Enhancing Molecular Conformer Generation via Fragment- Augmented Diffusion Pretraining
Authors: Xiaozhuang Song
YUZHAO TU
Tianshu Yu
Venue: Accepted by TMLR ()

Abstract: Recent advances in diffusion-based methods have shown promising results for molecular conformer generation, yet their performance remains constrained by training data scarcity---particularly for structurally complex molecules. In this work, we present Fragment-Augmented Diffusion (FragDiff), a data-centric augmentation strategy that incorporates chemical fragmentation techniques into the pre-training phase of modern diffusion-based generative models. Our key innovation lies in decomposing molecules into chemically meaningful fragments that serve as building blocks for systematic data augmentation, enabling the diffusion model to learn enhanced local geometry while maintaining global molecular topology. Unlike existing approaches that focus on complex architectural modifications, FragDiff adopts a data-centric paradigm orthogonal to model design. Comprehensive benchmarks show FragDiff's superior performance, especially in data-scarce scenarios. Notably, it achieves 12.2--13.4% performance improvement on molecules 3$\times$ beyond training scale through pretraining on fragments. Overall, we establish a new paradigm integrating chemical fragmentations with diffusion models, advancing computational chemistry workflows. The code is available at https://github.com/ShawnKS/fragdiff.

Published in Transactions on Machine Learning Research (06/2025)
Enhancing Molecular Conformer Generation via Fragment- Augmented Diffusion Pretraining
Xiaozhuang Song
zioozhuangsong/ @link. cafinkk.cch.eem
School of Data Science The Chinese University of Hong Kong, Shenzken
Yuzhao Tu
yuchaotu&@link.cukk. edu.cr
School Data Science
The Chinese University of Hong Kong, Shenzhen
Tianshu Yu
yutkonshauBcukk.edu..cm
School of Data Science The Chinese University of Hong Kong, Shenzhen
Reviewed on OpenReview: https: // opwp:evveepeeeee....mmmmm net/ forun? id- t5WzHON1AF
Abstract
Recent advances in diffusion-based methods have shown promising results for molecular con- former generation, yet their performance remains constrained by training data scarcity- particularly for structurally complex molecules. In this work, we present Fragment- Augmented Diffuusio (FRagDiff), a data-centric augmentation strategy that incorporates chemical fragmentation techniques into the pre-training phase of modern diffusion-based generative models. Our key innovation lies in decomposing molecules into chemically mean- ingful fragments that serve building blocks for systematic data augmentation, enabling the dilfusion model to learn enhanced local geomelry while mainlaining global molecular topology. Unlike existing approaches that focus on complex architectural modifications, FRAGDIFF adopts a data-centric paradigm orthogonal to model design. Comprehensive benchmarks show FRAGDIFF's superior performance, especially in data-scarce scenarios. Notably, achieves 12.2-13.4% performance improvement on molecules 3x beyond training scale through pretraining on fragments. Overall, we establish a new paradigm integrating chemical fragmentations with diffusion models, advancing computational chemistry work- flows. The code is available https://githin: wttchuu..comeee/ StwSSShaaaSaaaSSea
1 Introduction
The generation of molecular conformers serves as a foundational task in computational chemistry, molecular
biology, and drug discovery (Axelrod & Gomez-Bonee Bombarelll have witnessed a paradigm shift in conformer generation from mulebased methods deep learning-driven
2022
Abramson et al. 2024). Recent years
approaches [Have] 1998 Riniker & Landrum 2015 Jin al. 2018 Simm & Hernandezz 2020 Zhu
et al. 2022 particularly diffusion-based generative models (Xu et al. 2022 Wang al. 2023 Guo et al.
2024
These methods leverage the principles of iterative denoising processes, achieving excellent perfor-
mance in modeling the complex, high-dimensional energy landscapes of molccular structures (Rappé et al.
1992 Halgren 1996: Zhou et. al.) 2023). However, despile these advancements, the effectiveness of modern approaches remains constrained by limited training data - a pervasive challenge in real-world molecular datascts [Kirchmeyer et al. 2022; Rotskoff 2024). This paper investigates a critical rescarch question: Can we more effectively leverage existing data to improve the performance of diffussoo- basseddoo-aedd based conformer generation models, particularly in data-scarce scenarios?

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Fragmenti11
Fragmentation
FragmentH22
3ragmentii
Amoxycillin N,,,,
Figure 1: Fragmentation example on Amozicillin.
The inherent compositional and hicrarchical structure of molccules provides natural framework for ad- dressing data scarcity in conformer generation (Kulichenko et al.] 2024). Advances in fragment-based drug design have also demonstrated that molecular subsystems often exhibit transferable conformational pref- erences across diffcrent compounds (Brameld al. 2008). Computational chemistry has long exploited this structure through rule-based fragmentation techniques, which decompose molecules into chemically meaningful components to enable efficient modeling of molecular docking, property prediction, and other tasks (Rappé et al. 1992: Halgren 1996). For instance, the antibiotic Amoricillón (Fig. [ can be system- atically divided into functional subunits- 3-lactam ring, thiazolidine ring. amino group, hydrozyl group, and benzene ring each governing distinct aspects of molecular conformation and interactions. Despite their interpretability, these traditional approaches lack the flexibility modern generative models. Conversely, while diffusion-based methods achieve SOTA performance through data-driven learning, they often neglect encode this foundational chemical prior knowledge (Gordon et al., 2012] Kirchmeyer et al.] 2022 Rot- skoff 2024 This represents potential for improvement, molecular fragments' intrinsic geometric constraints could regularize model training and improve sample efficiency, and this gap be bridged by systematically integrating knowledge-driven fragmentation into both the architecture ure and training of data- driven models.
Thus, this work, we present Fragment-Augment Diffusion (FRAGDIFF), a data-centric augmentation strategy that incorporates traditional cherical fragmentation techniques into the pre-training phase of mod- ern diffusion-based generative models. Our two-phase learning paradigm first pretrains the model on de- composed molecular fragments to capture local fragments' structural patterns, then finetunes complete molecules to integrate global structural constraints. Comprehensive empirical evaluations of fragmentation pretraining on two distinct diffusion frameworks, GeoDiff and TorDiff, demonstrate consistent improvements across multiple datasets and settings, particularly in data-scarce regimes (Xu et al. 2022 Jing et al.) 2022).
The success of both paradigms highlights the versatility of fragmentation pretraining in geometric deep learn- ing for molecular conformation generation. Notably, FRAGDIFF also enables effective generation for molecules triple the size of training instances, overcoming conventional scale limitations. This capability demonstrates crucial practical value as real-world drug discovery often requires modeling complex macro-molecular struc- tures. The successful extrapolation suggests our fragment-aware paradigm establishes transferable chemical rules rather than memorizing size-specific patterns, opening new possibilities for generative modeling.
By bridging trnal knowledge-driven methods in computational chemistry with modern generative AI, FRAGDIFF underscores the power of data-centric strategies in improving generative models and highlight the importance of interdisciplinary synthesis in molocule generation rescarch. It serves a practical tool for practitioners and conceptual milestone, advocating for deeper integration of Comain-speciffe priors and machine learning in molecular science.
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2 Related Work
Diffusion-based Conformer Generation Diffusion models have emerged as prominent tools for molec- ular conformer generation, employing stochastic processes that gradually transform ordered structures into disordered states before learning their reversal through noural networks (Xu al., 2022 Guo et al. 2024: Hua et al. 2024). While early implementatiins utilized Cartesian coordinate diffusion with equivariant graph neural networks (Xu et al., 2022 Hoogeboom et al. 2022), these approaches suffer from high com- putational costs due to iterative denoising of full atomic coordinates (Shi et al. 2021: Luo et al. 2021) Another key advancement comes from Jing et al. (2022). who recognized that molecular flexibility arises primarily from torsional degrees of freedom. Their Torsional Diffusion framework restricts the diffusion pro- cess to torsion angles critical determinants of conformational energy landscapes (Kang et al. [996] while preserving bond lengths and angles. This dimensionality reduction strategy enhances sampling efficiency without compromising accuracy, addressing scalability limitations in prior methods.
Molecular Fragment Decomposition Molecular fragment decomposition critical concept in com- putational chemistry, enabling the simplification of complex molecular structures into smaller and more manageable units (Hann et al., 2001 Sliwoski et al.] 2014 Sadybekov & Katritch 2023 This approach facilitates the study of molecular propertics and interactions by focusing on individual fragments that retain key chemical characteristics of the parent molecule (Bemis & MMurkko, 1996] Jiisong et al. 2024). Frag- mentation rules enable systematic molecular decomposition along chemically meaningful boundaries. From a force field perspective, by preserving the local chemical environment around targeted torsions, fragmen- tation allows for accurate modeling of torsional potentials, ensuring that torsional characteristics can be effectively transferred back to the parent molecule (Horton et al. 2022; D'Amore et. al., 2022. Methods like BRICS and RECAP preserve essential functional groups while severing specific bond types (Lewell ct al. 1998 Degen et al. 2008), revealing intrinsic properties of molecular subunits and enhancing efficiency by reducing conformational complexity (Liu et al. (017). By analyzing these fragments, researchers can predict reactivity, optimize drug design, and explore novel chemical spaces with higher precision (Gordon et al. 2012). Beyond conformer generation, fragment- based approaches have been applied to 2D molecular graph generation. Methods like JT-VAE (Jin et al., 2018)) and MoLeR (Maziarz et al.) 2021) use fragments building blocks to simplify molecule assembly, differing from our approach that. leverages fragments for transfer learning in 3D space. These methods leverage fragmentation primarily to ensure chemical validity, whereas our approach uniquely applies fragment-basee knowledge transfer to enhance conformer generation through pre-training Overall, the integration of molecular fragment decomposition with advanced modeling techniques offers a powerful framework for generating accurate and diverse molecular conformers, ultimately advancing the fields of drug discovery and materials science (Jinsong et al. 2024
3 Methodology
3.1 Preliminaries
Notations and Problem Formulations Each molecule with n atoms is represented as an undirected graph G =V =V,E), where V =
( {m=) is the set of vertices representing types of atoms, and =={ I (i.j) C VxV} is the set of edges representing inter-atomic bonds. Each node 12 E V contains atomic attributes such as element type and hybridization state. Each edge Gi,j E represents a bond between atoms v, and ej. labeled with its bond type (e-g., single, double, triple). The task of molecular conformer generation involves creating stable and valid 3D conformers C' for given molecular graph G. These conformers are samples from a distribution that reflects the physical and chemical properties related to molecular stability, making it a conditional generative problem. For multiple graphs G, cach with its conformers C' as independent and identically distributed samples from a Boltzmann distribution, the goal is to learn a generative model po 9) that facilitates easy sampling and approximates the Boltzmann function (Hawkins) 2017 Computational approaches diverge in their geometric representations: Methods like GcoDiff (Xu et al. 2022) operate directly
in Cartesian coordinate space, while Torsional Diffusion (Jing et al.) 2022) employs internal coordinates through torsion angles to model rotational degrees of freedom.
