Table
Synthetic Datasets. We evaluate models public benchmarks, SpectraBase USPTO 4 and our self-curated SpectraNP dataset.
2 and
SpectraBase 22] contains molecules with elements C. O. and N. The original dataset comprises 142,894 tuples of (Canonical nonstereo SMILES, 28,000-8005 l..0nondi 'H NMR spectrum, 80-bin NMR spectrum) along with non-overlapping split indices in ratio of 0.8:0.1:0. for training, sets. H NMR spectra. After generating 3D conformations for all molecules, 141,489 valid conformations remain. The original dataset is available at httttt:://eene hww.a/anddd..gggeeerrrr//////aee CC-BY 4.0 license.
validation, and test sets. Each molecule in the dataset is unique. We remove 219 molecules with invalid
under the
USPTO 4 includes molecules derived from chemical reactions N. S. P. CI, Br, and I. The original dataset contains 794,40 tuples of (Canonical stereo SMILES. 10.000-dimensional 'H NMR spectrum, 10,000-dimensionnal 1&C NMR spectrum). We generate 3D conformations for each molecule. The final dataset contains 744,602 entries. The original split indices are preserved, resulting in post- post-filtering split ratio of 0.86:0.04:0. for training, validation, and test sets. The original dataset is available htttpss://eeoooo http://d......eeee///o////111111 the Community Data License Agreement- -harrin 1.0
41. containing elements C, H. O,
under
SpectraNP contains 11 111,181 unique natural products with elements C, H. O, N, S, P. CI, Br, and I. Around 31k molecules are sourced from the NPAtlas database [52), which includes small molecules from bacteria and fungi. The remaining molecules which includes natural products such as vitamins, minerals, probiotics, and small molecules from various natural sources. The dataset is randomly split into training, validation, and test sets in a ratio of 1.....
sourced from the NP-MRD database (72),
Experimental Datasets. To evaluate the ability of models trained on synthetic data to generalize to experimental data, we curate two experimental datasets.
SpecTeach includes the van Bramer dataset (65] The original dataset contains 247 tuples, but compounds lack corresponding SMILESS from the CAS ID, and 3 compounds have invalid experimen- tal spectra. The final dataset comprises 238 unique tuples. Most compounds are in CDCI, solvent, with few in DMSO solvent. The original dataset available CRuxnL6PYYBB under CC-BY 4.0.
google com/
NMRShiftDB2 34 is larger-scale dataset of C NMR spectra in various solvents. We subset of 23,457 molecules excluding SMILES in the training set of USPTO. The original dataset is under the nmrshiftdb2 Database License (https:/ hopos://mman http///mrshhht fmmrshiftdi nmr. uni koeen, dw/nnrshiiiiieeeeeee hnishffttbttml mmrshiffrab2lattalicceeee txt).
D Experimental Details
In this section, we provide experimental details for baseline models and CHEFNMR, including hyperparameters, training, and evaluation settings.
20

---

D.1 Baseline Settings
We compare CHEENMR with two existing chemical language models and introduce a graph-baset model to evaluate different molecular representations for the structure elucidation task.
Hu et al. 22 use 28,000 -ineennnnii 'H NMR spectra and 80-bin C NMR spectra for all datasets, except for the USPTO dataset, where D0.00o-dimensional "H NMR spectra are used (see Appendix Table This chemical language model employs two-stage multitask transformer to predict SMILES strings from raw ID NMR spectra. The method pre-defines 957 substructures and pre-trains transformer model on 3.IM molecules. This pre-trained model is then used to initialize a multitask transformer, which is fine-tuned on 143k data from SpectraBase.
For experiments, retrain the substructure toaiurrettt---IIi SMILES model on the same 3.1M dataset for 500 epochs. Then, we fine-tune the model on each synthetic benchmark dataset for 1500 epochs until convergence. During fine-tuning, the multitask model is initialized with the substructure -o--SMLESS transformer checkpoint that achieved the lowest validation loss during the pre-training phase. Model performance is evaluated on each dataset three independent runs, using the checkpoint with the lowest validation loss during training. Evaluation is conducted on A A10 GPU, with runtime varying between 30 minutes and 2 hours depending the dataset. Other hyperparameters are default in the original model [22].
Alberts et al. 4 develop transformer to predict stereo SMILES from text-based ID NMR peak lists and chemical formulas. Due to the unavailability of inference code and differences in input (peak lists vs. raw spectra) and output (stereo non-stereo SMILES), report their published results on the original USPTO (794,403 data points) and SpecTeach datasets.
NMR-DiGress uses 10.000-dimensional 'H NMR spectra and 80-bin C NMR spectra for all datasets (see Appendix Table 4). This graph-based based model, comprising 14.4M parameters, is trained on each dataset using 4 A 100 GPUs for 48 hours. Evaluation is performed using the checkpoint with the highest top-1 matching accuracy on the validation set.
Table 6: Number of filtered data.
Dataset
Data
SpectraBase
132,710 673,257
USPTO SpectraNP 106,020
Notably, molecules containing aromatic nitrogens are excluded from training and evaluation (see Appendix Table ()). This is because NMR-DiGress only uses heavy atoms (excluding hydrogens) as graph nodes, and RDKit [[] fails to reconstruct SMILES strings from molecular graphs with aromatic nitrogens.
D.2 CHEFNMR Settings
CHEFNMR use the preprocessed datasets described in Appendix Tables 4 a
Appendix Figure
illustrates the full architecture of the MMR-ConnFormer described in Section 3.1. Appendix Table lists the hyperparameters and optimizer settings for CHEFNMR.
All models trained in bf16-mixed precision. After training, we sample all molecules in the test set using the trained checkpoint for three independent runs per dataset. We select the checkpoint with the highest t matching accuracy on the validation set. For experimental datasets, we use the checkpoint trained on the synthetic USPTO dataset with 10,000-dimensional 'H NMR spectra and 80-bin I NMR spectra. Appendix Table summarizes daaas training epochs, and sampling time for CHEENMR on each dataset. Here, dara represents the standard deviation of the atom coordinates in the dataset. The classifier-free guidance (CFG) scale set to for SpectraBase, 1.5 for USPTO and SpectraNP, and I for SpecTeach and NMRShiftDer
Table 7: dataa training epochs, and sampling time per dataset for CHEFNMR. dataa the standard deviation of the atom coordinates in the dataset. Sampling time is the estimated average time I A100 or H100 GPU for three independent runs.
CHEFNMR-S
CHEFNMR-L
Dataset
Ubiaa
Train Epoch
Sample Time
Train Epoch
Sample Time
SpectraBase
2.02
10k
1h
5k
3h
USPTO
2.67
10k
8h
3k
17h
SpectraNP
3.28
26k
3.5h
18k
9h
21

