Template-Guided 3D Molecular Pose Generation via Flow Matching and Differentiable Optimization
Authors: Noémie Bergues
Arthur Carré
Paul Join-Lambert
Brice Hoffmann
Arnaud Blondel
Hamza Tajmouati
Venue: NeurIPS 2025 poster ()
Keywords: flow-matching
geometric deep-learning
graph neural networks
differentiable optimization
template-guided docking
computational chemistry
drug-design
3D pose generation
Primary area: machine_learning_for_sciences

Abstract: Predicting the 3D conformation of small molecules within protein binding sites is a key challenge in drug design. When a crystallized reference ligand (template) is available, it provides geometric priors that can guide 3D pose prediction. We present a two-stage method for ligand conformation generation guided by such templates. In the first stage, we introduce a molecular alignment approach based on flow-matching to generate 3D coordinates for the ligand, using the template structure as a reference. In the second stage, a differentiable pose optimization procedure refines this conformation based on shape and pharmacophore similarities, internal energy, and, optionally, the protein binding pocket. We introduce a new benchmark of ligand pairs co-crystallized with the same target to evaluate our approach and show that it outperforms standard docking tools and open-access alignment methods, especially in cases involving low similarity to the template or high ligand flexibility.

Template-Guided 3D Molecular Pose Generation via Flow Matching and Differentiable Optimization
Noémie Bergues'
Arthur Carré 1.33
Paul Join-Lambert'
Brice Hoffmann*
Arnaud Blondel
Hamza Tajmouati-
Iktos SA, 65 rue de Prony, 75017 Paris, France
Institut Pasteur, Université Paris Cité, UMR 3528, Paris, France
Doctoral school MTCI (ED 563), Paris Cité University, Paris, France
Abstract
Predicting the 3D conformation of small molecules within protein binding sites is a key challenge drug design. When a crystallized reference ligand (template) is available, it provides geometric priors that can guide 3D pose prediction. We present a two-stage method for ligand conformation generation guided by such templates. In the first stage, introduce molecular alignment approach based on flow-mate matching to generate 3D coordinates for the ligand, using the template structure reference. In the second stage, a differentiable pose optimization procedure refines this conformation based on shape and pharmacophore similarities, internal energy, and, optionally, the protein binding pocket. We introduce benchmark of ligand pairs co-crystallized with the same target to evaluate our approach and show that outperforms standard docking tools and open-access alignment methods, especially in cases involving low similarity to the template or high ligand flexibility.
Introduction
Drug design is complex and resource-ing iittensieeenneevveeeee process, with timelines that can span decade and development costs estimated to be on the order of one billion dollars per approved drug [Wouters et al., 2020). To address these challenges, computational approaches have emerged to accelerate carly-stage drug discovery and reduce associated costs. In particular, 3D-based methods show great promise by enabling in silico screening and optimization of candidate molecules, thereby reducing reliance on expensive and time-consuming experimental assays. Two major 3D computational approaches
widely used: 3D Ligand-Based
(LB) and 3D SStructure-Based (SB). LB methods leverage the
3D structure of known active compounds to identify or design structurally and functionally similar molecules [Acharya et al. 2011 Petrovic et al. 2022 Bolcato al. 2022]. whereas SB methods use
the 3D structure of the target receptor to predict ligand binding modes or affinities [Anderson 2003).
Popular examples include LB virtual screening tools such as Rapid Overlay of Chemical Structures
(ROCS) [Hawkins et al.) 2007]. and SSB molecular docking tools like AutoDock Vina [Trott and
Olson 2010) and Glide Friesner et [2004]
Small molecule 3D alignment, or superposition, an LB approach that aims to spatially align
molecule with known 3D template. A variety of methods have been developed for this task, reflecting the diverse ways in which molecular similarity can be defined and assessed. In their
"Equal contribution. Correspondence to: {noemie. bergues, arthur car.uu.corrr))tko..ccooo com
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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comprehensive review, Hönig et al. [Hönig et al., 2023] categorize six major classes of alignment strategies: Gaussian volume overlap. field- graph-based, volume overlap optimization. distance- based, and shape-based methods. Despite these advances, accurately aligning molecules remains challenging, particularly when the template and query share limited structural or chemical features. Additionally, small molecule superposition is inherently an appproaach [Hönig et al. 2023). meaning it does not incorporate any structural information from the target protein. potentially overlooking critical receptor-ligand interactions that can drive binding. Given that many drug discovery projects benefit from the availability of experimentally resolved receptor-ligand complexes [Hubbard] [005
Congreve et al. 2014). there is opportunity to develop hybrid methods that jointly leverage both ligand and receptor information to enhance the accuracy of molecular pose prediction.
This work introduces Flow Molecular Aligmment with Pose Optimization (FMA-PO) a template- guided method for 31D molecular pose generation, which combines [L alignment with structure- aware refinement. [FMA-PO employs a FFlow Matching (FM) model conditioned on a 3D template molecule. The model generates 3D conformers for a query molecule from its 2D structure, aligning them spatially with the template. The poses are then refined via a coordinate-level differentiable optimization procedure integrating constraints based on shape alignment, pharmacophore similarity, binding pocket complementarity, and internal energy. To evaluate the performance of our method, we introduce AlignDockBench, a new benchmark comprising 369 protein- proteii-liggadd (PL) template-peuuuee query pairs. Unlike existing cross- docking benchmarks such the one proposed by FitDock (Yang et al., 2022] which focuses on ligand pairs with high chemical similarity Amilarity-Alinni AlignDockBennch also includes pairs with lower similarity. This enables more challenging and realistic assessment of LB alignment and docking methods.
The main contributions of this work are as follows:
A template-guided 3D molecular pose generation model with FM capable of producing accurate ligand conformations even in cases of low template similarity.
A pose refinement protocol operating directly on all atomic coordinates, improving pose accuracy and quality.
AlignDockBench, a benchmark for evaluating template-based docking accuracy.
2
Related Work
3D Alignment Methods. In recent years, various advanced methods have been developed to improve the accuracy and efficiency doocckigg and virtual screening, including approaches based on 3D molecular alignment. One of the earliest and most widely adopted tools in this area is ROCS which performs molecular alignment based on the overlap of Gaussian functions that represent molecular shape and, optionally, pharmacophoric features such hydrogen bond donors, acceptors, and hydrophobic regions [Hawkins et al., 2007]. More recently, LS-align [Hu et al. 2018) introduced fast atom-level alignment algorithm that integrates interatomic distances, atomic mass, and chemical bond information, cnabling both rigid and flexible alignments. Another notable method, FitDock YYan al. 2022]. J. improves docking accuracy by using template fitting guide initial ligand conformations, followed by refinement with a scoring function derived from AutoDock Vina [Tron) and Olson 2010). ROSHAMBO [Atwi et al.) (2024) is another recent method that combines shape and pharmacophore similarity using Gaussian volume overlap to perform 3D molecular alignment and similarity scoring.
Flow Matching for Biomolecular Applications. FM is an emerging generative modeling frame- work that learns a continuous flow, mapping from source distribution target distribution. Its adaptability has led to increasing adoption in biomolecular applications, including 3D conformer
generation from 2D molecular graph [Hassan al. 2025). FMahss also been applied to molecular docking, with methods such as Harmonic Flow [Stakk et al. [2024] and FlowDock (Morehead and Cheng 2024), generating ligand conformations within protein binding pockets. AlphaFlow [Jing
et al. 2024] extends [M techniques to protein structure prediction, demonstrating their applicability
to macromolecular modeling. Recently, FM has been applied to Molecular Dynamics (MD) through
MD-GEN (Jing et al. 2025). method that learns to generate physically realistic MD trajecto-
ries. These advances underscore the growing potential FM to support a wide range of tasks in computational chemistry and structural biology.