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3.2 Molecular Fragmentations as Data Augmentation
To enhance molecular representation diversity while preserving key structural and geometric features, we employ fragment-based molecular modcling as form of data augmentation. By decomposing complete generate augmented data that encode local
molecular structures into chemically meaningful fragments, geometric and chemical information, thereby improving the training of diffusion models. Let the complete molecular structure be represented in a generalized coordinate space C, corresponding to internal coordinates such as bond lengths, bond angles, and dihedral angles. Fragmentation decomposcs the molecule into + Tragments, each associated with coordinate subspace C, derived from C, where b 1,..., B 1. The fragment coordinates Cg retain fragment-specifie internal coordinates relevant to their local structures.
Due to data limitations, the true isolated fragment coordinates C are often unavailable. Consequently, we approximate them using the corresponding subspaces C. extracted from the complete molecule's 's coordinates C, assuming Ö x Cg. However, fragmentation can modify electronic environments and steric interactions, potentially causing deviations between fragment gcometrics and those in the complete molccule (Sern et al., 2022 Horton et al. 2022). To reduce these discrepancies, is crucial to select fragmentation strategies that preserve key chemical features such as conjugation, resonance, steric effects, and hydrogen bonding. By doing so, the fragment properties remain consistent with those of the complete molecule, and E serves reliable proxy for C.. From information-theome
perspective, we aim to maximize the mutual information T(Ca; C)) between the fragment coordinate subspaces Co and the complete molecular coordinate space C. Maximizing I(Ć5; C) ensures that the fragments retain sufficient information about the global structure to accurately reflect molecular properties such as conformeral flexibility and stability. The mutual information is defined as
T(Cs: = HCC,, CC),
where (C,) is the entropy of the fragment coordinate subspace, and HC,, C) is the conditional entropy given C. Different fragmentation methods inftuence the approximation error and thus affect the mutual in- formation between C. and C. Therefore, careful selection of fragmentation strategies is essential to maintain chemical properties and minimize approximation biases. By optimizing these strategies, we can effectively leverage data augmentation in fragment-based molecular modeling to enhance model robustness and accu- racy. For a detailed analysis of the impact of different fragmentation methods on these errors, please refer to Appendix B.2.
Diffusion-basse Molecular Conformer Generation cerfusion-basedd models have emerged powerful tools for molecular conformer generation, particularly in drug discovery (Xu et al. 2022 Guo et al. 2024) These models employ stochastic differential equations (SDEs) to transition molecular structures from their stable equilibrium conformers to highly disordered states through a controlled diffusion process. The re- verse process generates samples from the data distribution by iteratively denoising and reconstructing the molecular conformers. In general framework, diffusion models operate directly on the molocular structures, capluring the geometric properties without being confined to specific internal coordinates such torsion an- gles. This approach allows for comprehensive exploration of the conformeral space, leveraging the intrinsic geometric relationships within the molecule.
Forward Process The forward diffusion process undergoes a transition from their stable equilibrium conformers C to state of increased disorder through a series of diffusion steps, which modeled as Markov chain that incrementally adds Gaussian noise to the molecular conformers C resulting in a sequence of increasingly disordered states CLT, At each time step I, noise is injected according to variance parameters 3r which control the scale of perturbation:
T CCCT CC) = II 1 (=d0 (Ct
=
This process ensures a gradual increase in randomness, eventually diffusing the molecular structure into a noise distribution similar to white noise after T iterations.
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Reverse Process The reverse diffusion process aims to reconstruct the original molecular conformer C from the noisy state C² guided by learnable conditional Markov chain. Beginning with chaotic particles C ~ p(C)) drawn from a standard Gaussian distribution, the model iteratively refines the conformers through reverse transitions:
T po (000-119,C")) = II 10." 19,0") (
where H4 is a neural network that estimates the mean of the denoised conformer at each time step t, conditioned on the molecular graph 9 and the noisy conformer C". The variance of may be predefined or learned during training. This reverse process systematically reduces the noise, producing realistic molecular conformers that align with the data distribution. This general diffusion framework enables flexible modcling of molecular structures, capluring both geometric and topological features.
Typically, diffusion frameworks parameterize μز to directly predict the denoising direction. Alternatively, the reverse process can be guided by approximating the score function Vc logoor((C), which indicates how to move from the current state loward the data distribution. To unily these perspectives, we employ a neural network So C² () to approximate this score function, where So is closely related to 140 through the relationship μig = C ofsa (Song & Ermon 2019 Xu et al., 2022 Jing et al., 2022). The score network Sy aims to match the true score function with the loss function defined as:
(O) = E, (()) Ct cxpppo(io)) (|s0(9)C',0) -Ver loggepoC c g)
Here, X(I) precomputed weighting factor to balance contributions across timesteps. Through this for- mulation, (g C*, explicitly learns to denoise the conformer by aligning with the score function, while maintaining consistency with the mean parameterization μa. The network thereby recovers stable molecular conformers from noisy initial states.
3.3
iitt-trransational Equivariant Network
For diffuusin models designed for molecular conformer generation, the network architecture typically adopts a roto-translational cquivariant design, also known as an (E(()-cquivariant network (Thomas et al., 2018 Geiger & Smidi 2022; Zhou al. 2024). This design ensures that the network's 's outputs are equivariant with respect rotations and translations, which an effective approach for modeling molecular structures that are inherently symmetric under such transformations. By incorporating cquivariance, the network accurately captures the geometric properties of molecules, leading to more physically plausible and consistent conformer generation.
The SE(3)-equivart) framework operates through distinct strategies: For instance, GeoDiff (Xu et al. 2022) directly models inter-atomic coordinates using equivariant graph neural networks that update node features and positions via message passing, while TorDiff (Jing et al., 2022) focuses on torsional degroes of freedom (dihedral angles within internal coordinates) by applying rotational transformations to substructures around chemical bonds. Both approaches enforce critical symmetries: SE(3) (equvviaive ensures invariance to global translations, and spatial inversion symmetry (p(C) = p(-C') preserves physical consistency under mir- ror reflections. These symmetries are embodded into score functions, where GcoDiff computes -in3aiint scalar updates through edge-wise interactions, and TorDiff encodes pseudoscalar transformations for torsional components. The architectures further ensure that gradient updates to atomic coordinates or torsional an- gles respect the antisymmetric property under spatial inversion (Ve pt (C 9) -Va log 9)), aligning with fundamental physical laws. A complete technical description of these frameworks, including their mathematical formulations and implementation details, is provided in Appendix A.1
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Fragmentation
Pretrain
Molecular Diffusion Model
Train Set
Finetune
Figure 2: An overview of the FRAEDIFF pipeline. Molecules from the training set will be fragmented based on randomly selected fragmentation edges. The resulting fragments will be further used as augmented data in the pretraining phase.
3.4 Tragment-Augmenttrr Diffusion Pretraining
In this work, introduce fragment-augmenteed diffusion pretraining approach, where molecules are de- composed into smaller meaningful fragments using specific rules. Figure 2 illustrates an overview of the Iragment-augmented diffusion pretraining pipeline. By pretraining on fragmented molecular data, the model learns rich representations that can be fine-tuned for downstream tasks. This pretraining paradigm aims to enhance the diffusion model's ability by leveraging fragment-level information, leading to better molecular conformer generation.
The fragmentation is guided by identifying key rotatable bonds functional groups, ensuring that cach fragment retains essential chemical and structural information (Jinsong et al. 2024). By focusing these fragments during pretraining, we enable the model to learn from smaller, more manageable substructures, which can be optimized independently while maintaining global molecular consistency through interactions between fragments. This yields + fragments per molecule (from decomposition edges), where each fragment constitutes an independent subgraph with preserved local connectivity. Once a molecule frag- mented into multiple fragments, each fragment is treated as an independent subgraph consisting of its own nodes (atoms) and edges (bonds). The conformer generation task for each fragment is performed indepen- dently in the pretraining phase. Molecules from the training set are fragmented based on randomly selected fragmentation edges, and the resulting smaller fragments are used as augmented data to pretrain the model.
The loss for cach fragment is computed scparately, and these losses are averaged to form the total loss function during pretraining. For each molecule in the datasel containing N samples, we compute fragment-specifie losses then aggregate across both fragments and molecules:
Seretrain
1 N
B;+1
E
so(C Vc log logP))(CC()) (0.0.. c-
l'
B
+1
b=1
where B; denotes decomposition edges count for molecule i, e( represents edges in the b-th fragment of molecule i, Cs presents the coordinates for atoms in fragment of molecule i, g denotes the local graph structure of fragment b in molecule i. sa((0) t) is the neural network parameterized score function that predicts the gradient of the log probability density at time step t, and Vc log (C)((()) represents the true score function of the perturbation kernel, describing the gradient of the log probability density of the noised coordinates given the original coordinates.
3.5 Model Training
Evidence Lower Bound (ELBO) Optimization Using the probability flow ODE, we compute the
likelihood of any sample Co lo
5 2 so(G, C2 1) dt. (Sng & Ermon

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De Bortoli 2022). Since directly computing the exact log-likelihood Ellog pa (C"lg) is intractable, we resort to maximizing its evidence lower bound (ELBO)):
2020
Pe (g) Q
Ellog ps [g) = E log
2 -By
Σ DKL DKL (1(C"=1100 (2) | Ipo((=+1
where q(C"=1IC* C²) is analytically tractable due to the properties of the forward diffusion process. Specif- ically, for any timestep t, the distribution q( ((C*)C)) can be expressed in closed form
((C*)C)) - N (C" Vār C (1-aa)))) aa))
where a₁ = 1 3r and at = II'= as This formulation allows us to derive (0 C²) analytically and efficiently. Building upon the insights from Ho et al. (2020) and Xu al. (2022), we can further simplify the ELBO by expressing the KL divergence wetween Gaussian distributions the predicted score function so(g, C t) and the target score Vei Toglog70 log Pyo C C) Consequently, independently sample conformers at various timesteps from g(C"t=IC*, (9) to optimize the objective more efficiently. By modeling the score function with Ss. we enhance the training process and improve the model's ability to generate accurate torsional angles (Xu et al. 2022
weighted Lg loss bet
Pretraining and Finetuning The pretraining phase employs fragment-based learning to enhance the diffusion network's ability on generating molecular substructures. Molecules are systematically decomposed into smaller fragments using predefined decomposition rules, and the network is trained on these individual fragments. This fragment-level training enables the network to learn representations of molecular sub- structures for generating accurate full molecular conformers. Following pretraining, the diffusion network undergoes fine-tuning using data from real-world molecular datasets accurately handle complete molecular geometries. This holistic fine-tuning process effectively combines fragment-level knowledge with empirical data, optimizing the network's ability to generate accurate and physically plausible molecular conformers.
Conformer Sampling To generate a stable conformer Co for a given molecular graph G, we begin by sampling noisy state CT from the prior distribution pr (CT), typically standard Gaussian distribution. Then, employing the trained reverse process p²(C"=1 G. C²) defined earlier, we ileratively sample C from Ot as decreases from T to 1. At each timestep. the neural network po(G, C* t) predicts the mean of the denoised conformer, guiding the refinement of particle positions. This sequential process gradually transitions the conformer from a chaotic state to an equilibrium state, yielding realistic molecular structures that align with the learned data distribution.