---

NMR Embed
Linear
Layer Norm & Dropout Linear
Dropout
Multihead Attention Pooling
GELU
Linear
Linear
Layer Norm
4 x Transformer Encoder Block
MaxPooltd
Linear
pool size
nn.Embedding
Dropout
2X
Patchify palch size stride
Multi-head
Self-Attention
Position Type Encoding
Convid out channel ke sernel _aie stride
Layer Norm
Tokenizer
Tokenizer
Tokenizer
Patch Tokenizer
Embed Tokenizer
HH NMR Spectrum
MC NMR Spectrum
Figure 6: Details of the NMR-ConVFormer architecture. For the 10.000-dimensional 'H or C NMR spectrum, we use a convolutional tokenizer comprising two convolutional layers with ReLU and max- max-pooling, outperforming the ViT-style patch tokenizer [67]. For the 80-bin C&C spectrum, learnable embeddings for each bin instead of the convolutional tokenizer. The standard transformer encoder comprises multi-hee heal self-attention and feed-forward networks with pre-layer norm and residuals. Hyperparameters such as out_channel and kernel_siiie ssize are listed in Appendix Table
Table 8: CHEENMR hyperparameters and optimizer settings.
Parameter
CHEENMR-S CHEFNMR-L
NMR-ConvFormer
General
Encoder Dimension (Dencodes
256
Dropout Rate
0.1
Convolutional Tokenizer
Number of Blocks
2 [64, 128]
Output Channels (out_channell)
Kernel Sizes (kernel_size)
[5. 9]
Stride Sizes (stride)
[1, 1]
Max Pooling Sizes spool_size)
[8. 12]
Transformer Encoder
Positional Encoding
Learnable Learnable
Type Encoding
Number of Blocks
Number of Attention Heads
8
Head Dimension
32
MI.P Ratio
Pooling
Pooling Strategy
Multihead Attention Pooling
DIT
Number of Blocks
24
Number of Attention Heads
16
Hidden Dimension
768
1024
MLP Ratio
4
Optimizer (Adam)
Learning Rate
Ic-4
Adam 31
0.9
Adam 32
0.95
Adam
le-8
22

---

Table 9: Ablation study on AoR-ConvFormer components.
Configuration
Tokenizer # Tokens
Transformer Pooling Dropout Acc 1% f
Sim@
Base (CHEFNMR-S)
Conv
183
Y
MAP
0.1
69.15
0.807+.002
Tokenizer Ablation
Conv Tokenizer
Patch Conv
183
Y
MAP
0.1
61.78
0.75611.00
Token Count Reduction
121
Y
MAP
0.1
66.28
0.789:
Transformer Ablation
Transformer Block
Conv
183
N
MAP
0.1
68.124.17
0.797:1.001
Pooling Ablation
MAP Pooling
Conv
Flatten
62.97:.114
0.758+t.02
Dropout Ablation
Dropout
Conv
183
MAP
0.0
65.48
0.777+
E
Additional Ablation Studies
In this section, we provide additional ablation studies to evaluate the impact of the MARR-CovFoord components and the impact of different NMR spectra CHEENMR's performance.
E. Ablation Studies for NMR-ConvFormer
We perform extensive ablation studies to evaluate the contributions of key components the NMR- ConvFormer the SpectraBase dataset using CHEFNMR-S, The results are summarized in Table of the main paper, with detailed configurations provided here.
The convolutional tokenizer replaced with patch tokenizer (see Appendix Figure using sestch_size_ 192 and stride 96 to maintain the same token count. - Token Count Reduction: The number of tokens is reduced from 183 121 by increasing max pooling sizes (pool_s sioo_ssiee Appendix Table [) from [8. 12] to [12, 20]. - MAP Pooling: The MAP pooling layer is replaced with a flattening layer, which reshapes the transformer encoder's output from (batch size, T. Dencoder) (batch size, T x Dencoder).
Some of the modifications in Appendix Table 9 are: - Cony Tokenizer:
We find that within the MMR-ConyFormer, the convolutional tokenizer outperforms the patch tokenizer, likely due its ability capture local features more effectively. Reducing the number of tokens leads to a drop in performance. The MAP pooling layer is more effective than flattening for aggregating features. Dropout regularization necessary to prevent overfitting.
E.2 Ablation Studies for Different NMR Spectra
We investigate the impact of using different NMR speetra NMR, NMR, or both) on model per- formance the SpectraBase dataset. The results presented in Appendix Table 10 CHEFNMR
Table 10: Performance SpectraBase using different NMR spectra.
Top-1
Top-5
Top-10
Spectrum Model
Acc%
Sim f
Acc% f
Sim 1
Acc% 1
Sim 1
et al.
4.50 2.15 0.2964 000
12.92+.11
0.460+.001
18.27 14 0.5234.00
3C
NMR-DiGress
10.874.08
0.3141:001
19.35+t.03
0.438:1.001
23.00=:02
0.477=.00
CHEFNMR-S
26.6911.66
0.469
39.90.1.3
0.612:1.001
44.59
0.651
CHEFNMR-L
30.28
0.510.1.00
47.33
0.672:1.000
53.53
0.718
Hu et al.
31.12+.15
0.569+.001
48.64
0.725++001
54
0.771=000
"H
31.13+.13
0.521+.00) 001
48.73+.24
0.682+.000 001
54.52
0.723=
CHEFNMR-S
57.97.1.5
0.720 002
72.641.22
1.002
76.58
0.867 ..02
CHEFNMR-L
59.37
0.739
74.91.1.11
0.857.1.01
79.20
0.884..000
Hu et al.
45.24
0.686:4.001
62,37+.08
0.815+.001
67.38=005
0.847=000
13C+'H
AMR-DiGress 43.56+.30
0.625+.002
62.47+.20
0.779+.002
68.39
0.817=0001
CHEFNMR-S 69.151.08
0.8074.002
82.09
0,90441002
85.30 04
0.922 .00
CHEENMR-L
72.044.02
0.8331.000
85.241.10
0.923
88.20
0.940=.000
23

---

consistently and significantly outperforms the baselines with 'H or/and C spectra. The combination of HH and 1&C spectra provides complementary information that yields the best performance.
Additional Results and Analysis
This section provides additional results and analysis across datasets, demonstrating the state-of-the-an performance and generalization ability of CHEENMR. Appendix [..] reports the Average Minimum RMSD metrics for generated 3D structures. Appendix [22 analyzes CHEENMR'S generalization ability to unseen molecular scaffolds and different solvents in NMR spectra. Appendix [33 presents a systematic failure mode analysis of CHEFNMR by molecular structures and domain shift between synthetic and real spectra. Appendix F4 and F.5 provide additional qualitative examples on synthetic
and experimental datasets respectively.
F.
RMSD Metric
Since CHEFNMR generates atomic 3D coordinates, we additionally report the top-k Average Mini- mum RMSD (AMR) of heavy atoms in Appendix Table [1] The RMSD for each predicted structure is computed against three ground-truth conformers and taken as the minimum value. We then select the minimum RMSD among the top-k predictions for each molecule and average across all molecules to obtain the top-k AMR Although RMSD is not size-indeper independent and thus less interpretable, the obtained results reasonable given the dataset complexity.
Table 11: Average Minimum RMSD in Å.
Dataset
Top-14
Top-S4
Top- 10,
SpectraBase
3.26
2.87
2.71
USPTO
4.59
4.14
3.96
SpectraNP
5.50
5.12
4.97
SpecTeach
2.10
1.71
1.56
WMRShiftDB2
3.23
2.83
2.68
F.2
Generalization Analysis
In this section, we analyze CHEENMR'S 's generalization ability to unseen molecular scaffolds (Ap- pendix F2.1 and different solvents (Appendix F22.2 in NMR spectra.
F.2.1 Generalization to Unseen Molecular Scaffolds
We evaluate CHEFNMR's generalization ability to unseen molecular scaffolds by creating test subsets with scaffolds not present in the training sets. Appendix Table 12 shows the subsets relatively chemically dissimilar to the training sets, based on Scaffold similarity (Scaff), fingerprint-based Tani- moto Similarity nearest neighbor (SNN) [51), and the absolute difference of standard deviation of
Table 12: Similarity analysis between training and test splits across datasets. Unseen: test subsets
with scaffolds unseen during training. Scaff: Scaffold similarity: SNN: Tanimoto similarity to nearest neighbor. iaai D:al: absolute difference of std of atom coordinates between training and test sets.
Train Set
Test (Sub)set
#Test Set Data
Scafft
SNNt
Øest ||
SpectraBase
SpectraBase
14137
0.959
0.659
0.004
SpectraBase
SpectraBase (Unseen)
3770 (26.7%) %
0.000
0.657
0.025
USPTO
USPTO
73059
0.980
0,698
0.005
USPTO
USPTO (Unseen)
14711 (20.1% %)
0.000
0.656
0.174
SpectraNP
SpectraNP
10952
0.894
0.722
0.012
SpectraNP
SpectraNP (Unseen)
2897 (26.5%)
0.000
0.655
0.144
24