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3 Method
3.1
Overview
The present work introduces a Flow-Matching Molecular Alignment model followed by a Pose Optimization protocol (FMA--PO). novel method for generating 3D molecular poses within a protein binding site from a 2D graph representation. [MA-PO uses a 3D reference ligand as a structural template (e.g., crystallized ligand bound to the target protein), which serves as spatial guide for predicting the pose of a query compound. The method consists of two main stages, as illustrated in Figurel
Flow Molecular Alignment (FMA), an initial 3D conformation of the ligand is generated using an FM model trained to produce conformer aligned with the reference ligand (template), given a 2D molecular graph as input.
2. Pose Optimization (PO), the initial pose refined through differentiable optimization on all coordinates using the following objectives:
alignment optimization: the pose optimized to maximize alignment with the reference ligand using shape and pharmacophore scoring functions. Pharmacophore is defined 3D arrangement of features (hydrogen bond donors/acceptors, hydrophobic groups, aromatic rings, etc.) for molecule using the RDKit chemoinformatics library [Landrum].
Shape and pharmacophore-
Internal energy optimization: the ligand's geometry is adjusted to minimize its internal (strain) energy. producing chemically valid conformations.
Protein pocket integration (optional): binding site information is incorporated to refine
the pose, improve pharmacophore complementarity, and prevent steric clashes.
Query graph
(1) Flow Now-Matching Molecular Alignmen:
(2) Pose Optimization on coordinates
Aligned Molecule
lemplate Molecule
3D Pocket (Optional)
Figure I: Overview of the FMA-PO pipeline. The method comprises two stages: (1) 3D FMA of the ligand the template; and (2) Pose Optimization, including shape and pharmacophores scores, energy minimization, and optional refinement based on protein pocket information.
3.2 Flow-Matching Molecular Alignment
The FMA module generates 3D conformations of query ligand conditioned the 3D structure of a reference ligand. Starting from a random 3D conformation of the query 2D graph, the model progressively denoises it to produce conformations that reproduce the ground-truth pose, spatially aligned with the reference ligand. This alignment process is illustrated in Figure 2 which shows the evolution of the query conformation in blue, from initial noise (t 0) to final alignment with the reference structure in pink (t 1). Inspired by pocket-guided generative models like DifIDock [Corso al. 2022 which condition ligand generation protein pocket geometry, our method instead uses the 3D structure of a template ligand as the conditioning reference. An illustration of FMA model pipeline is provided in Figure
FM model. FM Lipman et al. 2022 is a generative modeling approach that constructs a time- continuous mapping [0, RD Rdd to transport prior distribution Po to target distribution
P1. This transformation is learned through vector field (or velocity field) v [0, 1] x Rd - Rd governing the sample evolution, described by the ordinary differential equation (ODE):
2x(x) v=((.(x)). 6x(z)= x.
3