4 Experiments
4.1 Experimental setup
Dataset We utilize three subsets GEOM-QM9, GEOM-DRUGS, and GEOM-XL from the GEOM dataset (Axelrod & Kooez-Boomarelle 2022 which provides high-quality conformer ensembles generated using metadynamics in CREST (Pracht et al. 2020 GEOM-QM9 is dataset featuring significantly represents the most pharnaceutically rele- vant subset, comprising molecules with an average of 44 atoms. GEOM-XL. is created by selecting all species with more than 100 atoms from GEOM-MolcculaNett (Wu et al. 2018), allowing us to ovaluate models' generation quality on large molecules. For a detailed statistics for all three datasels are Appendix D.2
smaller molecules with an average of 11 atoms. GEOM-
Evaluation To assess both diversity and quality, we apply two key metrics: Average Minimum RMSD (AMR) and Coverage (COV). These metrics are reported for both Recall (AMR-R, COV-R) and Precision (AMR-P, COV-P). COV-R and AMR-R mcasure how well the generated ensemble covers the ground-truth ensemble, while COV-P and AMR-P assess the accuracy of the generated conformers. The calculations of COV-R and AMR-R are defined as:
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1
K
AMR-R ==
-
min RMSD(C&, CT) k=
I
1=1
1 L
COV-R
Σ
Jmin RMSD(C&; <
For precision metrics, COV-P and AMR-P are calculated by swapping the roles of the generated and reference sets. These metrics emphasize the quality of the generated conformers. In our evaluations, set the threshold 6 to 0.5 Å for the GEOM-QM9 dataset and 0.75 Á for the GEOM-DRUGS dataset. Higher COV scores or lower AMR scores indicate more realistic conformers, effectively balancing both diversity and accuracy.
Baselines To establish a comprehensive bascline for our proposed data augmentation methods, we compare them against both traditional computational techniques and state-of-the-art deep learning models. Among traditional methods, we utilize RDKit ETKDG (Havel 1998 Riniker & Landrum, 2015 a widely recognized open-source tool, Metrization (Havel 1998), a distance geometry-based conformer sampling approach, and OMEGA (Hawkins) 2017). commercial software known for its continuous development and reliability. the realm of deep learning. we benchmark against several leading models, including CGCF (Xu et al. 2021
ConfGF (Shi et al.
2021), GeoDiff (Xu et al., 2022 Torsional Diffusion (TorDiff) (Jing et al. 2022,, and DMCG (Zhu et al. 2022) We implement our FRAGDIFF approach through two established diffusion frameworks: GeoDiff (Xu et al. 2022] which models molecular geometry in continuous space, and TorDiff (Jing et al., 2022) which specializes in torsional angle sampling. The resulting implementations are denoted as FRAGDIPF-G and FRAGDIFP-T, maintaining the core architectures while integrating our fragment-based pretraining.
2021 GeoMol (Ganea et al.
Fragmentation Augmentation Setup In our main FRAGDIFF implementation, fragmentation edges are identified by combining those recognized by BRICS rules, RECAP rules, and graph-based fragmentation (Algorithm
D into a unified candidate pool. For given molecule, we identify all fragmentation-edges and randomly select B min(b, k) edges, where b is the total number of fragmentationn-edee and limits the maximum number of selected edges to avoid excessive small fragments. From the resulting B + I fragments, those with rotatable bonds are used to augment the training set. Our experiments use = 5. During fragmentation, only fragments larger than atoms are selected for augmentation. This ensures that the resulting fragments retain sufficient structural complexity and chemical information to contribute meaningfully to the training process. To explore the impact of reaction-related bonds on model performance, we also test models generated after removing these bonds, focusing on BRICS and RECAP rules (Lewell et al. 1998 Degen et al. 2008). Detailed introductions of these two chemical rules provided in the Appendix [.1 and additional results and discussions how the choice of the minimum fragment size parameter z affects fragmentation statistics are provided in Appendix D.2]
Experimental environment and Model Setup The detailed experimental environment and parameter settings for the experiments can be found in Appendix C
4.2 Conformation Generation
Performance GEOM-DRUGS As shown in Table our fragment-auugennted models demonstrate substantial improvements over existing approaches. FRAGDIFF-T achieves state-of-the-art performance, at- taining the highest mcan COV-R (70.07% vs TorDiff's 67. 67.49%) and COV-P (52.87% vs TorDiff's 's 49.53%), along with the lowest AMR-R (0.609 Á vs 0.634 A) and AMR-P (0.800 Á vs 0.827 Å). While DMCG outper- forms many baselines, FRAGDIFF-1 T still achieves substantially better results all metrics, demonstrating the effectiveness of diffusion models with fragmentation pretraining. This consistent superiority across both coverage and accuracy metrics underscores the effectiveness of our fragment- based augmentation strategy. The advantages of our approach particularly evident when comparing to baseline diffusion models. While
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Quality of generated conformers for the GEOM-DRUGS test in terms of Coverage (%) and Average Minimum RMSD (A) with 5 0.75 A. The results of CGCF, CONFGF are borrowed from Shi et al. (2021). The results of GeoMol, OMEGA, ETKDG are borrowed from Jing et al. (2022), the results of DMCG are obtained by evaluating the official checkpoint with the same 0.75 A, and the rest results are obtained by our own experiments.
Table 1:
Models
COV-R
(%) 1
AMR-R (A) 4
COV-P (%) 1
AMR-P (A)
Mean
Median
Mean
Median
Mean
Median
Mean
Median
Metrization
5.712
0.00
1.388
1.329
4.932
0.000
1.541
1.339
CGCF
5.810
0.00
1.248
1.224
0.200
0.000
1.857
1,806
ConfGF
9.150
0.50
1.162
1.159
3.060
0.250
1.721
1.686
ETKDG
38.40
28.60
1.058
1.002
40.90
30.80
0.995
0.895
GeoMol
44.60
41.40
0.875
0.834
43.00
36.40
0.928
0.841
OMEGA
53.40
54.60
0.841
0.762
40.50
33.30
0.946
0.854
DMCG
57.55
59.00
0.722
0.723
37.57
35.33
0.944
0.909
GeoDiff
45.61
49.32
0.862
0.852
21.47
14.55
1.171
1.123
FRAGDIFF-G
51.56
52.34
0.847
0.838
26.13
20.63
1.095
1.084
TorDiff
67.49
75.81
0.634
0.618
49.53
47.16
0.827
0.778
FRAGDIFF-T
70.07
78.35
0.609
0.588
52.87
54.17
0.800
0.749
Table 2: Quality of generated conformers for the GEOM-QM9 test set in terms of Coverage (%) and Average Minimum RMSD (A) with 8 0.5 A. The results of CGCF, ConfGF are borrowed from Shi et al. (2021)
The results of GeoMol, OMEGA, and ETKDG
borrowed from Jiin et al. (2022), the results of DMCG are borrowed from (Zhu et al. 2022) and the rest results are obtained by
experiments.
Models
COV-R (%)*
AMR-R (A) 4
COV-P (%) 1
AMR-P (A)
Mean
Median
Mean
Median
Mean
Median
Mean
Median
CGCF
78.0
82.4
0.421
0.390
36.5
33.6
0.662
0.643
CONFGF
88.4
94.3
0.267
0.268
46.4
43.4
0.522
0.512
ETKDG
85.1
100.0
0.235
0.199
86.8
100.0
0.232
0.205
OMEGA
85.5
100.0
0.177
0.126
82.9
100.0
0.224
0.186
GooMol
91.5
100.0
0.225
0.193
86.7
100.0
0.270
0.241
DMCG
96.3
100.0
0.206
0.200
87.2
91.0
0.287
0.292
GeoDiff
90.1
93.4
0.209
0.198
52.8
50.3
0.445
0.427
FragDiff-G
91.1
95.1
0.199
0.194
56.0
55.0
0.431
0.421
TorDiff
92.8
100.0
0.178
0.147
92.7
100.0
0.221
0.195
FragDiff-T
93.2
100.0
0.175
0.139
93.1
100.0
0.218
0.189
GeoDiff achieves 45.61% COV-R and 21.47% COV-P, our FRAGDIFF-G variant improves these to 51.56% and 26.13% respectively, while simultancously reducing AMR metrics by 0.015 Á (R) and 0.076 Á (P). This demonstrates the generalizability of our fragmentation paradigm across different backbone architec- tures. Notably, FRAGDIFF-T's performance improvement TorDiff (2.58-3.34% absolute improvement in coverage metrics with 0.025-0.027 Á AMR reduction) highlights the particular synergy between torsional diffusion frameworks and fragment-based pretraining. The results suggest that our augmentation strategy enables more comprehensive sampling of low-energy conformers while maintaining high structural fidelity, addressing the diversity-accurace trade-off observed in previous methods like ETKDG (38.40% COV-R) and OMEGA (53.40% COV-R but lower precision).
Performance GEOM-QM9 Table presents the performance the GEOM-QM9 test set, which primarily consists of small molecules, making it suitable benchmark for evaluating the ability of models to generate accurate conformers for relatively simple molccular structuros. The results are evaluated with a threshold of 8 = 0.5 Á. Our proposed model, FRAGDIFF-T, achieves the highest or compelitive performance on all metrics. DMCG achieves strong performance with 96.3% on COV-R, demonstrating the effectiveness of dircct coordinate regression for simpler structures. However, our FRAGDIPP-T still maintains superior performance in other metrics. The performance FRAGDIFF-TI on the GEOM-QM9 dataset highlights its effectiveness in capturing the simpler molecular structures. Notably, FRAGDIFF-G: our fragment-augmenteed

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Published in Transactions on Machine Learning Research (06/2025)
Table 3: Performance on the GEOM-XL dataset.
AMR-R +
AMR-P
Model
Mean
Median
Mean
Median
RDKit
2.92
2.62
3.35
3.15
GeoMol
2.47
2.39
3.30
3.15
TorDiff
2.05
1.86
2.94
2.78
PRAGDIFF-T
1.80
1.61
2.60
2.44
Table 4: Results of Property Prediction task.
Method E
Emin
Ae
Aemoz
RDKit 0.92
0.65
0.37
0.80
GeoMol
0.38
0.19
0.29
0.81
GeoDiff
0.26
0.14
0.31
0.70
FRAGDIFF-G
0.24
0.13
0.29
0.64
TorDiff
0.20
0.14
0.23
0.43
FRAGDIFF-T
0.19
0.13
0.20
0.43
variant of GeoDiff, also demonstrates significant improvements over its bascline. achieves a mean COV-R of 91.1% (vs. 90.1% for GeoDiff) and a median of 95.1% (vs. 93.4%), along with better AMR-R scores of 0.199A mean (vs. 0.209A) and 0.194Á median (vs. 0.198A). Similar improvements are observed in prediction metrics, with FRAGDIFF-G achieving higher COV-P (56.0% vs. 52.8%) and lower AMR-P (0.431 vs. 0.445A). These consistent improvements across all metrics demonstrate that our fragment augmentation strategy effectively enhances GeoDiff's conformer generation capability.