---

Table 13: Performance on unseen scaffold test subsets across synthetic datasets.
Top-1
Top-5
Top-10
Dataset
Model
Acc%
Sim 1
Acc%
Sim t
Acc% f
Sim
Hu et al.
39.59
55.43 0.653..002
0.7761.00 003
59.85.1.59
0.807
NMR DiGress
43,10#.29
59.70 0.607
0.759
64.83+..4
0.793+.002
SpectraBase
CHEENMR-S
64.09..32
0.7584.003
77.35=.20
0.871#0001
80.73+:22
0.892:t.011
CHEENMR-L
66.40
0.785-1.002
80.24+.33
0.891#.001
83.75+.24
0.912:t.001
Hu NMR-DiGress
25.80
0.59011.001
41.58
0.738
47.1244.7
0.778
12.93:.23
0,388:1.00
25.27
0.596#.000
.02
31.42:t.12
0.653:t.001
USPTO
CHEENMR-S
66.68:1.4
0.81411.01
81.31
0.921
84.81:104
1.00
CHEENMR-L
67.78:1.25
0.836:1.003
81.79
0.925
85.261.13
0.941
Hu et al.
7.68
0.478:1.00
16.16=.27
0.623 001
20.26+:27
0.659+.000
1.59
0.222++004
4.50= 24
0.389 002
6.18
0,436=#001
SpectraNP
CHEENMR-S
21.40.144
0,4171.001
35.30
0.641
40.14.1.09
0.69611.000
CHEENMR-L
21.82.1.24
0.477.1.002
37.04
0.6941.00
42.69 1.31
0.741
atom coordinates between training and test sets. Appendix Table shows the performance on these unseen scaffold subsets with different models. CHEFNMR still significantly outperforms baselines across these subsets, demonstrating its generalization ability.
F.2.2 Generalization Across Solvents in Experimental Spectra
We report top-10 10 zero-shot accuracy on 2k experimental 13C spectra paired with solvent information from NMRShiftDB2 34 in Appendix Table 14 CHEFNMR trained on synthetic 13C spectra with CDClg solvent shows generalization ability to various solvents except for C,D,N and CD3CN.
Table 14: Top-10 zero-shot accuracy of CHEFNMR WMRShiftDB2 34 across different solvents.
Solvent
#Molecules
Top- 10 Zero-shot Accuracy
CDCIs
1498
0.263
DMSO
232
0,323
CD;OD
197
0.102
C&D.N
57
0.035
C.Ds
48
0.188
D2O
36
0,500
CCL
33
0.788
CD&CN
11
0.000
(CDs)2C
0.500
F.3
Failure Mode Analysis
In this section, we systematically analyze the failure modes of CHEFNMR by molecular structures (Appendix E.3. and domain shift between synthetic and real spectra (Appendix F3.2
F.3.1 Failure Mode by Molecular Structures
Failure rate is defined as the proportion of molecules where the model fails to generate the correct structure within the top-10 predictions. We analyze the failure rate by molecular structures, including the number atoms, number rings, largest ring size, and functional groups of our CHEENMR on the synthetic SpectralP (Appendix Table 15 and 16). and experimental SpecTeach (Appendix Table T7 and [8] and WMRShiftDB2 (Appendix Table 19 20) datasets.
On all datasets, the model fails more often on molecules with the most atoms the largest number of rings due to less training data and increasing complexity of speetra and structures for larger molecules. However, the model is not systematically significantly failing in specific functional group category.
25

---

Table 15: Failure rate analysis on synthetic SpectraNP dataset by molecular properties.
By Total Atoms (including hydrogens)
Total Atoms
<40
41-80
81-120
121-160
161-200
>200
Total Molecules
2265
6168
1818
539
140
22
Failure Rate
0.296
0.315
0.411
0.492
0.707
1.000
By Heavy Atoms
Heavy Atoms <00
21-40
41-60
61-80
81-100
> 100
Total Molecules
2099
6563
1750
415 0.542
110
15
Failure Rate
0.298
0.311
0.431
0.773
1.000
By Number of Rings
Ring Count
0
1-2
34
5-6
7-8
>8
Total Molecules
559
3070
4437 0.332
2102
560
224
Failure Rate
0.250
0.317
0.381
0.407
0.571
By Largest Ring Size
Largest Ring
No rings
3-5
7-8
>8
Total Molecules
559
483
8061
778
1071
Failure Rate
0,250
0.383
0.322
0.382
0,490
Table 16: Failure rate by functional groups on synthetic SpectraNP dataset.
Category
Carbonyls
Amides
Esters
Ethers
Alcohols
Halogen
Sulfur
Nitrogen
Total Molecules
8148
1479
4389
8048
6861
477
138
3046
Failure Rate
0.352
0.411
0.354
0.342
0.355
0.356
0.341
0.386
Table 17: Failure rate analysis on experimental SpecTeach dataset by molecular properties.
By Total Atoms (including hydrogens)
Total Atoms
<10
11-15
16-20
21-25
26-30
>30
Total Molecules
10
76
48
26
18
Failure Rate
0.000
0.217
0.289
0.271
0.500
0.556
By Heavy Atoms
Heavy Atoms
<5
6-10
11-15
16-20
>2
Total Molecules
38
154
37
8
Failure Rate
0.105
0.240
0.676
0.500
1.000
By Number of Rings
Ring Count
>
Total Molecules
157
69
12 0.583
Failure Rate
0.210
0.449
By Largest Ring Size
Largest Ring
No rings
3-5
6
Total Molecules
157
4
77
Failure Rate
0.210
0.250
0.481
Table 18: Failure rate by functional groups on experimental SpecTeach dataset.
Category
Carbonyls
Amides
Esters
Ethers
Alcohols
Halogen
Nitrogen
Total Molecules
125
43
24
24
Failure Rate
0.304
0.667
0.435
0.448
0.256
0.208
0.542
26