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(a) L
(b) L 0.5
(c) L 0.75
(d) (d)==1
Figure 2: Evolution of the query ligand's conformation (in blue) during the FM-MA denoising process. The template ligand shown in pink. Starting from a noisy initial conformation (t = 0), the model progressively refines the 3D coordinates to align the query ligand with the template pose (t=1).
That is, (1)) represents the point transported along the vector field from time time l. To construct feasible transport trajectory. [Togg et al. 2023) [Albergo et al., 2023] introduces lime-differentiable interpolant:
Rd Rd Rd such that Io( z0 and ( 21
2025 we choose a linear interpolation between samples ~ Po and Following Hassan et al. D1 P1:
L (xo, x1) = 0x + 3,x0, where ar = t,
31 =-11-6 t,
and similarly define the conditional probability path pt (x X1) as Gaussian distribution centered on 1x(xo; x1) with variance o/:
(x(x|xo, x1) = (1)
where or = = av - t).
The time-dependent velocity field governing sample evolution is then given by: vr(x) = dt 0.81 + di
3,x0 + dl
0:2,
z N0,1).
This results in the explicit formulation: vx(x) Xi Xo
1-2t
2V1(1-()
Given the probability path Pt and the vector field v.. the FM training objective is defined as:
f = ==-- Va x) v
where vo is the learned velocity field. The optimal solution ensures that va generates the probability path flow Ps [Tong al. 2023
For inference, a sample drawn from Po. and the final conformation x obtained by numerically integrating the ODE using the Euler method and the learned velocity field
Xt+Ar = X, + va x. At.
More details on the training and sampling algorithms provided in supplementary A.2
Harmonic Prior. Unlike diffusion- models that typically require a Gaussian prior, the FM framework allows flexibility choosing the initial distribution Po. To better capture the structural properties of molecular graphs, a harmonic prior is used, following the formulations in [Jing et al. 2023) and (Stark et al., 2024] This prior ensures that atom positions in the initial conformation reflect molecular connectivity by encouraging bonded atoms to remain close in sampled structures. The harmonic prior is defined as:
Pn (Xx) exp (- (-xx Lxo
where is the laplacian the molecular graph, and vn RRIN representing one of the three Cartesian coordinates (x, or 2) of the N atoms in the molecule. This formulation ensures that the sampled initial conformations maintain local structural coherence. The sampling algorithm detailed in supplementary A.2

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Molecular Graph Construction. FMA is molecular graph neural network that encodes graph comprising both query and template ligands. It jointly represents their structures to predict the velocity field of the query ligand for conformation denoising. The graph representation is illustrated in Appendix A. and is constructed as follows:
Each heavy atom in both ligands is represented as a node with features encoding atomic properties, including atomic number, total degree, formal charge, chiral tag, total number of hydrogen atoms, and hybridization state.
Atomic-level nodes:
To capture higher-level chemical structures, ligands are decom- posed into functional groups using the BRICS fragmentation method (Degen et al. 20088. Each resulting fragment is treated as a distinct node in the graph, with a scalar feature encoding the fragment size (number of atoms) assigned each functional group node.
Functional group nodes:
Covalent edges:
Covalent bonds within each ligand are represented as graph edges, with associated edge features encoding bond type (e.g. single, double, triple, or aromatic), conjugation status, ring membership, and bond stereochemistry.
Functional group connections: Functional group nodes are connected to their correspond- ing constituent atoms, enabling feature aggregation from atomic-level representations. The edge features for these connections are scalar values set zero.
Dense edges: Functional groups within and across the query and template ligands are fully connected. Distances between functional groups are encoded using radial basis function (RBF), following [Unke and Meuwly 2019 and [Hassan et al. 2025
Model Architecture. The constructed molecular graph, which includes both the query and template ligands, is first processed by a multilayer perceptron (MLP) to embed node and edge features. Next, a Mulli-HHed Attention with Edge Bias (MHAwithEdgeeBla)) encoder [Qiao et al.) 2024] is applied to extract topological and contextual information from the molecular graph. The attention mechanism facilitates effective information exchange between the two ligands, ensuring that the query ligand remains informed by the reference ligand. Finally, a time-dependent Vector Field Network (VFN) inspired by [Qiao et al., 20024), predicts the velocity field of the query ligand, based on the molecular graph, the positions of the reference ligand, and positions of the query ligand at time t. Further architectural and algorithmic details are provided in Appendix A.3 and training details and hyperparameters in Appendix A.4
3.3
Pose Optimization
The initial pose of the query molecule, predicted by FMA atomic coordinates. This process is formulated as differentiable optimization problem, where gradient descent minimizes a weighted sum of scoring functions. These functions include ligand- based terms comparing the query ligand Mquery to the reference ligand Memplltes and optionally, receptor-bes based terms involving the template pocket Puemplate- Unlike traditional methods that optimize higid-body transformations or torsion angles, PO "'Judatess atomic positions directly, enabling flexible and fine-grained conformation refinement.
is refined by directly optimizing its
Each heavy atom in the molecular structure is modeled as spherical Gaussian function, following the molecular volume representation introduced by Grant and Pickup 1995), Grant et al. [196).. This formulation enables the computation of the molecular volume VA. and the overlapping volume Van of two molecules A and B, detailed in Appendix B.I Tanimoto (or Jaccard) score based on atoms Gaussian volumes provides a normalized measure of shape similarity:
Shappebaased Tanimoto Score (STS)
V AB
Tanimoto, (A, B)
V1
V8
Vo
where a refers to atom-based volumes. The STS between the template Mtemplate and the query Mqnery is defined as the T Tanimolo, similarity between atoms:
SSTs (Mquryy MMeuer Tanimoto, (anrimoto,MMMuenn (Mquery Mref),
and is differentiable with respect to the query ligand coordinates.
5