Performance on GEOM-XL To assess generalization capabilities beyond standard benchmarks, we specifically evaluate FRAGDIFF-TI T on the challenging GEOM-XL dataset containing molecules with ~3x more atoms on average than the training GEOM-Drugs set. As shown in Table 3 the fragment-angmennted model demonstrates remarkable improvements over existing approaches. Notably, FRAGDIFF-T reduces the mean AMR-R by 12.2% and median AMR-R by 13.4% compared to the base TorDiff model, establishing new state-of-the-art recall performance. The precision metrics show similar gains, with mean AMR-P improving 11.6% and median AMR-P decrcasing 12.2%. The significant performance gap underscores the advantages of our approach: the fragmentation pretraining strategy enhances robustness for handling larger molecular systems beyond training domain scales, while local fragment-basee based learning captures structural patterns that generalize to extended molecular architectures. These results further validate that fragment-level data augmentation alleviates the scale limitations.
Property Prediction Tasks We adopt the property prediction task setup from Xu et al. (0022): Shi et al. 2021). ,, where 30 molecules from the GEOM-DRUGS dataset are used, with 50 samples generated for each molecule. The PS14 toolkit is employed to compute the energy (E) and HOMO-LUMO gap (e) for each conformer, and comparisons are made with the ground truth for average energy (E), minimum energy (Emin), average gap (Ae), and maximum gap (Aemaz). As shown in Table 4 our fragment augmentation strategy brings consistent improvements to both GeoDiff and TofDiff. Specifically, FRAGDIPP-G enhances the performance of GeoDiff, reducing the average energy error from 0.22 to 0.20 and the HOMO-LUMO gap error from 0.23 to 0.21. Similarly, FRAGDIFF-T improves upon Tof across all metrics, achieving the lowest average energy error (0.19) and HOMO-LUMO gap error (0.20) among all methods. These improvements demonstrate that our fragment augmentation strategy effectively enhances the conformer generation quality of existing methods. By incorporating local structural information through fragmentation, both GeoDiff and TorDiff variants achieve more accurate predictions of quantum chemical properties.
Model Performance Across Different Training Sample Sizes Table illustrates the performance of our proposed models FRAGDIFP-T and FRAGDIPP-G compared the bascline methods DofDiff and GooDiff, respectively, across varying training sample sizes. FRAGDIFF-T consistently outperforms TorDiff across all metrics and training sample sizes. For 1000 samples, FRAGDIPP-T achieves COV-R of 49.39%, which is
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Table 5: Quality of generated conformers for the GEOM-DRUGS test set with 5 = 0.75 A on varying available training samples n. (Mean)
Models Metric
FRAGDIFP-G
GeoDiff
COV-R
AMR-R
COV-P
AMR-P
COV-R
AMR-R
COV-P
AMR-P
1000
13.07
1.250
7.658
1.346
8.780
1.347
2.191
1.433
5000
15.69
1.159
10.03
1.251
13.83
1.242
6.327
1.383
10000
30.30
1.051
21.02
1.166
16.78
1.175
9.196
1.261
Models
FRAGDIPF-T
TorDiif
Metric
COV-R
AMR-R
COV-P
AMR-P
COV-R
AMR-R
COV-P
AMR-P
1000
49.39
0.7928
33.84
1.0455
34.60
0.9833
20.84
1.1897
5000
51.17
0.7519
34.51
1.0389
44.61
0.8209
25.77
1.1104
10000
62.82
0.6736
43.10
0.9081
52.76
0.7507
33.88
1.0458
Table 6: Quality of generated conformers for the GEOM-DRUGS test set in terms of Coverage (%) and Average Minimum RMSD (A) with 5 = 0.75 A with 5000 training samples.
Models
COV-R (%) f
AMR-R (A)
COV-P (%)
AMR-P (A) 1
Mean
Median
Mean
Median
Mean
Median
Mean
Median
FIAGDIFF-T
51.17
50.10
0.7519
0.7503
34.51
21.61
1.0389
1.0224
w/o BRICS
50.85
49.61
0.7568
0.7575
33.93
20.57
1.0461
1.0313
W w/o RECAP
49.38
48.42
0.7609
0.7639
34.18
21.21
1.0420
1.0247
w/o B & R
48.60
46.89
0.7684
0.7708
33.74
19.86
1.0492
1.0377
42% higher than TorDiff's 34.60%, and reduces AMR-R to 0.7928 Á compared to TorDiff's 0.9833 A. When the training size increases to 5000 samples, FRAGDIFF-T maintains its advantage with a COV-R of 51.17%, outperforming TorDiff's 44.61%, and lowering AMR-R to 0.7519 Á versus Dor 0.8209 Å. At the largest sample size of 10000 samples, FRAGDIFF-T achieves COV-R of 62. 82%, which is 19% higher than TorDiff's 52.76%, and further decreases AMR-R to 0.6736 A compared to TorDiff's 0.7507 Á. Similarly, FRAGDIFF- G demonstrates superior performance over GeoDiff across all metrics. At 1000 samples, FRAGDIPE-G attains a COV-R of 13.07%, which is 48.80 48.86% higher than GeoDiff's 8.78%, and reduces AMR-R to 1.250 Á compared to GeoDiff's 1.347 Å. With 5000 samples, FRAGDIFF-G achieves a COV-R of 15.69%, surpassing GcoDiff's 13.83% and an AMR-R of 1.159 A versus GooDiff's 1.242 A. At 10000 samples, FRAGDIFF-G's COV-R increases to 30.30%, which is 80% higher than GeoDiff's 16. 78, and AMR-R decreases to 1.051 Á compared GeoDiff's 1.175 Å. Additionally, both FRAGDIFF-TT and FRAGDIFF-G consistently deliver superior performance in COV-P and AMR-P metrics across all sample sizes, demonstrating their enhanced capability to generate conformer ensembles that are both diverse and accurale, even with limited data. These results highlight the robustness and scalability of our FRAGDIFF models, particularly in data-scarce environments, while also demonstrating their capacity to improve with larger datasets.
4.3 Further Experimental Results
Impact of Chemical Fragmentation We explore the individual contributions of different fragmentation strategies by selectively removing edge lypes from the candidate pool. Here, 'removing' means excluding the bonds identified by that method from consideration as potential cutting points during fragmentation. We further explore the impact of chemical fragmentation strategies on the performance of FRAGDIFF- T.Table t shows the effect of removing BRICS and RECAP reaction edges on conformer generation. The full FRAGDIFF-T model, which includes both, achieves the best performance with a mean COV-R of 51.17% and COV-P of 50.10%. Removing BRICS (w/o BRICS) has a larger impact on precision, reducing COV- P to 33.93% and increasing AMR-P to 1.0461 Å, indicating BRICS edges are crucial for precision. In contrast, removing RECAP (w/o RECAP) affects recall more, with COV-R dropping 49.38% and AMR- R rising to 0.7609 Å, showing RECAP edges are key for coverage. The largest performance drop occurs when both BRICS and RECAP edges are removed (w/o B & R), with COV-R al 48.60% and COV-P at 33.74% highlighting the complementary roles of BRICS and RECAP-related bonds. These results underscore the potential of incorporating chemical semantic knowledge, such as BRICS and RECAP reaction edges, in enhancing chemical generative models, as both play crucial roles in generating diverse and accurate conformers.
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Table 7: Training with and without conformer matching (CM) on the GEOM-DRUGS test in terms of
Coverage (%) and Average Minimum RMSD (A) with 0.75 Á.
Models
COV-R (%)
AMR-R (A)
COV-P (%) t
AMR-P (A)
Samples
Mean
Median
Mean
Median
Mean
Medlan
Mean
Medlan
1000
FRAGDIFF-T
49.39
46.66
0.7928
0.7844
33.84
21.23
1.0455
0.9823
w/o CM
47.68
45.45
0.8101
0.7861
33.39
20.93
1.0526
L.0056
TorDif
34.60
17.23
0.8933
0.8909
20.84
5.56
1.1897
1.1795
w/o CM
45.39
39.44
0.8190
0.8040
28.74
15.00
1.0667
Full n = 10000
FRAGDIFF-T
62.82
69.70
0.6736
0.6505
43.10
37.72
0.9081
0.8840
w/o CM
43.95
36.43
0.8353
0.8224
29.18
14.22
1.1038
1.0426
DorDif
52.76
54.10
0.7507
0.7379
33.88
20.64
1.0458
1.0371
w/o CM
43.15
36,36
0.8478
0.8291
28.11
13.06
1.1051
1.0676
FRAGDIFF-T
70.07
78.35
0.6092
0.5876
52.87
54.17
0.8003
0.7486
w/o CM
37.52
25.00
0.8866
0.8863
23.73
8.22
1.1598
1.1307
Diffif
67.49
75.81
0.6339
0.6178
49.53
47.16
0.8269
0.7782
w/o CM
34.99
20.88
0.9326
0.9174
23.08
8.13
1.1803
1.1340
FragDiff-T (AMR)
FragDiff-T (COV)
FragDiff-T (AMR) TorDiff (AMR)
FragDiff-T (COV) TorDiff (COV)
TorDiff (AMR)
TorDiff (COV)
70
0.90
0.70
65
COV-P(%)
AMR-R
COV-REXA
AMR-P
45
60
0.85
0.65
40
55
0.80
10
20
10
20
Reverse Step Number
Reverse Step Number
(a). Mean AMR-R & COV-R.
(b). Mean AMR-P & COV-P.
Figure 3: Reverse steps w.s. generation quality.
Conformer Matching Ablation Table presents an ablation study analyzing the impact of Conformer Matching during Training on the GEOM-DRUGS test set. reveals several key observat ions regarding the impact of Conformer Matching during training on the GEOM-DRUGS test Generally, models trained with CM outperform those without it, achieving higher Coverage percentages (COV-R and COV-P) and lower Average Minimum RMSD values (AMR-R and AMR-P).
However, an intriguing phenomenon occurs with TorDiff at n 1000: training without CM yields better performance than training with CM (mean COV-R of 45.39% vs. 34.60%, and mean AMR-R of 0.8190A v.s. 0.8933A). This suggests that, with limited data, directly using actual conformer structures for training may enhance TorDiff's generalization ability more than CM. As the dataset size increases, this advantage diminishes, and models trained without CM exhibit declining performance. This inverse relationship indi- cates that training actual conformer data without CM may lead to overfitting to specific conformers, specialized on the training set. Con- hampering generalization to unseen data the model becomes and inference conformer distributions, versely, CM helps prevent distributional shifts by aligning training which becomes increasingly beneficial with larger datasets. FRAGDIPP-T consistently outperforms TorDiff when CM is applied, suggesting it more effectively leverages CM for improved conformer generation. Fig. 3 we further vary the number of stops used the reverse diffusion process on GEOM-DRUGS for TorDiff and FRAGDIFF-T, showing that FRAGDIFF-T can generate better quality conformers under fewer steps. We provide additional experimental results, visualizations, and statistics in Appendix D
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5 Conclusion
Diffusion (FRAGDIFF), novel approach that incorporates traditional chemical fragmentation techniques into the pre-training phase of diffusion- generative mod- els. By decomposing molecules into smaller, meaningful fragments, FRAGDIFF enables the diffusion process to learn enhanced local geometry patterns while preserving global molecular topology. This data-centric strategy allows FRAGDIFF to bypass the need for complex diffusion model designs, offering a complementary pathway improve conformer generation. Our comprehensive experiments across diverse datasets reveal that FRAGDIFF consistently surpasses statc-of-the-art methods, especially in scenarios characterized by lim- ited data availability and tasks involving the generation of large molecules. Overall, FRAGDIFF bridges traditional computational chemistry and modern diffusion models, enhancing conformational exploration and offering promising applications in drug discovery and materials science.