---

Table 19: Failure rate analysis experimental NMRShiftDD2 dataset by molecular properties.
By Total Atoms (including hydrogens)
Total Atoms
<20
21-40
41-60
61-80
>80
Total Molecules
6484
13685
2806
417
65
Failure Rate
0.351
0.689
0.916
0.947
0.985
By Heavy Atoms
Heavy Atoms
<10
11-20
21-30
>>30
Total Molecules
5591
13855
3504
507
Failure Rate
0.326
0.664
0.917
0.982
By Number of Rings
Ring Count
1-2
3-4
5-6
7-8
Total Molecules
2955
14763 0.592
5192
514
33
Failure Rate
0.334
0.862
0.977
1.000
By Largest Ring Size
Largest Ring
No rings
3-5
6
7-8
>8
Total Molecules
2955
3031
16552
682
237
Failure Rate
0.334
0.630
0.666
0.871
0.916
Table 20: Failure rate by functional groups on experimental NMRShiftDB2 dataset.
Category
Carbonyls
Amides
Esters
Ethers
Alcohols
Halogen
Sulfur
Nitrogen
Total Molecules
11096
2562
4320
9699
3756
6248
1207
12074
Failure Rate
0.681
0.713
0.726
0.723
0.759
0.528
0.725
0.674
F.3.2 Domain Shift between Synthetic and Real Spectra
To quantify the domain shift between synthetic and real spectra, we simulate synthetic spectra for molecules the SpecTeach dataset using MestReNova, and compute the cosine similarity between synthetic and real spectra following [.. We also report the average cosine similarity of successful and failed predictions on the SpecTeach. Appendix Table 21 shows that ..000-ddimeniioal HH NMR spectra have significantly lower cosine similarity than 80-bin 13C NMR spectra, indicating need for more robust representation of H NMR spectra. In addition, failed predictions have lower similarity between synthetic and real 'H spectra. We note that it is non-trivial to develop systematic metries to quantify the spectra domain shift, and we leave to future work.
Table 21:
Cosine similarity between synthetic and experimental spectra of molecules in SpecTeach, and successful and failed predictions by CHEENMR.
Type
Count
Cos Sim (IH)
Cos Sim (13C)
All
238
1.17
0.743
Success
167
0.197
0.747
Fail
71
0.1
0.735
E.4 Additional Qualitative Results Synthetic Spectra
We present more examples of CHEENMR's predictions on the synthetic SpectraBase dataset (Appendix Figure 7). the synthetic USPTO dataset (Appendix Figure 8). and the synthetic SpectraNP dataset (Appendix Figure 99. The quantitative results demonstrate that CHEENMR effectively elucidates diverse chemical structures across various synthetic datasets.
F.5
Additional Qualitative Results on Experimental Spectra
We present additional examples of CHEENMR's zero-shot predictions on experimental datasets, including the SpecTeach dataset (Appendix Figure 10P and the NMRShiftDB2 dataset (Appendix Figure TTP. These results highlight CHEENMR robustness to experimental variability, such as differences in solvents, impurities, and baseline noise.
27

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(a)
HO
OH
HN
OH
OH
(b)
Target
Prediction
Target
Prediction
Target
Prediction
0.405
0.432
Figure 7: Examples of CHEFNMR's 's predictions the synthetic Spectraßase dataset. (a) Correctly predicted structures in top-1 predictions. (b) Incorrect top-1 predictions with corresponding Tanimoto similarity scores.
(a)
NH,
(b)
Target
Prediction
Target
Prediction
Target
Prediction
X
0.719
0.338
0.264
Figure 8: Examples of CHEFNMR's predictions on the synthetic USPTO dataset. (a) Correctly predicted structures in top-1 predictions. (b) Incorrect top-1 predictions with corresponding Tanimoto similarity scores.
28

---

(a)
(b)
Target
Prediction
Target
Prediction
Target
Prediction
0,940
0,760
0,401
Figure 9: Additional examples of CHEENMR'S predictions the synthetic SpectraNP dataset. (a) Correctly predicted structures in top-1 predictions. (b) Incorrect top-1 predictions with corresponding Tanimoto similarity scores.
(a)
Correct Prediction
Prediction
(b)
H NMR
"C NMR
Target
NM
NMR
Target
Prediction
Prediction
Figure 10: Examples of experimental spectra from the SpecTeach dataset and corresponding CHEENMR predictions. (a) Correct top-1 predictions. (b) Incorrect top-1 I predictions with corre- sponding Tanimoto similarity scores.
29

---

(a)
IBC NMR
Correct Prediction
TCC NMR
Corract Pradiction
1C NMR
Correct Prediction
CM
B
(b)
TA NMR
Target
TC NMR
Target
13 NMR
Target
0.145
0.507
0.089
Figure 11: Examples of experimental spectra from the NMRShiftDDN dataset and corresponding CHEFNMR predictions. (a) Correct top-1 predictions. (b) Incorrect top-1 predictions with corre- sponding Tanimoto similarity scores.
30