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Pharmaccppore- Tanimoto Score (PTS) Pharmacophoric features are represented using spherical Gaussian functions similar fashion. Each pharmacophoric feature type (c.g.. hydro- gen bond donor, acceptor, aromatic) is treated independently in the similarity computation. We define a pharmacophore-hasee
alignment score that quantifies the degree of overlap between the pharmacophoric volumes of two Higands-highed values indicate that lígands share similar 3D phar- macophoric profile. This approach does not require explicit matching or pairing of features between the template and query molecules. Instead, the overlap between Gaussian spheres with the same pharmacophoric label is directly accumulated into the final pharmacophoric overlapping volume score. The PTS computed the pharmacophoric volumes between the query M Mqqery and the reference Mref iS then defined as:
Spts Mtemplate) I a (Mqueryy MeMerurreeeeepplle Mttmpiate),
where p refers to pharmacophorr-baeel volumes with details provided in Appendix B.2
Protein Pocket Score (Optional). Receptor- terms are optionally included in optimization. Both atoms and pharmacophoric features of the template pocket P template are modeled using Gaussian functions, Two scores are computed between the query ligand and the template pocket:
A shape clash penalty based on atomic overlap, using Ptemplate and Mquery-
STS
measure overlap between
A pharmacophoric complementarity, using PTS
to evaluate the alignment between the query ligand and template pocket pharmacophores. For pocket pharmacophore types, inversion is applied to model complementary interactions. More details are provided in Appendix [B2
The resulting receptor-based pocket score is defined as:
Spockes = Sprs(MMueery (Mquery, Premplate) - SSTS (eers(MMurryy P Premplate)-
This formulation encourages pharmacophoric alignment while penalizing steric clashes between the ligand and the template binding pocket.
Internal Energy. Optimizing atomic coordinates directly, rather than restricting moves to transla- tions, rotations, and torsions, offers greater flexibility but can easily lead to physically unrealistic molecular conformations. To ensure physically plausible structures, we incorporate the ligand's inter- nal energy into the optimization process, thereby mitigating artifacts such as unrealistic bond lengths and angles that can arise from other scoring terms. The internal energy, Einternals computed using molecular force fields, specifically (General Amber Force Field 2 (GAFF2) [Wang et al. [204]. which defines energy functions based on atomic types and spatial configurations. The detailed formulation is provided in Appendix B.3
Optimization Objective. function defined follows:
The optimization objective combines scores into weighted loss
Coprim SSTS ( (Mquery Mhemplate) - 3 SpTs (MrqueMyrr MaaaeayyMMaaaae Mremplate)
Spocksr (M P Prsmplane) + Einteraal (M Mqqury)-
Further details on the optimization algorithm and hyperparameters are provided in Appendix B
3.4 Benchmark and training dataset construction
AlignDock BlignDockBench is a curated benchmark designed evaluate cemplate-based molecular docking and 3D molecular alignment methods. Unlike common docking benchmarks such as PoseBusters (Buttenschoen et al. 2024]. which do not include reference ligands, AlignDockBench provides co-crystallized template ligndds for each query. This enables the evaluation of methods that leverage known references guide 3D conformation prediction. The benchmark includes query structures, each associated with corresponding [L templatee structure. To construct BoignDDoc we selected 61 diverse diverse/P templates from the DUD-E [Mysinger al. 2012) and DEKOIS [Bauer et al.] 2013 datasets, spanning major target classes such as kinases, proteases, nuclear receptors, and GPCRs. For each template, we searched the Protein Data Bank (PDB) for query PL complexes whose binding pockets could be structurally aligned to the pocket template.

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Binding pockets were defined as all residues within 12Á of the ligand. Using TM-align Zhang and Skolnick]. we rigidly aligned (via translation and rotation) query pocket to the pocket template and retained only those with a backbone Root Mean Square Deviation (RMSD) below 1.2A. To ensure sufficient 3D structural similarity between ligands, we further filtered query-template pairs with an STS score greater than 0.5. The mapping of queries and associated templates is provided in Appendix C.I, along with complex preparation details in Appendix C.2 Protein class diversity is summarized in Figure S6
The benchmark is available at Zenodo
Training set. Training IMAArequine dataset of molecular pairs with ground ground-truth alignments. Following the protocol used in BlinnDockBench, we selected ligand pairs from the PDB that bind to the same protein pocket, assuming that co-binding implies structural and functional similarity. We further restricted to pairs in which both ligands have molecular weights above 170 Da. Additionally, the training set was augmented with compounds from the ChEMBL database following protocol similar to that used for constructing the BindingNet and BindingNet2 datasets [Li et al. 2024 Zhu al. 2025]. To prevent train-test leakage, we excluded any training molecule with a Morgan finger- print Rogers and Hahn, 2010) Tanimoto similarity greater than 0.5 to any ligand in Align Bench (Figure (S)) The resulting training set contains 301, 348 complex pairs covering 111,678
678 unique
molecules.
4 Experiments
Experimental Setup. We evaluate H-MA-PO on AlignDockBench, comparing its performance to both traditional docking tools and ofate-of-the-art open-access alignment methods. Docking baselines include Vina (v1.2.5) [Trott and Olson, 2010) and rDock (v24.04 04. 204-lygy [RuizCarmona et al.) 2014), while alignment baselines include FitDock (v1.0.9) (Yng al. 2022]. LS-align (Version 1201704171741) [Hu et al. 2018). and ROSHAMBO Atwi et al. 2024]. Detailed configurations and hyperparameters used for each method are provided in Appendix D.I Alignment-basse
evaluate|FMMA-PO
methods
receive the 2D graph of the query molecule along with the 3D structure of the template ligand and, optionally, the protein. In contrast, in our experiments, docking methods do not use the template ligand information. For each method, we generate 10 candidate poses and evaluate the top-ranked one using the scoring function originally designed for that method. The selected pose is then assessed by computing the RMSD to the experimental ligand structure. Pose selection of our method is guided by a scoring function defined as:
Sucore SSTS (Muurrr Meemplate + SyTS SSprs(MMerry (Mquery, Miemplate) -Svima (Mgueryy Ptemplate)
where Syina represents the Vina docking score [Toott and Olson 2010 rescaled to [0, 1] interval using Min-Max normalization across the samples. Two pose selection strategies are explored:
FMA-PO The top-ranked pose predicted by FMA
according to Sworr. is selected and
subsequently refined via PO
IM All sampled poses are first refined through PO and the final pose is selected according to Sucore.
Table D summarizes the performance of each method in terms of mean RMSD the proportion of molecules with RMSD below 2A, and the average runtime per molecule. Both FMA, POA-PPPM-PPOO outperform competing methods, achieving the lowest mean mean[R RMSD and the highest proportion of alignments with RMSD below 2Å. Examples of poses generated with each method are provided in Figure
Results.
To assess the effect of template similarity on alignment performance, AlignDockBench was divided into two similarity bins (00, 0.5 and [0.5, 1.0)). based on Tanimoto similarity between the query and template compounds. The similarity was computed using two approaches: first, with standard Morgan fingerprints (Rogers and Hahn 2010] derived from the complete molecular structures (Figure Bab; and second, with Morgan fingerprints computed on the molecules' Generie Murcko scaffolds
Bemis and Murcko 1996), which capture the core chemical framework by removing side chains and
https://www www.wwwbbi... ac. uk/ chembl/
7