In this work, we introduced
Acknowledgments
This work is supported by grant from ChemLex Technology Co., Ltd.. We would like to express our sincere gratilude to the editor and reviewers for their constructive comments and suggestions.
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A Supplementary Theroms and Proofs
A.1 Diffusion Frameworks and Equivariance.
In the field of molecular conformer generation, diffuusion models are employed to model the distribution of molecular structures, fully accounting for the inherent symmetry and degrees of freedom of molecules. Methods like GeoDiff Xu et al. [2022) operate directly on the Cartesian coordinates {x of atoms, where each conformer C is represented as a set of 3D points corresponding to the atomic positions X; E R GeoDiff utilizes diffusion process on these coordinates by adding noise to the atomic positions and then learning to denoise them using an (equiueauiaai graph neural network. Specifically, it updates the node features ha and coordinates x; through message passing over the molecular graph G. The messages the node features, edge features ei and pairwise distances ||x; xy|l- The score function se se((x;, predicts S SE(33) scalar quantities for each chemical bond, which are used to update the positions:
computed based
Σ (EN(()
& (h,, b |x - x²11, (1l.ea);0))
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where @ is function parameterized by 0 that aggregates the information from neighboring atoms M(1). This approach ensures that the model's predictions are equivariant to rotations and translations, simplifying the learning process by making the predictions independent of the molecule's global position and orientation.
TorDiff Jing et al. (022) focuses on the intrinsic torsional degrees of freedom of molecules. Rather than explicitly defining each torsion angle T;, leverages the fact. that adjusting T can be directly applied to the 3D atomic coordinates. Geometrically, changing torsion angle corresponds to rotabing a portion of the molecule around chemical bond in threo-dimensional space. For rotatable chemical bond (b;, c2), this
rotation be represented
Xx()) = R (0 xo.) Xu(e:))
where R (0be,
(0 axis beg Xx, Xb, |xx,-
SE(3) is the rotation matrix corresponding to rotation of angle 0 around the passing through point X,,, and X((a.) are the positions of atoms bonded to atom Through this method, TorDiff directly manipulates the molecular geometry in three-dimensional space, simplifying the conformer generation process by focusing on internal rotational degrees of freedom.
X -x,,1
Both methods consider an important symmetry: the invariance of physical energy under spatial inversion (mirror reflection), which is a fundamental property in physical systems Quack (2002). This implies that the learned probability density should satisly p(C) = p(-C), where -C = {-x x E C}. For the conditional distribution of conformers, this symmetry enforces consistency between original and inverted coordinates:
p(C 9) p(-C 9). Therefore, their score functions are designed to be invariant under SE(3) transfor- mations but change sign under spatial inversion, outputling pseudoscalars in R Mathematically, for all diffusion times t, this property can be expressed as:
Velogp: 9) = - log.:(C-C))))
where 9 denotes the molecular graph structure. By incorporating these symmetries into the model archi- tecture, the models enhance their gencralization ability, ensuring that prodictions are physically meaningful and adhere to the fundamental symmetries of molecular systems Xu et al. (2022).
B Fragmentation-Based Decomposition and Error Analysis
B.1 Fragmentation Methods
To validate the effectiveness and differences of various decomposition methods in learning conformer struc- tures in the fragmentation torsion space, we analyzed several fragmentation rules in FRAGDIFF-T imple- mentations. These methods provide domain knowledge and deeper insights into the task. The analyzed rules used include the BRICS method and RECAP method, and a graph-based fragmentation method can be employed by analyzing the connectivity of molecular graphs, which is also the method that Torsional Diffusion used for selecting the rotatable bond (Gordon et al., 2012 Storn et al. 2020 Jing et al.] 2022).. this method identifies cut edges by examining whether the removal of an edge disconnects the graph inlo separate components.
RECAP (Retrosynthetic Combinatorial Analysis Procedure) Lewell et al. 1998 RECAP is a classical technique aimed at decomposing complex molecules into smaller, manageable fragments through retrosynthetic analysis. The core principle involves identifying and cleaving chemical bonds that are common in organic synthesis, such as ester, amide, and ether bonds. These bonds are selected based on their prevalence and the ease of cleavage, prioritizing those that connect functional groups to generate fragments with clear chemical functionalities.
BRICS (Breaking of Retrosynthetically Interesting Chemical Substructures) Degen el al. 2008 BRICS applies a comprehensive set of rules to identify and cleave key substructures in chemical com- pounds, considering not just bond types but also the surrounding chemical environment, such as aromaticity and heterocycles. This allows BRICS generate complex and diverse fragments, supporting multi-function group cleavage to produce synthetically feasible and biologically relevant. fragments.
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Algorithm Graph-based Molecular Fragmentation.
Require: Molecular structure M
Ensure: Set of rotatable bonds R, Set of fragments F
1: C Conver(ooGraph(MM)
Convert molecular structure to undirected graph
2: R x-- 0
D Initialize set of rotatable bonds
3: F +
D Initialize set of fragments
4: for each edge e E C.edges do
Cremp + CC {e}
Temporarily remove edge
Ct GelCoonnetelCComppeetttt
if [C] > and Ve E C: |c|
then
Check disconnection and size > Add to rotatable bonds
+ [c(e}
F+FUC
b Add components as fragments
10: end if
11: end for
12: return F
Graph-based Fragmentation Gordon et al. 2012 Stern et al.) 2020 Jing et al. 2022) We consider bond freely rotatable if severing the bond creates two connected components of the total graph, each of which has at least two atoms. It guarantees that torsion angles in cycles (or rings), which cannot be rotated independently, are considered part of the local structure. It can be described as in Algorithm, [ Thus, it allows for the identification of edges that, when removed, split the molccular graph into mcaningful substructures. The algorithm ensures that fragments retain their connectivity, making it particularly useful for identifying torsion-related substructures.
B.2 Fragmentation Augmentation Error Analysis
In fragment-based augmentation, breaking down molecules into smaller components introduces approxi- mation error, e, between the true molecular coordinates, C, and the reconstructed coordinates, Ć. This error results from the loss of structural and conformational information, influenced by factors like the selection of cutting edges and disruption of chemical interactions. To assess this error's impact on retaining information about the original molecule, we analyze the mutual information, [[C; C), between Ô and C. This is expressed as T(C; C) HCC) HCC C)2 where HC)) the entropy of the molecular coordinates, and HC C) the uncertainty in C given Č. Since Ô perturbed version of C, this conditional entropy equals the entropy of the error e. Assuming follows zero-mean multivariate Gaussian distribution with covariance matrix Σ, its differential entropy is H()) 1 In ((2Te)* det E), where k is the dimensionality of the molecular coordinate space. The error reduces the mutual information between Ö and C. As e increases, mutual information decreases, meaning less information about C' can be inferred from Ć. Therefore, minimizing fragmentation errors is crucial for improving molecular modeling and conformation prediction. By quantifying e's impact on mutual information, we compare different fragmentation strategics. Strategies that minimize preserve more mutual information, leading to more accurate predictions. This highlights the importance of choosing fragmentation methods that retain as much structural and conformational information as possible.
Energy Perspective Building upon the previous analysis of fragmentation errors and their impact on mutual information, we now examine these effects from an energy perspective. In molecular simulations, the force field (FF) describes the potential conformational energy Econt of a molccular system, using math- ematical expressions and associated parameters to model both bonded and non- non-bonded interactions. The accuracy of the estimated conformation Ć intrinsically linked to how well these energy terms are captured during the fragmentation process. Bonded interactions account for atoms connected by chemical bonds and include bond stretching, angle bending, and dihedral (torsional) rotations:
Ebonded
Σ ko(b 60)2 bonds
Σ angles
(
0o)
Σ dibedrals
Σ
Vn [1 + cos(nó 7n)] 2
(1)
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where the bond stretching term is modeled using a har- monic potential with hy representing the bond force con- stant, 6 the bond length, and bo the equilibrium bond length; angle bending is similarly described using he as the angle force constant, as the bond angle, and 0o as the equilibrium bond angle; and dihedral rotation is expressed as a Fourier series expansion with Vx denot- ing the torsional barrier amplitude, n the periodicity, & the dihedral angle, and 7n the phase offset. Non-bonded interactions consider pairs of atoms not directly bonded and include Van der Waals forces and rosttros inter- actions:
Fognastition
Fust Facsh Ee
Figure 4: Visualization of energy- based analysis.
Exonbouded = Eieg
O1 Fts
Q:0; A
(2)
where the Van der Waals interactions are described by the Lennard-Jones potential potentia--dependenr dependent on Eg (the depth of the potential well); dzy (the finite distance at which the interparticle potential is zero), and ra (the distance between atoms i and jnd the electrostatic interactions are modeled using the Coulombic potential with di and qj as the partial charges, Eo the vacuumn permittivity, and &, the relative permittiv- ity (dielectric constant). To minimize the error variance o² and maximize the mutual information [(,; C) between the fragment conformation C' and the full molecular conformation C, fragmentation methods must carefully consider several key factors. Each factor affects the molecular conformational properties by influ- encing the potential energy surface and conformational distributions (Stern et al., 2020 Horton et al. 2022 Stern et al. 2022
Discussions on the Effectivenesses of Fragmentation Methods Fragmentation plays a crucial role in molecular simulations by altering both bonded and non-bonded interactions, which in turn affects the conformational energy landscape. When molecular bonds are severed to create fragments, the local chemical enviromment is modified, impacting energy parameters and the balance of forces that dictate molecular conformations. For bonded interactions, fragmentation influences torsional energy terms, such as barrier heights (V₂) and phase offsets (7n) associated with dihedral angles (d). This is particularly significant when fragmentation disrupts conjugation or resonance effects (Horton et al. 2022 Stern et al. 2022). For instance, cutting bonds in conjugated systems or aromatic rings interrupts electron delocalization, altering the torsional potential energy surface. These changes can be quantified by comparing the electron density distributions of the fragment (P)ragr)) and the full molecule (Pha(rr), where r represents the spatial positions of the clectrons. Additionally, removing bulky substituents near torsional bonds reduces steric hindrance, lowering torsional barriers and shifting equilibrium angles. This results in deviations between the conformations of the fragment (C) and the full molecule (C), increasing error variance and reducing the mutual information T(;; C) between the fragment conformation (C) and the full molecular conformation (C). For non-bonded interactions, fragmentation affects the balance of Van der Waals and electrostatic forces, which are essential for conformational preferences (Stern et al. 2022). The removal of atoms and groups decreases the number of atom pairs contributing to Van der Waals interactions, especially those spanning the fragmentation site, altcring the balance of attractive and repulsive forces. Similarly, the delction or modification of charged or polar groups impacts rlsctrostatic interactions by changing the distribution of partial charges (4 and q;). Disruption of hydrogen bonds and other electrostatic interactions can significantly reshape the energy landscape, particularly in systems dominated by Coulombic potentials, which are highly sensitive to the spatial arrangement of charged species.