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Reviews:
[{"review_id": "NUZBxeW8zT", "reviewer": "Reviewer_Jfo2", "summary": "In this paper, the authors tackle the challenge of predicting the chemical structure from the combined 1H and 13C-NMR spectra. To this end the authors develop a hybrid diffusion framework consisting of a Transformer based on encoder (with the spectra ingested via patches) and a diffusion transformer generating the molecular structure. Both 1H and 13C spectra are passed into the model as 10,000 dimensional vectors and the molecule is generated as a 3D structure. The authors train and evaluate their framework on synthetic data as well as perform evaluation on experimental spectra. Across all experiments the authors model outperform baselines.", "questions": "- The authors modelling approach should work equally well when only applied to 1H or 13C NMR spectra. Is there a reason why only the combination of 1H and 13C was considered? Training the model on only one type of spectra would make benchmarking easier while making the paper more convincing.\n\n- The paper would highly benefit from further benchmarking on experimental data as well as an expanded discussion of the performance on experimental data. Both [1] and [2] evaluate their modelling approaches on experimental 13C data from the nmr db2 [3]. While this database only provides peak positions the data could be easily converted into vector form. [4] also shows performances on the van Bramer dataset and may prove an interesting model to benchmark against.\n\nI am willing to increase my score if my concerns above are sufficiently addressed.\n\n[1]: J. Phys. Chem. Lett. 2022, 13, 22, 4924–4933\n[2]: Jonas, NeurIPS 2019\n[3]: https://nmrshiftdb.nmr.uni-koeln.de/#:~:text=nmrshiftdb2%20is%20a%20NMR%20database,spectra%2C%20structures%20and%20other%20properties.\n[4]: Alberts 2025, DOI: 10.26434/chemrxiv-2025-q80r9", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- Very pertinent topic with high impact on chemistry\n- Novel modelling approach\n- Extensive ablations\n\nWeaknesses:\n- Limited experimental evaluations and benchmarking against existing models", "was_revised": true, "final_justification": "The authors have addressed all my concerns with additional experiments. Accordingly I have raised my score to 5.", "rebuttal": "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.\n\n**[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. \n\nTo 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. \n\n**Table 1: Performance on SpectraBase dataset using $^1$H or ${}^{13}$C spectra.**\n\n| Spectrum Type      | Model         | Top-1  | Top-5 | Top-10  |\n|----------------|--------------|---------|---------|----------|\n|                |              | Acc% ↑ / Sim ↑ | Acc% ↑ / Sim ↑ | Acc% ↑ / Sim ↑ |\n| ${}^{13}$C   | Hu et al.  | 4.50 / 0.296 | 12.92 / 0.460 | 18.27 / 0.523  |\n| ${}^{13}$C  | NMR-DiGress  | 10.87 / 0.314 | 19.35 / 0.438 | 23.00 / 0.477  |\n| ${}^{13}$C  | NMRDiff3D-M | 53.11 / 0.655 | 64.46 / 0.768 | 68.13 / 0.797  |\n| ${}^{13}$C  | NMRDiff3D-L | **57.07 / 0.693** | **67.43 / 0.791** | **70.85 / 0.817**  |\n| $^1$H        | Hu et al. | 31.12 / 0.569 | 48.64 / 0.725 | 54.92 / 0.771  |\n| $^1$H        | NMR-DiGress | 31.13 / 0.521 | 48.73 / 0.682 | 54.52 / 0.723  |\n| $^1$H        | NMRDiff3D-M | 67.29 / 0.768 | 77.87 / 0.862 | 80.91 / 0.884  |\n| $^1$H        | NMRDiff3D-L | **67.87 / 0.779** | **78.39 / 0.868** | **81.59 / 0.890**  |\n\n**[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.\n\nThank 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.\n\nThank you again for your helpful feedback. We believe the revisions will directly address your concerns and improve the clarity and impact of the paper.\n\nReferences:\n\n[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.\n\n[2] Jonas, Eric. \"Deep imitation learning for molecular inverse problems.\" Advances in neural information processing systems 32 (2019).\n\n[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.\n\n[4] Alberts, Marvin, Nina Hartrampf, and Teodoro Laino. \"Automated Structure Elucidation at Human-Level Accuracy via a Multimodal Multitask Language Model.\" (2025)."}, {"review_id": "iFSHMgtPWa", "reviewer": "Reviewer_5F4B", "summary": "This paper presents a novel, state of the art approach to generating the complete structure of a small molecule using a diffusion model from 1D NMR (Carbon and Hydrogen) experiments and the molecular formula. They outperform a previous model as well as a version of their model that generates graphs. The model is quite promising for aiding biochemists in structure determination from these measurements. They also present a new training dataset, SpectraNP, of predicted 1D NMR measurements generated by MestreNova. So the model is trained with simulated spectra, but they then test it on experimental data with excellent results.\n\nI have read the authors' response, and I am satisfied to keep my score as is.", "questions": "Please answer any questions that arose in my review, thanks!", "limitations": "The only obvious limitation is the training set; a larger dataset would lead to better results. \n\nAlso, I wonder if MestreNova would object to the public release of a dataset of over 100k molecules' predicted 1D NMR (H & C) that was computed with their commercial software?", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\nQuality\n\nThis is a high-quality paper. The model is fairly clearly described, the results are very good, they even provide an alternative baseline model that generates graphs rather than 3D coordinates. Their model outperforms Hu et al. and Alberts et al. often by very large amounts (e.g., 86.6 vs. 73.4 Top-1 accuracy on UCPTO). \n\nClarity\n\nThe approach is well-described. They will release their code when the paper is published.\n\nSignificance\n\nThis is a tool that would gain significant usage by the Natural Products community, if it was posted on the web with a user-friendly interface. Is there a plan to do that?\n\nOriginality\n\nThere exist models that are end-to-end for 1D NMR that predict structure (their reference 20), but doesn’t use diffusion.\nThere also exist models that use diffusion to generate 3D structure (their references 19, 44, 65, 38)\nbut don’t generate molecules conditional on some data, like here, 1D NMR + chemical formula.\nSo, AFAIK, this is the first model to use 1D NMR plus molecular formula to conditionally generate molecular structure. \n\nWeaknesses: \n\nThe paper claims to have created the first and largest 1D NMR database, with over 100k computed spectra: \n\"To scale to the complex chemical groups found in natural products, we curate SpectraNP, a large-scale dataset of synthetic 1D NMR spectra for 111,193 complex natural products (up to 274 atoms), significantly expanding the chemical complexity of prior datasets (≤101 atoms) [20, 4].\"\n\nThere are at least two datasets that belie this claim:\n\n1. Your reference [4] has 790k molecules, but (with respect to your claim) only molecules with fewer than 35 heavy atoms were included. You mention 274 atoms, but how many heavy atoms were included?\n\n2. Your reference [60], NP-MRD has 200k 1D spectra, and is available to the public. As one example, NP-MRD provides the predicted 1D NMR spectra of QS-III (C104H168O55), which has 327 atoms. So this seems to have more molecules $and$ a larger number of atoms. \n\nIs there any advantage of SpectraNP over either of these?\n\nIt would be relatively easy to get even more NP structures and simulate them from https://coconut.naturalproducts.net/ which has nearly 700k 2D structures of natural products, so this would be a good source for expanding your dataset. \n\nThe assumption of molecular formula from mass spec: This is an NP-Hard problem, and the larger the molecule, the more intractable it gets to compute the formula. Anything over 200 heavy atoms (neglecting hydrogen) gets difficult, although the vast majority of natural products are below that (in coconut, at least). \n\nPresumably, MestreNova has some limitations on the use of its software. Is it within the user agreement to make public a dataset of over 100k computed spectra (for each of 1H and 13C) using their software?\n\n\nMinor comments/typos/wordsmithing:\n\nEquations 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?\n\nSection 3.2: Pardon my ignorance; I don’t work with diffusion models (yet!). Presumably the output is a certain (fixed) dimension, right? (Correct me if I’m wrong). Do you simply have a maximum dimension and just 0-pad it? \n\nLine 134: Are these thresholds annealed during training?