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Table 1: Performance comparison 3D molecular alignment and docking methods on AlignDock- Bench in crossdocking scenario. Methods marked with an (*) use GPU. For methods that did not align all 369 molecules, percentages are reported as X/Y, where the first value calculated over aligned molecules only, and the second over the total set of 369 molecules.
of Molecules Aligned
Mean RMSD (Å L)
% of Molecules
Average Runtime (s)
Method
with RMSD < 2Å (1)
FMA*
369/369
1.97 + 1.36
64.77
0.83
FMA-PO
369/369
1.86 1.42
69.38
3.66
FMA-PO+*
369/369
1.62 1.33
77.78
27.96
FitDock
313/369
3.73
53.67 / 45.53
19.71
LSalign
368/369
2.50
54.35 / 54.2
5.67
ROSHAMBO"
369/369
30.35
4.90
rDock
369/369
4.52
34.42
20.68
Vina
368/369
3.39 2.81
47.28 / 47.15
72.98
replacing all atoms with carbons (Figure 3b). We further analyzed how molecular complexity affects performance by evaluating results with respect the number of atoms (Figure 33) and the number of rotatable bonds (Figure (3d) in the query molecules. For each bin and each method, we plotted the fraction of molecules achieving RMSD below 2Å (Figure 3
As expected, alignment accuracy generally declines with decreasing molecular similarity to the template or increasing structural complexity. Nonetheless, FMA-PO and FMA-POO- consistently outperform all baselines across all similarity and complexity bins, demonstrating their robustness in challenging scenarios. Indeed, [MMAleeneaate poses without relying on explicit structural similarity, instead leveraging global spatial priors derived from the reference conformation. When the query molecule shares high similarity with the template, 3D LB alignment methods such as LS-align and FitDock tend to outperform Vina and rDock SB approaches, highlighting the value of exploiting reference ligand information to guide pose generation these scenarios.
All results were obtained under cross-docking setup, where the pocket structure of the template ligand is used, simulating the realistic scenario which the query ligand's pocket structure is unavailable. Additional experiments were conducted under redocking setup. using the query ligand's own crystal pocket. Results are provided
Table We further assessed the quality of generated poses using the PoseBusters test suite [Buttenschoen al. 2022)), with detailed results
available Appendix D.3 Ablation studies are presented in Appendix D.4 Comparison to Harmonic
Flow Stark al. 2024 provided in D.2.3
Runtime. terms of computational efficiency. FMA-PO achieves a competitive average runtime of 3.66 seconds per molecule. As expected, (FMA incurs a higher runtime (27. .96 per molecule) due the additional PO steps involving all samples but resulting improved alignment accuracy. Both FMA-PO and FMA-POI- benefit from GPU acceleration during the FMA stage, whereas conventional methods such as rDock and FitDock were executed using a single CPU core, and Vina was run with four CPU cores. More details are provided in D.2.4
5 Discussion
Ligand alignment methods followed by LD similarity calculations are commonly used in virtual screening for hit identification (Jiang et al. 2021]. [MA-POO,, combined with scoring function that integrates STS PTS and optionally Spockets fits naturally within this framework. Furthermore, generative design workflow reward
the proposed method could be integrated into de signal, encouraging the generation of compounds that exhibit shape and pharmacophore similarity to reference ligand, as well complementarity to the protein binding pocket. Indeed, biasing molecular design towards compounds similar to known actives is particularly relevant during the hit discovery and hit-to-lead optimization stages [Boleato et al. 2022
'Experiments
single NVIDIA T4 Tensor Core GPU.

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100
100
Molecules with RMSD < A(%)
300
Molecales RASD A
htDock
PiDooh
230
ROSHANSO
Salign
Number moleculla
Fallags
ROSHAMB0
Vine
200
Number of
40
150
40
100
100
20
20
30
0.5)
10.5,
10. 0.53
10.5.
Similarity the template
Murcic similarity with template
(a) Stratified by the structure similarity between query template.
(b) Stratified hy complate.
similarity between query
100
250
100
Molecules with RMSD 2
Molecules RMSSD 2
FH--FO-
200
Ritteek
LSaiig
200
LSaign
INSHANTO
60
60
150
rDock
40
100
Number
40
20
Number
Number rotatable bonds
(c) Stratified by the number of atomss query ligand.
(d) Stratified number of rotatable bonds query ligand.
Figure 3: Performance of molecular alignment and docking methods on BlignDockBennh in cross-docking scenario. Bar plots (left y-axis) indicate the percentage of molecules with RMSD below 2Å, while the line plot (right y-axis) shows the number of molecules in each bin. Each figure stratifies the results based on a different structural or chemical property of the query ligand.
FMA-PO capable of generating 3D poses of candidate compounds that are directly suitable for downstream activity prediction tasks. Indeed, both deep learning-baas based scoring functions [Shen]
al. 2023 Valsson et al., 2025 and physics-based approaches [Greenidge et al. 2013) rely on a 3D
representation of the receptor-ligand complex. In addition, using |-MA-PO- generated alignments to
augment training datasets represents a promising strategy enhance the performance of predictive or generative models. This aligns with recent efforts such BindingNet V2 (Zhu et al.) [005)] which uses alignment-bren
data augmentation to boost the performance of deep learning models. In particular, [MA [MM|itself ittelf could benefit from such augmented data to improve its performance in an iterative training process. Future work could explore conditioning FMA on either a single or a set of reference ligands, along with the protein binding pocket, thereby incorporating more structural context into the pose generation process Guan et al. 2025]. Additionally, addressing flexible receptor scenarios, where both the 3D receptor and ligand predicted, could be interesting. It is worth noting that, compared to non-deep learning methods, FMM-PO remains computationally more intensive, suggesting potential direction for efficiency improvements.
6 Conclusion
This work presents a template-guiee guided framework for 3D molecular pose generation that combines the strengths of FM generative models with differentiable optimization. By conditioning the model reference ligand, the (MM-oO approach achieves accurate molecular alignment, outper- forming both classical docking tools and open-access alignment methods on the AlignDockBench cemplate-based based cross- coos-docking benchmark. It remains robust even in challenging scenarios with low molecular similarity the template and high ligand flexibility. These results highlight the potential of integrating known ligand geometries into generative frameworks to enhance pose prediction in structure-ber based drug design. Beyond performance gains, our framework enables sampling for data augmentation and direct integration with downstream predictive models. Future directions include incorporating receptor context into the generative process, extending the approach to flexible receptor scenarios (e.g., induced-fe -fit,, and assessing its impact molecular design applications.