Bridging the Analysis with Experimental Results The experimental data presented in Table D cor- roborate our theoretical analysis regarding the impact of fragmentation methods on approximation errors and mutual information I I(C,; C). The comprehensive FRACDIFF-T model, which integrates graph- fragmentation using both BRICS and RECAP odges, demonstrates superior performance across all metrics. It achieves the highest mean COV-R (51.17%) and COV-P (50.10%), alongside the lowest AMR-R and AMR-P values. Excluding BRICS edges results in decline in precision metrics, with COV-P decreasing
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to 34.51% and AMR-P rising to 1.0461 A, underscoring the critical role of BRICS fragmentation in en- hancing precision during conformer goneration. Similarly, the omission of RECAP edges negatively impacts recall metrics, as evidenced by a reduction in COV-R to 49.38% and an increase in AMR-R to 0.7609 A, highlighting the importance of RECAP fragmentation for achieving comprehensive conformational coverage. The most pronounced performance degradation occurs when both BRICS and RECAP edges are removed, resulting the lowest COV-R (48.60%) and COV-P (46.89%) as well as the highest AMR-R and AMR-P values. This emphasizes the complementary nature of BRICS and RECAP in maintaining essential molecu- lar structural features for accurate conformer generation. These results validate our theoretical framework, suggesting that optimal fragmentation strategies that maximize mutual information I(Cs: C) and mini- mize approximation errors are pivotal for enhancing model performance. Therefore, selecting fragmentation stralegies that align with theoretical insights particularly those preserving chemical properties as defined in Section B.1 is vital for optimizing model efficacy in practical applications.
C Reproducbility
pretraining and finetuning phases, we adopted the setup used in Torsional Diffusion (Jing et al.) 2022) Specifically, for conformer generation on GEOM-DRUGS, we mainly followed the sctup used in Jing et al. (202)) We trained the Torsional Diffusion models on NVIDIA RTX A100 GPUs for 250 epochs using the Adam optimizer for GEOM-DRUGS and GEOM-QM9. The primary hyperparameters were optimized using the validation set, resulting in the following configurations: an initial learning rate of 0.001, a learning rate scheduler with a patience of 20 epochs, 4 network layers, a second-order maximum representation, a cutoff radius r mmax of 10 A, and the inclusion of batch normalization. Specifically, following the setup used in (Jing al. 2022).. ; we used the model trained from GEOM-DRUGS for GEOM-XL evaluation. The results reported for FRAGDIFF-TI T utilize 20 reverse diffusion steps, consistent with the approach in Jiin et al. (2022). The minimum fragment size was set to 10 for both GEOM- DRUGS and GEOM-XT, while no such limit was applied in the GEOM-QM9 experiments. The maximum fragmentation edge number x. is set to 5 for all datasets. For FRAGDIFF-G pretraining and finctuning, we employed the same setup as GeoDiff (Xu et al.) 2022). This ensures that our approach is consistent with existing methodologies while allowing for a fair comparison of results across different models and datasets. Consistent with the approach in Jing et al. (2022), for each molecule that has K ground truth conformers, we generate 2000 conformers. The datascts with sizes as follows: for GEOM-DRUGS, there are 243,473 training samples, 30,433 validation samples, and 1,000 test samples; for 1M9, there are 106,586 training samples, 13,323 validation samples, and 1,000 test samples. Since GEOM-XL is used solely for testing, its test set includes all 102 molecules from the MoleculeNet dataset that contain at least 100 aloms. Torsional Diffusion (Jing et al., 2022). an effective design is introduced for training generative models in torsional space, which we adopt in our work. Recognizing that the set of possible stable local structures L for a given molecule is highly constrained and can be accurately predicted using fast cheminformatics methods like RDKit ETKDG (Riniker & Landrum, 2015 we use RDKit to provide approximate samples from pa (T). This allows us to focus on developing difiusion- based generative model to learn the distribution (T L) over torsion angles т, conditioned on the given graph and local structure. To enhance the performance of our model, we employ a conformer matching procedure as described in Jing et al. (2022), , where training on synthetic conformers produced by conformer matching has shown significantly better results than using ground truth conformers alone. Specifically, for a molecule with K conformers, we generate K random local structure estimates L using RDKit. To align these estimates with the ground truth conformers C, compute K x K cost matrix, where each entry represents the lowest Root Mean Square Deviation (RMSD) achievable by adjusting the torsion angles of L to match C. Solving the lincar sum assignment problem on this cost matrix {Crouse 2016 Stärk et al.) 2022) we find the optimal matching between the true conformers C and the estimates C. For each matched pair, we refine the aligument by performing a differential evolution optimization over the torsion angles to obtain the optimal conformer č (Méndez-Lucio et al. 2021). This comprehensive matching and refinement process ensures consistency between the local structures seen during training and inference, effectively preventing any distributional shift.
Experimental Details For the FRAGDIFF-T
randomly divided into training, validation, and test sets
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Algorithm 2 FIFGDIFF Training and Inference
Input: Molecular graphs (Go....,yy, with ground truth conformers (C Csx.k); learning rate a; number of conformers K; diffusion steps T;
maximum selected edges k; minimum fragment size
Output: Trained score model Se; generated conformers {CI..... Ck}.
Pretraining Phase:
Initialize augmented training sot + for all molecular graph G E (9o,..., 9v] do Identify cut-edges Eeut S & in g Let B Eout be the total number of cut-edges 5: Select K min( B, σ) edges from Ecut
6: Decompose G into B + 1 fragments {9h]b= 1B-1
Remove fragments with [V(G)) <
8: Add remaining fragments to F with C₁ t- ExtracttSussacee(g..)
end for
10: TRAIN(F) Finetuning Phase:
11: TRAIN((9......
Training Procedure:
12: function TRAIN(D)
13:
for epoch = 1 to epoch max do
14:
for all G E D or 9, E D do
15:
Sample t ~ Uniform(1, ( T}
16:
Sample C ~ {Cg.1 Cg.x)
17:
Compute = 11 (1 3.)
18:
Sample e (0,
19:
Perturb C Va,Co v are
are
20:
Compute So so
21:
Calculate L E [[|se- Vei log Pejo PC)
22:
Update O t O VoL
23:
end for
24:
end for 25: end function
Inference Procedure:
26: for all molccular graph G do
27:
Initialize C I)
28: for = downto 1 do
29:
Compute μi Ja, - - C* t)) Sample Ct-1 ((u,,
1
30:
31: end for
32: Output C as generated conformer
33: end for
D Further Results and Statistics
D.1 Further Visualizations Conformation Generation for Large Molecules (GEOM-XL)
Table Sable&pronee provides additional visualizations of conformer generation results on the GEOM-XL dataset, focusing on large molecules. These examples complement our earlier discussion on the superior generalization perfor- mance of FRAGDIFE-T on large molecules. The table compares the generated conformers from FRAGDIFF- T and TorDiff with the reference structures. shows that FRAGDIFF-T produces conformers that closely resemble the reference structures on given examples, further elucidates the performance improvements pre-
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Table Visualizations on conformer generation examples on GEOM-XL.
Graph
Reference
FRAGDIP-TT
TorDiff
Fragment Per Molecule
0.3
Graph
Fragment Per Malecule
Graph BRICS
Fragment Per Molecule
Graph
BRICS
BRICS
RECAP
1.0
RECAP
1.00
RECAP
0.75
0.5
0.50
0.1
0.25
0.0
0.0
0.00
10
110
150
(a). GEOM-QMB QM9
(b). GEOM-DRUGS
(c). GEOM-XL
Figure 5: Average Fragment Number w.s. Minimum Fragment Size z different fragmentation methods.
sented in Table 8 highlighting FRAGDIFF-TTs exceptional ability to handle large and complex molecules by generating conformers that closely match the reference structures.
D.2 Further Fragmentation Statistics
Figure Fillustrates how the minimum fragment size z affects the average number of fragments per molccule for the Graph-based, BRICS, and RECAP fragmentation methods across the GEOM-QM9, GEOM-DRUGS, and GEOM-XL datasets. GEOM-QMA comprising small molecules averaging 11 atoms, shows that the Graph-basod method generates significantly more fragments when 2 small, but the fragment count drops rapidly increases due the limited molecular size. BRICS and RECAP produce fewer fragments with less sensitivity to changes. In the GEOM-DRUGS dataset, with molecules averaging 44 atoms,
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Table 9: RMSD comparison between extracted and energy-minimize fragment conformations.
Method
Mean RMSD (A)
Median RMSD (A)
BRICS
0.4935
0.3962
RECAP
0.5380
0.4371
Graph
0,4673
0.3753
all methods produce more fragments, but the Graph- based method still leads, and the decline in fragment numbers with increasing is more gradual. For the GEOM-XL datasct, containing large molccules averaging 132 aloms, all methods generate higher number of fragments, and the differences between methods become less pronounced as & increases. The Graph-based method remains the most sensitive to changes in while BRICS and RECAP display steady decreases. Overall, these trends highlight that larger molecules permit more fragmentation, and the Graph-based method consistently yields more fragments, especially at smaller & values, whereas BRICS and RECAP are less influenced by the minimum fragment size due their inherent fragmentation rules.
D.3 Further Experiments Fragment Conformational Validity
To validate our assumption that fragment. conformations extracted directly from larger molecules (C&) provide reasonable approximations of their relaxed, isolated conformations (Cb), we conducted empirical analysis comparing extracted fragments with their energy-minimized structures. This analysis helps quantify the approximation error inherent in our fragment-based angmentation approach. We randomly sampled 1000 molecules from the GEOM-DRUGS dataset, selecting one conformer from each molecule for testing and analysis. For each fragment generated through our different fragmentation methods (BRICS, RECAP, and graph-based). we performed energy minimization using the MMFF94s force field implemented in RDKit obtain relaxed conformations. We then calculated the Root Mean Square Deviation (RMSD) between the original extracted conformations and their corresponding minimized structures. The results are summarized in Table g
The results reveal that the geometric deviation between extracted and relaxed fragment conformations is relatively small, with median RMSD values consistently below 0.5 Å. This is particularly noteworthy as these deviations are well below the threshold 0.75 Á used our GEOM-DRUGS evaluations for considering conformers similar. The graph-based method shows the smallest deviation (median RMSD 0.3753 A), followed by BRICS (0.3962 A) and RECAP (0.4371 Á). These findings support our theoretical analysis in Section B suggesting that our fragmentation methods effectively preserve local chemical environments and structural Teatures. The small RMSD values indicate that fragments extracted from larger molecules maintain reasonable geometric validity, justifying their use as training data without the need for additional relaxation steps. This conformational stability likely contributes to the effectivencss of our fragment- augmentation strategy in improving conformer generation performance.
We further provide visual comparisons between the original and energy-min minrimzzid conformations for several fragments obtained specifically using the graph-based fragmentation method, as illustrated in Figure B demonstrating the minimal structural changes that occur during energy minimization. As shown in the examples, even for diverse molccular structures ranging from simple ring systems (Example 1) to more complex heterocyclic compounds (Examples 7-10), the extracted fragments maintain their structural integrity pretraining.
well after energy minimization, further validating the reliability of
D.4 Further Results on Boltzmann generation
For Boltzmann generation experiments, we follow the experimental setup from Jing et al. 2022 to evaluate FRAGDIPP-T. Compared to DorDiff and annealed importance sampling (AIS), FRAGDIRF-T achieves supe- rior effective sample size (ESS) across temperatures" (Table 10). demonstrating enhanced sampling fidelity.