\n\nLines 143-144: You should include these (scaling functions) in the appendix so the paper is self-contained. \n\nFig 4: Is NMRDiff3D-L covered by the curve for NMRDiff3D-M in the middle and right hand graph?", "was_revised": true, "final_justification": "I have read the authors' response, and I am happy to keep my (accept) score. They have addressed all of my concerns.", "rebuttal": "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.\n\n**[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.\n\nWe 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.\n\n**[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. \n\n**[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.\n\n\n**[Minor questions]**\n \n> 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?\n\nThe 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.\n> Section 3.2: Can you clarify the output dimension of your diffusion transformer?\n\nThe 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.\n\n> Line 134: Are these thresholds in the smooth LDDT loss annealed during training?\n\nNo, the thresholds in the smooth LDDT loss remain fixed during training.\n\n> Lines 143-144: You should include the scaling functions in the appendix so the paper is self-contained.\n\nWe have included the scaling functions in Appendix L29, and we are happy to clarify this in L143 of the main paper in our revisions.\n\n> Fig 4: Is NMRDiff3D-L covered by the curve for NMRDiff3D-M in the middle and right-hand graphs?\n\nNo. 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.\n\n> 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?\n\nYes, we plan to release a user-friendly web interface for NMRDiff3D and the SpectraNP dataset in future work.\n\nThank you again for your helpful feedback. We believe the revisions will address your concerns and improve the clarity and impact of the paper.\n\nReferences:\n\n[1] Alberts, Marvin, et al. \"Unraveling molecular structure: A multimodal spectroscopic dataset for chemistry.\" Advances in Neural Information Processing Systems 37 (2024): 125780-125808.\n\n[2] Wishart, David S., et al. \"The natural products magnetic resonance database (NP-mrd) for 2025.\" Nucleic Acids Research 53.D1 (2025): D700-D708.\n\n[3] Sajed, Tanvir, et al. \"Accurate prediction of 1H NMR chemical shifts of small molecules using machine learning.\" Metabolites 14.5 (2024): 290.\n\n[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"}, {"review_id": "H6gKih51ED", "reviewer": "Reviewer_Kxkp", "summary": "The paper introduces NMRDiff3D, a diffusion based framework to predict the 3D structure of organic molecules conditioned on the 1D NMR spectra (both H and C spectra) and the chemical formula. The model was trained on a curated set of synthetic data, which is around 100k in size. The paper introduces two metrics about accuracy and similarity and compares their method to two LLM based methods and one graph based method.", "questions": "- Can you clarify the technical contributions to the model in the introduction (i.e. what components needed to be changed for this specific problem)?  \n- If you are generating 3D structures (and have loss terms on the coordinates) why is there no RMSD metric on the atom positions?\n- How generalizable is the method across different atom types and different solvents? Are there limitations here? \n- Can you elaborate on why graph methods are limited to 64 atoms?", "limitations": "- Are there better ways to quantify the performance of the method? Can you can compare to any physics based methods or methods that are currently used by the community? If that isn't possible, what is level of accuracy needed to see this method widely adopted? There are lots of reasons to like this paper but without more context/clarity on the impact, it is hard to recommend accept.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n- The paper is well written and is of sufficient quality for NeurIPS \n- This is a very interesting/relevant problem that not a lot of people focus\n- As far as I can tell (I have not specifically worked on this problem), the paper presents a novel diffusion based approach to the inverse problem of spectra to structure\n\nWeaknesses:\n\n- While the idea is novel the pieces used are not, it would be good to clarify what required new thinking vs what was putting together existing pieces\n- It is difficult to assess how good/useful the method actually is, the baselines seem quite weak.  \n- The paper emphasizes a scalable non-equivariant approach but are training on small datasets < 1M in size, being non-equivariant is fine but in the small data regime it might actually be beneficial to enforce symmetries because those models have been shown to be very data efficient. Interesting to note that coord augmentation had the largest impact out of all ablations shown table 3.", "was_revised": true, "final_justification": "The paper addresses an interesting problem: 3D structure prediction from NMR spectra. The authors successfully apply a diffusion transformer to new problem space. My main concerns were: weak evaluations/baselines and questions about the generalization of the method. Both of these were addressed in the rebuttal. The authors added a number of evaluations/baselines based on my and other review comments. Also, the authors provided additional evidence the model can generalize to most of the solvents used in NRM. \n\nOne issue not fully resolved is the framing of equivariance. There wasn’t any direct evidence provided that learning symmetries through data augmentation is better than using a symmetry aware network for the task in this paper, so this design choice should be left as an open question. This is a minor issue that can be resolved in the camera-ready version. \n\nOverall it is a solid contribution so I lean towards acceptance, with the caveat being I’m not expert in NMR and I don't understand the standard techniques used in the field (I'm taking the authors word on that).", "rebuttal": "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.\n\n**[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.\n\n**[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.\n\n**[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).\n\n**[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.\n\n| Dataset  | Model | Top-1 AMR ↓  | Top-5 AMR ↓ | Top-10 AMR ↓ |\n|-|-|-|-|-|\n| SpectraBase | NMRDiff3D-M | 1.146 | 0.818 | 0.713 |\n| SpectraBase | NMRDiff3D-L | 1.153 | 0.813 | 0.700 |\n| USPTO | NMRDiff3D-M | 1.518 | 1.090 | 0.950 |\n| USPTO | NMRDiff3D-L | 1.525 | 1.094 | 0.954 |\n| SpectraNP | NMRDiff3D-M | 2.108 | 1.666 | 1.533 |\n| SpectraNP | NMRDiff3D-L | 2.106 | 1.666 | 1.539 |\n| Real-SpecTeach | NMRDiff3D-M | 0.885 ± 0.032  | 0.613 ± 0.025 | 0.529 ± 0.019\n| Real-SpecTeach | NMRDiff3D-L | 0.870 ± 0.017  | 0.577 ± 0.002 | 0.503 ± 0.014 |\n| Real-5mer-D2O | NMRDiff3D-M | 2.814 ± 0.050 | 2.194 ± 0.104 | 2.065 ± 0.056 |\n| Real-5mer-DMSO | NMRDiff3D-M | 2.906 ± 0.164 | 2.240 ± 0.065 | 2.025 ± 0.105 |\n\n**[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.\n\nAdditionally, 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. \n\n**Table: Top-10 accuracy by functional group on the SpectraNP test set.**\n| Functional Group | Carbonyls | Amides | Esters | Ethers | Alcohols | Halogen | Sulfur | Nitrogen |\n|-|-|-|-|-|-|-|-|-|\n| # Molecules | 8149 | 1480 | 4389 | 8048 | 6862 | 477 | 139 | 3047 |\n| Top-10 Accuracy | 0.651 | 0.727 | 0.642 | 0.654 | 0.662 | 0.738 | 0.755 | 0.678 |\n\n**[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.\n\n**[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. \n\nThank you again for your careful reading. We believe these clarifications and planned revisions will substantially strengthen the paper.\n\nReferences:\n\n[1] Wang, Yuyang, et al. \"Swallowing the bitter pill: Simplified scalable conformer generation.\" arXiv preprint arXiv:2311.17932 (2023).\n\n[2] Axelrod, Simon, and Rafael Gomez-Bombarelli. \"GEOM, energy-annotated molecular conformations for property prediction and molecular generation.\" Scientific Data 9.1 (2022): 185.\n\n[3] Geffner, Tomas, et al. \"Proteina: Scaling flow-based protein structure generative models.\" arXiv preprint arXiv:2503.00710 (2025).\n\n[4] Jonas, Eric. \"Deep imitation learning for molecular inverse problems.\" Advances in neural information processing systems 32 (2019).\n\n[5] Huang, Zhaorui, et al. \"A framework for automated structure elucidation from routine NMR spectra.\" Chemical Science 12.46 (2021): 15329-15338.\n\n[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."