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Acknowledgment
We would like express our sincere gratitude to the Iktos team for their exceptional contributions to this project. The authors would like to thank IKTOS for supporting this study. We are also grateful to the reviewers for their valuable comments and suggestions, which have improved the manuscript. We further thank Ennys Gheyouche, Maoussi Lhuillier-Akakpn and Juan Sanz García for their feedback and review of an early draft of this work.
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21

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A Flow-Matching Molecular Alignment model details
FMA
frnt
Jook
Molecular
Encoder
Vector field Network
feige
fudge
Hirtar postisoss
Template graph
2,
(a Lomplllte 24 a
cut+
Ro
$,,000
Harmonio
Droiution
t=
Iopt
Outpuc
[=1
Templote positions
gempplate
Figure $1: Illustration of FMA model pipeline.
A.1 Molecular graph construction
The FMA model operates hybrid molecular graph & constructed from both the query and template ligands. The total number of atoms denoted Natoms Aquuery + attoms where Nauurry and Nztemplate are the numbers of atoms in the query and template molecules, respectively. The graph contains two types of nodes: atomic-level nodes and functional group nodes. Let Noodss denote the total number of nodes in the graph, including both atoms and functional groups. Edges include covalent bonds, dense inter-ligand functional group connections, and hierarchical links between atoms and their corresponding functional groups. The total number of edges denoted by Nedgess
A.2 Flow-Matching Training and Inference Algorithms
The inference and training procedures of the FMA model are outlined in Algorithm ST and Algorithm S2] respectively. addition, the harmonic sampling process used to generate an initial random conformation from the reference structure is described in Algorithm S3
Algorithm S1: INFERENCE
Input: Query 2D graph G Gguery, template molecule Mtempiates number of sampling steps N,, number of samples K
+ Construct graph with Gouery and Msemplate
for i +- 1 to K do
Sample query positions C. ~ HARMONICSAMPLING (Qquery)) Center C₁ MMtemplte
for n + 0 to t N
do
Predict vector field 4 FMA
Update positions C, f C, +0 At
return C1...,, CK
A.3 FMA Molecular Alignment model
FMA (Algorithm S4) takes as input molecular graph G representing both query and template ligands, along with their atom coordinates. Positional features concatenates the ground-truth positions of

---

Atomic nodes
group Dense edges Covalent
group connoctions
Figure S2: Molecular graph 9 with query and template ligand. Blue nodes represent atoms, while orange nodes denote functional groups. The graph incorporates multiple edge types: purple edges for covalent bonds, green edges for dense intercomnections, and orange edges linking functional groups their constituent atoms.
Algorithm S2: TRAINING
Input: Query molecules with 2D graphs (G querys a. queryl true coordinates [CL .... CKK and associated template molecules [M] [etepiitee ..y templatel number of epochs N Nepochs: learning rate a.
GK
MK
for n < Nepochs do
for i 4- 1 to K do
Sample time t (0 1])
g + Construct graph with G query and M template
Sample query positions Cj HARMONICSAMPLING (query)
Center Co on M Miemplate
Sample C = x C + (1 - C + 021 1)2, ~~,1(111
Compute vector field uz C Cj
1-2t
2/1(111)
Predict vector field 0g +- FMA Ct
Compute loss C f ||0g - uel
Take gradient step 0 +- 0 AgL
return Trained Up
Algorithm S3: HARMONICSAMPLING
Input: 2D Molecular graph G
L + Laplacian of G
L E R Natomo N Natumn D, P E Natama X Natoms RR
D,P < Diagonalize Laplacian L
Sample ~ I)
PD ir
return æ
the template atoms with the query atom coordinates at diffusion step l. The model outputs the vector field yguery used for query pose prediction. Initially, node and edge features independently embedded into vectors of dimensions en and çe, respectively, using separate MLPs. All node and