The comparison focuses the effective sample size of samples per malecule, which quantifies how closely the generated samples match the Roltzmann distribution.
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Example
Example
Complete
Fragment
Minimized
RMSD
Complete
Fragment
Minimized
RMSD
0.2568
0.3652
Example 3
Example 4
Complete
Fragment
Minimized
RMSD
Complete
Fragment
Minimized
RMSD
0.3384
0.4554
Example 5
Example 6
Complete
Fragment
Minimized
RMSD
Complete
Fragment
Minimized
RMSD
0.4662
0.5778
Example 7
Example 8 Minimized
Complete
Pragment
Minimized
RMSD
Complete
Fragment
RMSD
0.3365
0,4033
Example 9
Example 10
Complete
Fragment
Minimized
RMSD
Complete
Fragment
Minimized
RMSD
0,1412
0.3348
Figure 6: Visualization of fragment conformational stability. For each example, show the complete molecule (left), the fragment extracted using the graph-bases method (middle), and its energy-minimized version (right). RMSD values quantify the structural differences between extracted and energy-minimized fragments. These visualizations demonstrate that fragments maintain their structural integrity with minimal geometric changes after energy minimization.
Table 10: Comparison of different methods at various temperatures.
Temp. (K)
Method
1000
500
300
Uniform
1.71
1.21
1.02
AIS
3.12
1.76
1.30
TorDiff
11.42
6.42
4.68
FRAGDIFF-T
11.65
6.78
5.02
At 300K, it attains an ESS of 5.02 (v.s. TorDiff's 4.68), with consistent improvements at higher tempera- tures. The results validate that fragment-based diffusion better captures the true Boltzmann distribution than global sampling approaches.
D.5 Pretraining Only Model Performance
To validate the effectiveness of our training approach, we conducted an ablation study comparing our full FRAGDIFP-T model with a variant that uses only fragment pretraining without the subsequent finetuming stage. This experiment helps isolate the specific contribution of each stage in training pipeline.
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Table 11: Comparison of pretraining-one versus full FRAGDIFF-T model on the GEOM-DRUGS test set with threshold ò = 0.75 A(Mcan).
Models
COV-R (%)
AMR-R (A) L
COV-P (%)
AMR-P (A) +
Mean
Median
Mean
Median
Mean
Median
Mean
Median
Pretraining-only
44.12
37.12
0.849
0.816
33.09
20.67
1.047
1.011
FRAGDIFF-T
70.07
78.35
0.609
0.588
52.87
54.17
0.800
0.749
Table 12: Comparison of torsional angle errors between TorDiff and FRAGDIPP-T on the GEOM-DRUGS dataset.
Method
Mean Torsional Error Median Torsional Error
TorDiff
0.2645
0.2709
FRAGDIFF-T
0.2562
0.2618
We trained model using only the fragment pretraining stage on the GEOM-DRUGS dataset, maintaining identical hyperparameters, network architecture, and training iterations used in our full FRAGDIFF-T model. During inference, this pretraining-only model was directly applied to generate conformers for the test set molecules without any molecule-level finetuning. Table II presents the performance comparison between the pretraining-only model and our full FRAGDIFF-T model on the GEOM-DRUGS test set with threshold = 0.75 A.
The results demonstrate that while fragment pretraining alone provides reasonable performance, the full ap- proach with subsequent finetuning substantially outperforms the pretraining-only variant across all metrics. Specifically, the full FRAGDIFF-T model achieves approximately 59% higher COV-R (70.07% vs. 44.12%) and 60% higher COV-P (52.87% vs. 33.09% compared to the pretraining-only model. Similarly, the full model reduces AMR-R by 28% (0.609 A vs. 0.849 A) and AMR-P by 24% (0.800 Á vs. 1.047 A).
These findings confirm that while fragment pretraining contributes significantly to model performance by helping the model learn generalizable patterns from fragment substructures, the molecule-level finetuning stage essential for optimal conformer generation. The finctuning phase allows the model to effectively integrate the knowledge learned from fragments into whole-molecule contexts, accounting for long-range interactions and global molecular properties that cannot be fully captured through fragments alone.
D.6 Further Results on Torsional Angle Error Measurements
In addition to the RMSSD-based metrics (Coverage and AMR) commonly used in conformer generation evalu- ation, we also assessed the direct torsional angle accuracy of our models. Unlike global RMSD measurements that capture overall structural similarity, torsional angle errors provide insight into the model's ability to accurately predict local geometric features that determine molecular conformation.
For this analysis, we compared the torsional angles of generated conformers with the reference conformers from the ground truth conformers. The torsional error is calculated as the absolute difference between the generated and reference angles, accounting for the circular nature of angular measurements. Specifically, we identified all rotatable bonds (non-ring single bonds) in the molecules, calculated the dihedral angles formed by the four atoms across each rotatable bond, and measured the minimum angular difference between corresponding angles in the reference and predicted conformers.
Table 12 presents the mean and median torsional errors for both TorDiff and our FRAGDIFF-T approach on the GEOM-DRUGS datasct. The results show that FRAGDIFF-T achieves lower torsional angle errors compared to TorDiff, with improvements in both mean and median measurements. This indicates that our fragment-basee pretraining approach enhances the model's understanding of local torsional preferences, complementing the improvements observed in the global RMSD-based metrics. The consistent enhancement across both local and global metrics further validates the effectiveness of our fragment augmentation strategy in improving conformer generation quality.
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Table 13: Comparison between pretrain- finetune and joint loss approaches on the GEOM-DRUGS test set with 8 0.75 A.
Models
COV-R (%) 1 AMR-R (A)
COV-P (%) t AMR-P (A) +
FRAGDIFF-I T (Joint Loss)
68.84
0.622
51.02
0.813
FRAGDIFF-T (Pretrain--inellune)
70.07
0.609
52.87
0.800
Table 14: Quality of generated conformers for the GEOM-DRUGS test set in terms of Coverage (%) and
Average Minimum RMSD (A) with = 0.75 A.
Models
COV-R (%) f
AMR-R (A 4)
COV-P (%)
AMR-P (A
Mean
Median
Mean
Median
Mean
Median
Mean
Median
DMCG
57.55
59.00
0.722
0.723
37.57
35.33
0.944
0.909
DMCG-Frag
56.50
57.76
0.726
0.726
37.11
34.07
0.944
0.910
GcoDiff 45.61
49.32
0.862
0.852
21.47
14.35
1.171
1.123
PRAGDIPP-G
51.56
52.34
0.847
0.838
26.13
20.63
1.095
1.084
TorDiff 67.49
75.81
0.634
0.618
49.53
47.16
0.827
0.778
FRAGDIFF-T 70.07
78.35
0.609
0.588
52.87
54.17
0.800
0.749
D.7 Comparison with Joint Loss Training
Intuitively, our sequential approach offers several advantages: (1) it establishes robust representations of
local chemical patterns before integrating them into global molecular contexts; (2) it prevents boundary artifacts at fragmentation sites from immediately affecting wholc-molecule predictions; and (3) it creates a beneficial curriculum effect where the model first masters simpler fragment-leve patterns before tackling more complex molccular relationships.
To empirically validate our design choice of using a sequential pretrain-finet approach rather than single- stage joint training method, we conducted additional experiments comparing these two methodologies. The joint loss approach simultancously trains on both fragment data and complete molecules by averaging losses across both data types within each training batch, rather than using separate training phases.
Table 13 presents the performance comparison between our Cettrain-fintune strategy and the joint loss approach. To ensure fair comparison, we allocated equivalent computational resources both methods, with the joint loss model receiving twice the standard training resources to match the total compulation our two- phase approach. The results demonstrate that our sequential pretrain-fintune strategy consistently delivers better performance across all metrics compared to the joint loss approach. These empirical findings align with our thcoretical understanding and provide further justification for our chosen methodology, particularly considering its enhanced generalization lization capabilities for larger molecules and data-scarce scenarios as shown in Section and Table
D.8 Comparison with Direct Molecular Conformation Generation
The main scope of this study discusses the fragmentation pretraining strategy as an enhancement for diffusion- based molecular conformation generation models. To further provide insights on whether simi- lar benefits extend to non-diffusiin approaches, we conducted additional experiments with DCMG (Zhu) et al., 2022), a represcntative coordinate regression method that directly predicts 3D coordinates through iterative GNN blocks with specialized loss functions ensuring rolo-translation and permutation invariance.
We implemented the fragment pretraining strategy for DMCG (denoted as DMCG-Frag) following the same procedure described in Section 3 Table 14 presents a comprehensive comparison of all methods on the GEOM-DRUGS dataset with 5 0.75 A. Notably, our FRAGDIFF-T substantially outperforms DMCG across all metrics. While GeoDiff underperforms compared to DMCG, our FRAGDIFF-G enhancement sig- nificantly narrows this gap. Interestingly, when applying the fragmentation pretraining stratogy to DMCG (DMCG-Frag), performance slightly decreases rather than improves, suggesting that the fragmentation ap- proach particularly benefits liffusion-based models. Table 15 shows results the GFOM-QM9 dataset with
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Published in Transactions on Machine Learning Research (06/2025)
Table 15: Quality generated conformers for the GEOM-QM9 test set in terms of Coverage (%) and Average
Minimum RMSD (A) with 5 0.5 A.
Models
COV-R (%) t
AMR-R (A 4)
COV-P (%)
AMR-P (À 4)
Mean
Median
Mean
Median
Mean
Median
Mean
Median
DMCG
96.3
100.0
0.206
0.200
87.2
91.0
0.287
0.292
DMCG-Frag
96.3
100.0
0.214
0.215
88.7
92.6
0.284
0.288
GeoDiff
90.1
93.4
0.209
0.198
52.8
50.3
0.445
0.427
PRAGDIFE-G
91.1
95.1
0.199
0.194
56.0
55.0
0.431
0.421
TorDiff 92.8
100.0
0.178
0.147
92.7
100.0
0.221
0.195
FRAGDIFP-T 93.2
100.0
0.175
0.139
93.1
100.0
0.218
0.189
Table 16: Quality of generated conformers for the GEOM-DRUGS test set with 8 0.75 Å varying
available training samples n. (Mean)
Models
FRAGDIFF-G
GeoDiff
Metric
COV-R
AMR-R
COV-P
AMR-P
COV-R
AMR-R
COV-P
AMR-P
1000
13.07
1.250
7.658
1.346
8.780
1.347
2.191
1,413
5000
15.69
1.159
10.03
1.251
13.83
1.242
6.327
1.383
10000
30.30
1.051
21.02
1.166
16.78
1.175
9.196
1.261
Models
FRAGDIFF-T
Diffiff
Metric
COV-R
AMR-R
COV-P
AMR-P
COV-R
AMR-R
COV-P
AMR-P
1000
49.39
0.793
33.84
1.046
34.60
0.983
20.84
1.190
5000
51.17
0.752
34.51
1.039
44.61
0.821
25.77
1.110
10000
62.82
0.674
43.10
0.908
52.76
0.751
33.88
1.046
Models
DMCG-Frag
DMCG
Metric
COV-R
AMR-R
COV-P
AMR-P
COV-R
AMR-R
COV-P
AMR-P
1000
0.451
1.488
0.101
1.493
0.412
1.540
0.073
1.501
5000
0.467
1.477
1.135
1,300
0.578
1.491
0.931
1.359
10000
7.568
1.279
8.047
1.187
6.405
1.295
7.162
1.190
8 0.5 Å. We acknowledge that DMCG demonstrates excellent performance on this dataset, which consists of sinaller molecules. DMCG's direct coordinate regression approach appears particularly effective for QM9's small molecules, where the conformational space is less complex and more amenable to end-to-end prediction. However, it's worth noting that while DMCG excels in COV-R metrics, our FRAGDIPF-T achieves better AMR scores and superior COV-P and AMR-P metrics, indicating higher quality of generated conformers even for these smaller molecules.