}, {"review_id": "0HfAsDU0m6", "reviewer": "Reviewer_1WdQ", "summary": "The paper introduces NMRDiff3D, a hybrid convolutional transformer and 3D atomic coordinate diffusion model for predicting small molecule structures directly from 1D NMR spectra and chemical formula, achieving state-of-the-art results on both synthetic and semi-real benchmarks.\nThe authors also present SpectraNP, a large-scale synthetic NMR dataset tailored for natural products, which fills a critical gap in available training data, especially on more complex (i.e., >101 atoms) molecules.", "questions": "- Can you provide scaffold-level and fingerprint-based diversity analyses to substantiate the generalization claim, and have you evaluated performance on a scaffold-based split or filtered out scaffold overlaps during testing?\n- Can you provide a systematic failure mode analysis, especially on experimental spectra?", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n- NMRDiff3D achieves state-of-the-art performance on synthetic and semi-real benchmarks and shows consistent prediction quality across a wide range of molecular sizes. \n- The paper includes ablation studies isolating the contributions of individual components and attempts to evaluate results on experimental data, although this evaluation is very limited in scale.\n- While the model does not handle stereochemistry, this aligns with the protocol followed by prior work (Hu et al., 2023) and is therefore appropriate given the benchmark comparison.\n\nWeaknesses: \n\n- The paper claims that joint training on USPTO and SpectraNP demonstrates generalization across chemically dissimilar datasets. However, this claim remains insufficiently substantiated due to the absence of scaffold-level or fingerprint-based diversity analysis; the fact that only 306 molecules are shared between USPTO and SpectraNP does not preclude significant scaffold or chemotype overlap that could lead to memorization rather than true generalization. As it stands, there paper lacks: (1) Bemis-Murcko scaffold overlap analysis to assess shared core structures and rule out memorization; (2) dissimilarity-based splits or stratified performance metrics to evaluate generalization to unseen scaffolds; and (3) fingerprint similarity statistics or distribution plots (such as Tanimoto similarity histograms of ECFP4 / MACCS keys) between datasets to quantify molecular diversity. Without these, it is unclear whether performance gains arise from genuinely transferable representations or interpolation within familiar chemotypes, undermining the central generalization claim.\n- The lack of a systematic categorization of failure types (such as incorrect functional groups or misconnected substructures), or failure mode analysis based on specific compound classes (such as halogenated molecules, sugars, large rings), prevents understanding the boundaries of the model’s reliability and might inflate generalizability claims (like performing well on average classes but failing systematically on important ones). There are also no metrics quantifying the domain shift from synthetic to experimental spectra. A calibration of prediction confidence (e.g., likelihood of correctness across different noise levels, so an evolution of the general confidence score cited in Future Works in the Conclusion) and measurement of accuracy degradation due to factors like solvent noise, peak shifting, or missing atoms would also be appreciated.\n- While the authors do state that stereochemistry was excluded from their input/output space and note that Alberts et al [3]. included it, they fail to clearly articulate that this renders the tasks non-equivalent. Including stereochemistry significantly increases the complexity of the structure elucidation problem, and this difference should be explicitly highlighted to avoid misleading comparisons.", "was_revised": true, "final_justification": "The rebuttal addressed the initial concerns I had, and the authors show strong results in all proposed aspects.", "rebuttal": "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.\n\n**[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.\n\n| Test Set | Train set | Scaff(Test, Train) ↑ | SNN(Test, Train) ↑ |\n|-|-|-|-|\n|SpectraNP | SpectraNP | 0.894 | 0.722 |\n|SpectraNP | USPTO | 0.213 | 0.430 |\n\n**[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.\n\n|Dataset| Model| Top-1| Top-5| Top-10|\n|-|-|-|-|-|\n||| Acc% ↑ / Sim ↑ | Acc% ↑ / Sim ↑ | Acc% ↑ / Sim ↑ |\n| SpectraBase | Hu et al. | 39.59 / 0.653  | 55.43 / 0.776 | 59.85 / 0.807 |\n| SpectraBase | NMR-DiGress | 43.10 / 0.607 | 59.70 / 0.759 | 64.83 / 0.793 |\n| SpectraBase | NMRDiff3D-M | 65.06 / 0.746 | 75.22 / 0.846 | 78.01 / 0.868 |\n| SpectraBase | NMRDiff3D-L | **68.80 / 0.789** | **77.59 / 0.867** | **80.35 / 0.886** |\n| USPTO | Hu et al. | 15.86 / 0.503 | 23.95 / 0.626 | 26.73 / 0.657 |\n| USPTO | NMR-DiGress | 12.93 / 0.388 | 25.27 / 0.596 | 31.42 / 0.653 |\n| USPTO | NMRDiff3D-M | 74.52 / 0.834 | 84.25 / 0.916 | 86.85 / 0.932 |\n| USPTO | NMRDiff3D-L | **75.75 / 0.844** | **84.71 / 0.918** | **87.05 / 0.933** |\n| SpectraNP | Hu et al.| 6.29 / 0.450 | 13.56 / 0.594 | 17.35 / 0.633 |\n| SpectraNP | NMR-DiGress | 1.59 / 0.222 | 4.50 / 0.389 | 6.18 / 0.436 |\n| SpectraNP | NMRDiff3D-M | 30.78 / 0.473 | 42.27 / 0.645 | 45.66 / 0.686 |\n| SpectraNP | NMRDiff3D-L | 33.30 / 0.504 | 43.04 / 0.655 | 46.31 / 0.692 |\n| SpectraNP | NMRDiff3D-L (JT) | **38.81 / 0.549** | **50.05 / 0.701** | **53.36 / 0.739** |\n\n**[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. \n\n**Table: Failure rate by total number of atoms on SpectraNP**\n|# Atoms| ≤40 | 41-80 | 81-120 | 121-160 | 161-200 | >200 |\n|-|-|-|-|-|-|-|\n| # Molecules | 2265 | 6168 | 1819 | 539 | 140 | 22 |\n| Failure Rate | 0.315 | 0.353 | 0.345 | 0.282 | 0.400 | 0.636 |\n\n**Table: Failure rate by number of rings on SpectraNP**\n| # Rings | 0 | 1-2 | 3-4 | 5-6 | 7-8 | >8 |\n|-|-|-|-|-|-|-|\n| # Molecules | 559 | 3071 | 4437 | 2102 | 560 | 224 |\n| Failure Rate | 0.229 | 0.322 | 0.339 | 0.380 | 0.393 | 0.451 |\n\n**Table: Failure rate by largest ring size on SpectraNP**\n| Largest Ring Size | 3-5 | 6 | 7-8 | >8 |\n|-|-|-|-|-|\n| # Molecules | 483 | 8061 | 778 | 1072 |\n| Failure Rate | 0.406 | 0.329 | 0.477 | 0.368 |\n\n**Table: Failure rate by functional group on SpectraNP**\n| Functional Group | Carbonyls | Amides | Esters | Ethers | Alcohols | Halogen | Sulfur | Nitrogen |\n|-|-|-|-|-|-|-|-|-|\n| # Molecules | 8149 | 1480 | 4389 | 8048 | 6862 | 477 | 139 | 3047 |\n| Failure Rate| 0.349 | 0.273 | 0.358 | 0.346 | 0.338 | 0.262 | 0.245 | 0.322 |\n\n**Table: Failure rate by total number of atoms on Real-SpecTeach**\n| #Total Atoms | ≤10 | 11-15 | 16-20 | 21-25 | 26-30 | >30 |\n|-|-|-|-|-|-|-|\n| Total Molecules | 10 | 60 | 76 | 48 | 26 | 18 |\n| Failure Rate | 0.000 | 0.133 | 0.184 | 0.354 | 0.423 | 0.389 |\n\n**Table: Failure rate by number of rings on Real-SpecTeach**\n| # Ring | 0 | 1 | >1 |\n|-|-|-|-|\n| # Molecules | 157 | 69 | 12 |\n| Failure Rate | 0.191 | 0.304 | 0.500 |\n\n**Table: Failure rate by largest ring size on Real-SpecTeach**\n| Largest Ring Size | 3-5 | 6 |\n|-|-|-|\n| # Molecules | 4 | 77 |\n| Failure Rate |0.250| 0.338 |\n\n**Table: Failure rate by functional group on Real-SpecTeach**\n| Functional Group | Carbonyls | Amides | Esters | Ethers | Alcohols | Halogen | Sulfur | Nitrogen |\n|-|-|-|-|-|-|-|-|-|\n| # Molecules | 125 | 3 | 46 | 58 | 43 | 24 | 0 | 24 |\n| Failure Rate| 0.200 | 0.667 | 0.348 | 0.328 | 0.256 | 0.042 | 0.000 | 0.417 |\n\nWe 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.\n\n| Dataset | Cos Sim (1H)  | Cos Sim (13C) |\n| --- | --- | --- | \n| Real-SpecTeach | 0.174 ± 0.195 |  0.047 ± 0.072 |\n| Real-5mer-D2O | 0.079 ± 0.063 |  0.030 ± 0.012 |\n| Real-5mer-DMSO | 0.089 ± 0.039 | 0.022 ± 0.034 |\n\nWe 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.\n\n| Prediction | Count | Cos Sim (1H)  | Cos Sim (13C) |\n| --- | --- | --- | --- |\n| Success | 181 | 0.190 ± 0.202 | 0.047 ± 0.072 |\n| Fail | 58 | 0.126 ± 0.166 | 0.048 ± 0.072 |\n\n**[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.\n\n|Spectra|Model| Top-1| Top-5| Top-10|\n|-|-|-|-|-|\n||| Acc% ↑ / Acc% (w/o stereo) ↑ | Acc% ↑ / Acc% (w/o stereo) ↑ | Acc% ↑ / Acc% (w/o stereo) ↑ |\n| 1H | Alberts et al. | 64.99 / NA | 81.94 / NA | 84.07 / NA |\n| 1H | NMRDiff3D-M | **76.88 / 84.71** | **89.49 / 92.27** | **92.43 / 93.92** |\n| 1H + 13C | Alberts et al. | 73.38 / NA | 87.94 / NA |  89.98 / NA |\n| 1H + 13C | NMRDiff3D-M | **78.08 / 86.18** | **90.27 / 93.05** | **93.05 / 94.54** |\n\n**[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.