---

edge embeddings are projected into a common feature space with identical dimensionality, thereby transforming the heterogeneous graph into homogeneous representation. To preserve type-specific information, each node and edge is annotated with its corresponding type attribute. The resulting representation is processed by a stack of N.HHA WHAWITHEDGEBIAS layers (Algorithm S3 in (Qiao et al. 2024)), ). jointly updating node and edge embeddings. The processed node embeddings are then passed to the VECTORFIELDNETTE layers of
model (Algorithm S5), which applies a stack of PV (Algorithm S8 [Qiao et al. 2024]). followed by a GATEDUPDATE layer (Algorithm S6), adapted from [Qiao et al. 2024 J. These blocks operate directly on scalar and vector node representations, denoted Js and fo respectively, incorporating positional information r and diffusion time to produce the final learned vector field yauery.
Algorithm S4: FMA
Input: Molecular graph G with adajency matrix X, nodes features Snode, edges features Sedges time t. template-query positions r E RaNacom x3 at time t, NMHA NMHA NVENN NVEN
heads
for j in nodes types do fnode + MLP(Snode for in edge types do Padge & MLP edgee
fnode RN mades Xcn
Sedge E IR RRNee x
G + TOHOMOGENEOUS(()
1/ Convert to Homogeneous Graph
for k = 1 to N do blocks
fnoder -1 t MHAWITHEDGEBBAS (Snode, Inode, Sedges X, Notads
Inode E RR-NnodexXe.
fuode &- MLP + fnode) ) + fnode
fuode Nuodes XCn Sedge E Nedgee XCn
Sedge f- MLP (Sedge + (LINEARNOBIASS(E) + Sedge
fo + IR-nodaa x3xen;
11 Initialize vector features as zero tensors
f- mean(x):
// Center positions E R Nodees X3 V R Natoms X3
VEETORFFELDNNTWORKI
for fedge t,, NVFN blocks heads
Extract atomic nodes from
query +- Extract Query vector from
yuery E R Veaerg x3
return query
Algorithm S5: FECTORFFEEDDNEWORK
Input: Scalar features f @NnodexXX, vector features fu RNonees x3xea, edges features
fe E RRNedgex query-template positions time I, Nolocks, Nheads fs Nuudes x(e,+
fs + CoNCAT(fs,t
for k to N blocks do
fs, fu + PONYSUAATERTOOWWHHBBBBSSSSSSS.. fe, Nncads)
fs E RRNandea ((c. fu fo E Nanae x3x
fs. fu GATEDUPDATE& fs Nuuotco ((,, (l,, ff f Noodes x3x
+
<- GATEDUPDATE([s, fv,1)
E Rander x3
return v
A.4 Training Details and Hyperparameters
We trained FMA for 100 epochs with batch size of 128 on a single NVIDIA GeForce RTX 2080 Ti GPU. We used the AdamW optimizer with learning rate of 3 x 10-1 and weight decay 10-5 Hyperparameters are detailed in Table SI
3

---

Algorithm S6: GATEDUPDATE
Input: Scalar features fs E RR-nndde XCn, vector features fo E R Nnodea x3xen, output dimension
d
Sloc - CONCAT(fs, l1fell2)
floc E R.Nnedd x (Cn +ox)
Sion + LAYERNORMMLP(/AM
Jioe E RRNnndd x(cnt)) fs E RNodee xe Sgate E Xo
f8. fgate + (foo)
fgate SIGMOID
fO LINEARNOBIAS(
fv E XRNnndea X3xd // Element wise multiplication
fo t fu O fgate:
return fu
Table $1: Hyperparameters used for the training of FMA.
Hyperparameter
Nodes embedding dimension (c,)
128
Edges embedding dimension (ce)
32
MHAWITHÉDGEBIAS heads (NHHA)
MHAWITHEDGEBIAS blocks blocks
VECTORFFIELDNETTWOK heads ( (NN
VECTORFIEEDDEETWORK blocks ( (N blocks
Noise scale (ar)
0.1
Total parameters
3.5M
B Pose Optimization details
B.1 Shape-based Tanimoto Score
Following the molecular volume representation proposed in [Grant and Pickup
1995 Grant et al.
1996), each atom in the molecular structure is modeled spherical Gaussian function. An atom located coordinates R; (Ii, Mr, z;) with radius o; is represented by Gaussian density function:
pa(ri) = pt exp(-aar?) with as
where r; |r - defined as distance vector from the atomic center R. and parameters Pt, h; are atomic-type-specific chosen to ensure that the Gaussian atomic volume matches the van der Waals hard-sphere volume: V/8"
R.
4 where the exponent a refers to atom-based gaussian volumes.
According to the Gaussian product theorem, the product of two Gaussian spheres results another Gaussian function. Utilizing this property, explicit formulas can be derived to compute the intersection volume between two atomic Gaussians, enabling the calculation of both molecular volumes and overlapping volumes between molecules (Grant and Pickup 1995 Grant al. 1996.. volume between atoms and j is expressed as:
The intersection
a,a,R
ViS P.P P.P Key
3//2 with Kg exp(
0, ag
a; az
where Rij is the distance between atoms and j. The total volume of a molecule is expressed as:
V
V
Σ
Vij.
i<j<
Similarly, the overlapping volume between molecules and given by:
V
Σ ve
Σ va
Σ
Vij
+
iEA.EEB
A.EAAKEB

---

For computational tractability, we approximate the overlapping volume by truncating this series at second order, thus including only pairwise and triplet intersections.
B.2 Pharmacophore scoring
Pharmacophore-basee Tanimoto Score. Pharmacophores a molecule are 3D) arrangements of specific chemical features, such as hydrogen bond donors, hydrogen bond acceptors, hydrophobic groups, and aromatic rings. These features are identified using RDKit. Each pharmacophore feature positioned at the barycenter of the corresponding atomic group and assigned specific type (e.g.. hydrogen donor, hydrogen acceptor, aromatic, etc.). Pharmacophores are modeled as spherical Gaussian functions with a fixed radius of 1.7A, comparable to the van der Waals radius of a carbon atom. The overlapping pharmacophore volume between molecules A and B is given by:
V
Σ iEA,JEB
Vi ((r0=T0))
Σ KEE KEB
ijk (T7))
Σ AEB
VP iik (())-))))M
where Vi represents the intersection volume between Gaussians pharmacophores of types T(i) and T() from molecules A and B. The indicator function L(T({)=(()) ensures that only pharmacophores of the same type are considered for overlapping volume calculations. In practice, we approximated the overlapping pharmacophore volume by truncating this series the first order, including only pairwise interactions.
Figure S3: Aligned ligands with pharmacophores overlapping. Ligands carbons shown in grey. Gaussian pharmacophore spheres are depicted as sphere mesh. The color of each sphere encodes specific pharmacophoric feature: cyan for hydrogen bond donors, magenta for hydrogen bond acceptors, red for negatively charged groups, blue for positively charged groups, and limon for aromatic groups.
Pharmacophoric complementarity. The concept of pharmacophoric complementarity in our method stems from Gaussian- based shape similarity modeling. Specifically, once Gaussian sphere is labeled with a pharmacophoric feature (c.g.. hydrogen bond donor (HBD), hydrophobic, etc.), it becomes possible to compute pharmacophoric similarity between two ligands based on the overlap of these labeled Gaussian volumes.
When introducing the protein pocket into the PO process, we extended this idea to model complemen- tarity between ligand and pocket by maximizing the overlap between complementary pharmacophoric Gaussians. For instance, Hydrogen Bond Donor (HBD) and HHdrogen Bond Acceptor (HBA) were defined as complementary, as well as cationic and anionic features (Figure (5). During the PO the SpTs term of the objective function increases the overlap between such complementary features from the ligand and the pocket, whereas the shape -SyTS term prevents sterie clashes by penalizing excessive overlap between atoms.
5