To further evaluate the data efficiency of our approach compared to DMCG, conducted experiments in limited-data scenarios GEOM-DRUGS. Table 16 presents the results with varying numbers of training samples. The performance gap becomes even more pronounced in these low-data regimes, with DMCG essentially collapsing (near-zero coverage with 1K or 5K training molecules), while FRAGDIFF methods maintain relatively strong performance. This demonstrates that our fragment-angnnentee diffusion approach dramatically improves sample efficiency when data is scarce precisely the setting that plagues many real- world drug discovery datascts. Notably, while DMCG-Frag shows slight improvements over the basc DMCG model in the extremely low-data regime, these improvements are marginal compared to the substantial gains achieved by F FRAGDIFF models.
The observed performance differences can be attributed to fundamental architectural distinctions between the approaches. DMCG employs direct coordinale regression through iterative GNN blocks to predict 3D coordinates an end-to-end fashion. While effective for shholemmoeccule prediction, this direct approach may struggle leverage partial structure information offectively, it's designed to learn global molecular geometries rather than building them from local structural components. In contrast, diffusion inlfusioo-bbsed methods might offer better compatibility with fragmentation through their probabilistic, step-wise denoising process
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Published in Transactions on Machine Learning Research (06/2025)
that operates in lower-dimensional spaces (torsional or distance geometry), requiring fewer examples to model conformational distrriutiins compared to direct coordinate regression approaches and improves data efficiency.
E
Limitations, Future Directions and Broader Impact
While our fragment-based pretraining augmentation approach has demonstrated significant improvements in generating accurate and diverse molecular conformers, there are several limitations that present oppor- tumities for future research. First, when applying fragmentation methods as a general data augmentation tochnique for data-driven computational models, we may encounter unmanagcable data volumes, especially when training with large molecular datasets and setting low fragment size thresholds, as discussed in our appendix fragmentation statistics. This highlights the need for more data-efficient. frameworks. Lever- aging prior domain knowledge, such scaffold networks or molecular graphs (Quinn et al. 2017 Nothias ct al. 2020 Kruger et al. 2020), could enhance data efficiency during the fragmentation process, reducing the computational burden while preserving essential chemical information.
From a methodological standpoint, while fragment-based augmentation has delivered impressive results within the torsional diff'usion framework, there is room for further improvement to fully capitalize on the benefits of data augmentation. The current framework relies on cutting edges in graph structure algorithms, which introduces limitations- as difficulty in modeling fully connected supramolccular structures where rolating edges alone cannot capture reasonable conformers. Potential solutions include introducing additional variations in Euclidean space, like incorporating conng-cnnncting edges from junction trees and allowing non- rigid rotational edges that permit changes in relative atomic distances (Jin et al., 2018). Additionally, integrating bond stretching and angle bending components into conformeral energy modeling could address challenges in representing fully connected structures, effectively combining elements of methods like GeoDiff with Torsional Diffusion (Jing al.) 2022 Xu et al.] 2022). By exploring the chemical underpinnings of fragment effectiveness, can gain deeper insights that enable the development of more effective chemical modeling processes, reduce errors, and enhance data learning efficiency through interdisciplinary collabora- tion. Moreover, our method has the potential to significantly advance computation-driven approaches by greatly increasing the amount of available data, which is crucial for the success of machine learning models. By utilizing our fragmentation approach to augment data and scaling up model parameters, we open new avenues for designing and training larger computational models physical chemistry, potentially unlocking novel applications in chemical and materials science (von Lilienfeld al. 2020 Frey et al. 2023 Sadybckov & Katrilch 2023).
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Reviews:
[{"review_id": "KFdQm82lZ2", "reviewer": "Reviewer_sbPU", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n- (S1): FragDiff is a general method, designed to be agnostic to the particular model backbone. The experiments, which are carried out for both a coordinate-based and a torsion-angle-based model, demonstrate this generality convincingly by showing improvements in both settings.\n- (S2): The quantitative results show that FragDiff can deliver good performance gains across models, metrics, and datasets; it thus appears it will be useful to the community even as models/datasets continue to evolve.\n\n**Weaknesses**\n- (W1): From the main paper, it should be clearer what fragmentation method is used in the main (non-ablated) version of FragDiff. While authors spend a considerable amount of time discussing how the choice of fragmentation method is important, present an information-theoretic view on this question, and mention several strategies such as BRICS and RECAP, it was not clear to me which method is the one used. In Section 4.3, the authors perform an ablation on \"removing\" BRICS and RECAP bonds, but it may not be clear whether \"removing\" means \"not considering these bonds in the set of bonds to potentially cut\" or \"removing them from the graphs thus effectively always cutting these bonds\". Appendix B provides further discussion, which suggests that FragDiff uses a *combination* (set sum?) of bonds suggested by BRICS, RECAP, and a third method; if so, I assume the ablation from the main paper means not including the respective submethod into this combined set. Nevertheless, I think clarity around this aspect could be improved.\n- (W2): I find it somewhat surprising that the simple augmentation method proposed by the authors works so well. As far as I understand, the fragment coordinates used in pretraining come directly by \"copying\" the coordinates from the larger molecule. I wonder how far these coordinates are from a real conformation, which one could get by relaxation. I wonder if the authors considered to quantify this. Ideally, one could even try to show that for fragments obtained differently (e.g. by cutting random bonds), the conformation in isolation and the conformation when part of the larger molecule diverge more than for the fragments obtained by the proposed method.\n- (W3): As a minor point, the discussion of related works could include works on molecular graph *generation*, such as JT-VAE [1] and MoLeR [2], which employ similar fragmentation techniques to FragDiff, but with the purpose of simplifying the generation task rather than transfer learning from fragments to full molecules.\n\nNitpicks:\n- Broken sentence at the end of Section 3.1.\n- Claim in Section 3.3 that equivariance is \"essential for accurately modeling molecular structures\" may be slighty overstated given recent works such as AlphaFold 3 [3] that go towards *removing* equivariance; one could thus soften this statement a little.\n- Duplication in the first two sentences of Section 4.1.\n- At the end of Section 4.1 there's a typo in \"chenmical\", superfluous capitalization of \"Additional\", and inconsistent capitalization of the title of the last paragraph.\n- Missing space after the first sentence of Section 4.3.\n- \"RECAPS\" instead of \"RECAP\" in Appendix B.\n\n[1] Jin et al, \"Junction Tree Variational Autoencoder for Molecular Graph Generation\"\n\n[2] Maziarz et al, \"Learning to Extend Molecular Scaffolds with Structural Motifs\"\n\n[3] Abramson et al, \"Accurate structure prediction of biomolecular interactions with AlphaFold 3\"", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work introduces FragDiff: a general method to enhance the performance of diffusion-based conformer generation models by first pretraining on molecular fragments before finetuning on the downstream molecule distribution. The authors explain the method, and show promising results when FragDiff is combined with two different diffusion-based frameworks across several datasets.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I would request the authors address the weaknesses from above. Ideally, it would be nice to also resolve the nitpicks to make the paper read smoother.", "broader_impact_concerns": "This is a basic research work, and hence doesn't have direct ethical implications, which would have to be analyzed per specific applications.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "lRGZihmysh", "reviewer": "Reviewer_gM3R", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength:\n\n1. A fragment based data augmentation method.\n2. 2 stage pretrain.\n3. Evaluation on GEOM-XL.\n\nWeakness:\n\n1. Inconsistent results of baselines. According to baseline papers, GeoDiff has much better results (table 1), TorDiff also has better results compared with FragDiff (table 1). Please explain the difference. Compaing these results, it is unclear whether FragDiff produces significant improvements over baselines.\n2. Limited technical contribution. FragDiff seems a combination of molecule decomposition methods (BRICS, RECAP) and conformation prediction models (GeoDiff, TorDiff).\n3. BRICS and RECAP are proposed for retrosynthetic. However, the synthesisability of FragDiff generated molecules are not evaluated.\n4. Lack of ablation. Some of the designs are not evaluated, e.g., 2-stage pretraining.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a data augmentation method for molecular conformation generation, based on molecule decomposition. This method is intuitive and model-agnostic. The pretraining is conducted in 2 stage, fragment-level and molecule-level. Through experiments on GEOM, FragDiff shows improvements on both precision and recall, and also generates reasonable results for much larger molecules.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please explain weakness 1-4. 1, 2, 3, which are critical. \nImproving weakness 4 should strength this work.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "dsDGokiuwN", "reviewer": "Reviewer_byGy", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n - Adding data augmentation improves both GeoDiff and TorsionalDiffusion for QM9, DRUGS, and DRUGS-XL\n- Very similar to SMILES enumeration for molecular LLM's. Its very intuitive. It also pulls more value out of existing datasets.\n\nWeaknesses\n- Table 2 seems like an unfair comparison since by limiting the data but allowing one side to be pretrained and then finetuned does not keep compute constant. If compute is left constant, what happens?\n- The same impact general impact of fragment-based pretraining on the diffusion model can be achieved by averaging the loss over fragments rather than doubling the compute cost.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "FragDiff explores fragmentation-based pretraining for molecular conformer generation, enhancing local geometry learning while preserving global topology. It improves performance in data-scarce settings, with proposed gains achieving up to 13.4% on large molecules.  They employ a two-phase learning paradigm that first pretrains the model on decomposed molecular fragments to capture local fragments’ structural patterns, then finetunes on complete molecules to integrate global structural constraints.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- What is the average torsional angle error with and without fragment pretraining? The current conformer generation metrics are quite globular and not very practically useful as they record the minimum rmsd over 2K samples. But for a model that only specifies torsions one could measure the error in degrees. Does the fragment-based pretraining lower the error of predicted angles? Or does it only improve the model in the best of 2K?\n\n- Furthermore, what is the relaxation energy of the generation structures of each model? If you use xTB would we see that we are generating lower energy structures by leveraging fragment-based pretraining outside of just RMSD metrics?\n\n- How does the total number of training steps compare with TorDiff and FragDiff-T? If you were to train Torsional Diffusion for twice as long without data augmentation, what would happen?", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The authors address the problem of small molecule conformation generation. The method involves two steps: first, pretraining on molecular fragments to extract greater value from the dataset, and then fine-tuning on downstream tasks. Notable performance improvements are observed on the GEOM-Drugs and GEOM-QM9 benchmarks. While reviewers noted that the technical novelty is somewhat limited, this paper is well-executed with rich experiments, making it valuable for readers.

==

As discussed during the review phase, please open-source the code to a non-anonymous GitHub repository.
Decision: Accept (poster)