\n\n\nThank you again for your helpful feedback – we believe the revisions will directly address your concerns and improve the clarity and impact of the paper.\n\nReferences:\n\n[1] Polykovskiy, Daniil, et al. \"Molecular sets (MOSES): a benchmarking platform for molecular generation models.\" Frontiers in pharmacology 11 (2020): 565644.\n\n[2] Alberts, Marvin, et al. \"Unraveling molecular structure: A multimodal spectroscopic dataset for chemistry.\" Advances in Neural Information Processing Systems 37 (2024): 125780-125808.\n\n[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."}, {"review_id": "3r8WSRSUOQ", "reviewer": "Reviewer_BFWB", "summary": "NMRDiff3D is proposed to predict the 3D structure of molecules from 1D NMR spectra. The model uses a transformer encoder over a 1D convolutional layer to predict 3D atom coordinates. Diffusion is used as the training strategy, and data augmentation is applied to learn SE(3) equivariance by scaling up. Results show that NMRDiff3D outperforms previous methods on synthetic and experimental datasets.", "questions": "I have questions linked to my concerns above. I would be happy to increase the grades if these questions are answered.\n\n\n1. Can you comment on the accuracy of the synthetic data generation? How reliable is the used MestreNova software for natural products? Is there a way to verify the generated structures?\n2. Why did you remove stereochemistry from the dataset? How does it affect the evaluation of the model?\n3. Can you report the 2D and 3D structural similarity between the train and test splits? If these splits are similar, can you run experiments on distant splits to reveal the generalization of the model and the benchmarks?\n4. How long does it take to train one NMRDiff3D model?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 3, "strengths_and_weaknesses": "I congratulate the authors. I truly enjoyed reading the work.\n\nOriginality: \n- First approach that uses diffusion to predict 3D coordinates from 1D NMR spectra. Diffusion is a well-motivated choice for this task due to its recent success in 3D generation.\n- The developed deep learning architecture is a well-motivated architecture and fits the data modality.\n- Learning equivariance at scale, despite not being a novel idea, is a good choice to simplify the model.\n\n\nClarity:\n- Very well-structured and written paper. It was easy to follow top to bottom, although I am not an expert in NMR spectroscopy.\n\nQuality:\n- Experimental pipelines are well thought out and executed. \n\n\nSignificance\n- The performance gain over the benchmark is significant.\n- It can replace the existing methods for 3D structure prediction from 1D NMR spectra. I cannot estimate the size of this potential, though, due to my background.\n\n\n**Weaknesses**\n\nI believe the work is already in good shape. I have several concerns about the applicability domain and evaluation of the model. I will happily update my grades if these concerns are addressed.\n\nQuality\n\n1. (L260) The model size indeed increases the performance, but a big performance boost is already observed with NMRDiff3D-M. This can be emphasized. I believe this would help readers appreciate the quality of the model and the ideas behind it better. 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.\n2. The authors generate the synthetic data via MestreNova. However, the applicability of this method to generate 3D structures of natural products is not discussed.\n3. Stereochemistry is removed when generating the dataset. However, the studied task is in 3D by nature, and natural products are *known* to have rich stereochemistry. This can make the evaluation task artificially easier.\n\nSignificance\n1. The structural and 3D similarity between the train and test splits is not reported. This is very important to measure the generalization of the model, as well as its real-world applicability.\n\nClarity\n\n1. (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.\n2. 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.", "was_revised": true, "final_justification": "The use of diffusion and the designed architectures is novel in the task. The contribution of each component is well-studied in ablation studies. The experiments support the claims made in the paper, and I believe this can be a high-impact paper in NMR field. \n\nMy concerns about the applicability domain are addressed by the authors in the rebuttals experiments. \n\nI updated my rating accordingly.", "rebuttal": "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.\n\n**[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.\n\n**[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.\n\n|Spectra|Model| Top-1| Top-5| Top-10|\n|-|-|-|-|-|\n||| Acc% ↑ / Acc% (w/o stereo) ↑ | Acc% ↑ / Acc% (w/o stereo) ↑ | Acc% ↑ / Acc% (w/o stereo) ↑ |\n| 1H | Alberts et al. | 64.99 / NA | 81.94 / NA | 84.07 / NA |\n| 1H | NMRDiff3D-M | **76.88 / 84.71** | **89.49 / 92.27** | **92.43 / 93.92** |\n| 1H + 13C | Alberts et al. | 73.38 / NA | 87.94 / NA |  89.98 / NA |\n| 1H + 13C | NMRDiff3D-M | **78.08 / 86.18** | **90.27 / 93.05** | **93.05 / 94.54** |\n\n\n**[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.\n\n| Train set | Test (Sub)set | # Test set data | Scaff ↑| SNN ↑| $\\|\\sigma_\\textrm{train} - \\sigma_\\textrm{test}\\|$ ↓|\n|-|-|-|-|-|-|\n| SpectraBase | SpectraBase | 14178| 0.959 | 0.659 | 0.004 |\n| SpectraBase | SpectraBase (Unseen Scaffolds) | 3786 (26.7%) | 0.000 | 0.657 | 0.025 |\n| USPTO | USPTO | 73438 | 0.980 | 0.698 | 0.005 |\n| USPTO | USPTO (Unseen Scaffolds) | 14796 (20.1%) | 0.000 | 0.656 |0.174|\n| SpectraNP | SpectraNP | 10925 | 0.894 | 0.722 | 0.012 |\n| SpectraNP | SpectraNP (Unseen Scaffolds) | 2898 (26.5%) | 0.000 | 0.655 | 0.144|\n\nWe 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. \n\n|Dataset| Model| Top-1| Top-5| Top-10|\n|-|-|-|-|-|\n||| Acc% ↑ / Sim ↑ | Acc% ↑ / Sim ↑ | Acc% ↑ / Sim ↑ |\n| SpectraBase | Hu et al. | 39.59 / 0.653  | 55.43 / 0.776 | 59.85 / 0.807 |\n| SpectraBase | NMR-DiGress | 43.10 / 0.607 | 59.70 / 0.759 | 64.83 / 0.793 |\n| SpectraBase | NMRDiff3D-M | 65.06 / 0.746 | 75.22 / 0.846 | 78.01 / 0.868 |\n| SpectraBase | NMRDiff3D-L | **68.80 / 0.789** | **77.59 / 0.867** | **80.35 / 0.886** |\n| USPTO | Hu et al. | 15.86 / 0.503 | 23.95 / 0.626 | 26.73 / 0.657 |\n| USPTO | NMR-DiGress | 12.93 / 0.388 | 25.27 / 0.596 | 31.42 / 0.653 |\n| USPTO | NMRDiff3D-M | 74.52 / 0.834 | 84.25 / 0.916 | 86.85 / 0.932 |\n| USPTO | NMRDiff3D-L | **75.75 / 0.844** | **84.71 / 0.918** | **87.05 / 0.933** |\n| SpectraNP | Hu et al.| 6.29 / 0.450 | 13.56 / 0.594 | 17.35 / 0.633 |\n| SpectraNP | NMR-DiGress | 1.59 / 0.222 | 4.50 / 0.389 | 6.18 / 0.436 |\n| SpectraNP | NMRDiff3D-M | 30.78 / 0.473 | 42.27 / 0.645 | 45.66 / 0.686 |\n| SpectraNP | NMRDiff3D-L | **33.30 / 0.504** | **43.04 / 0.655** | **46.31 / 0.692** |\n\n\n**[Minor questions or suggestions]**\n\n> (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.\n\nThank 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.\n> (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.\n\nThank 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.\n\n> 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.\n\nWe 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.\n\n> How long does it take to train one NMRDiff3D model?\n\nFor 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. \n\nThank you again for your helpful feedback – we believe the revisions will directly address your concerns and improve the clarity and impact of the paper.\n\nReferences:\n\n[1] Alberts, Marvin, et al. \"Unraveling molecular structure: A multimodal spectroscopic dataset for chemistry.\" Advances in Neural Information Processing Systems 37 (2024): 125780-125808.\n\n[2] Polykovskiy, Daniil, et al. \"Molecular sets (MOSES): a benchmarking platform for molecular generation models.\" Frontiers in pharmacology 11 (2020): 565644."}]

Author rebuttal:

Meta-review: The paper introduces  NMRDiff3D, a diffusion-based framework that directly predicts 3D molecular structures from 1D NMR spectra and molecular formulas. The work is technically novel, addresses an underexplored problem in chemistry, and demonstrates consistent state-of-the-art performance across synthetic and experimental datasets, supported by extensive ablations and additional evaluations after rebuttal. While questions remain around equivariance and dataset scope, the authors provided convincing clarifications and new experiments, leaving the community with a practical tool that can accelerate small-molecule discovery.
Decision: Accept (poster)