---

Regarding hydrogen bonding in particular, we model the HBD pharmacophoric center as Gaussian sphere located at the position of the donor hydrogen atom. If this hydrogen atom (and thus its associated Gaussian sphere) is positioned near an HBA-labeled Gaussian from the pocket, the overlap between these spheres is maximized, effectively favoring geometries consistent with hydrogen bond formation. The geometry naturally tends toward favorable X X-H ... X angle close to 180", since this configuration maximizes Gaussian overlap. Simultaneously, the internal energy term in the PO loss encourages the donor group (e.g., C-X-HI to remain in energetically favorable conformations.
Figure $4: Illustration of pharmacophoric complementarity within PL. binding site. 3D structure of the human M2 muscarinic receptor in complex with the ligand QNB (PDB ID: 5ZK3) (Suno et al. 2018), shown in grey. Gaussian pharmacophore spheres are depicted as sphere mesh to illustrate key interaction features within the binding site. The color of each sphere encodes specific pharmacophoric feature: cyan for hydrogen bond donors, magenta for hydrogen bond acceptors, red for negatively charged groups, and blue for positively charged groups.
As illustrative example, consider the protein-ligand complex (PDB: 1NJS) shown in Fig. S5 The ligand KEU (sequence number 510, chain A) contains two hydroxyl groups, C5-0A1 and C5 - 0A2, both positioned near the carboxylate group of ASP 144 (chain A):
The hydroxyl oxygen OA1 belongs donor group (C5-0A1-H1) and lies near the acceptor DD1 of ASP 144.
The second hydroxyl oxygen OA2 (in (5-0A2-H2) close to the second acceptor OD2.
At the beginning of PO hydrogen atoms H1 and H2 are added by RDKit without considering the protein pocket. However, optimization begins, complementary HBD Gaussians assigned to these hydrogens, and their overlap with HBA Gaussians on DD1 and OD2 maximized.
B.3 Internal Energy components
Internal energy components are computed using GAFF2 Wang et al. 2004 force field parame- ters that depend on atomic and chemical bond properties. These parameters are parsed using the OpenMM (astmmn et al. 2023) package and energy equations are implemented in Py PyTooch, ensuring differentiability with respect to ligand coordinates. Following OpenMM formulation, the internal
energy is decomposed into two main components:
Bonded forces: These include harmonic bond forces, harmonic angle forces, and periodic torsion forces, which account for bond stretching, angle bending, and torsional rotations.
Non-bonded interactions: These include Lennard-Jones interactions, modeling van der Waals forces, and Coulomb interactions, which account for electrostatic forces between partial atomic charges.
Hence, internal energy is computed as follows:
Eiteernat Ebond Eangle + Etorsion + Eij + Ecoutombs

---

D.D.pprr
Ionsion
Hydregen Bend Distances
Hydrogen Bond Angles
325
Distnce HL H. Acceptorl Disanca AcAcepptr22
3.00
140
2.75
Dintace 84
Angle (deg)
120
2.50
2.25
2.00
1.75
60
Angle Donori- H. Acceptooi
1.50
Angle Donorz H2 H, Acceptor2
100
Rteraion
teraaion
Iteration
beniiion
Meration
Iteration 1:3
Angles Hydrogen-Bond
Hydrogens
GAFF2 Energy
17500
Angle C-H. Donor2 H1
GA-F2 Energy
140-
Angle C-H. H2_
15000
12500
120
7500
2500
60
300
100
Reration
Iteration
Figure S5: Illustration of iterative optimization hydrogen bonding interactions in protein- ligand complex. 3D structure of the human GAR Tfase (carbons in cyan) in complex with the hydrolyzed form of 10-trifluoroacetl-5, 10-iyli-,,-ddidaaaaaaaa sarpa-accyciii-5..7.--eerea
acid /hang et al.) 2003 (carbons in grey). (A) The protein-ligand binding site shows two HBD) (Donor1, Donor2) and two HBA (Acceptor. Acceptor2). (B) Time evolution of donor-acceptor distances (H1-Acceptorl,, the optimization iterations.
(C) Time evolution of hydrogen-bond angles (D) Representative ligand conformations at selected iterations (20, 40, 70, 113), illustrating the progressive stabilization of hydrogen bonds in the binding pocket. (E) Evolution of the angles between the carbon atoms bound to hydrogen-boo bond donors and their respective hydrogens (C- Hooooroo-HH C-Hponorz HH). (F) GAFF2 energy profile across iterations, showing convergence from initially high-energy conformations toward stabilized minimum.
H2 H2-Acceptor2)
(Donorl-Hll-Accettrrr

---

where each term is described below.
Harmonic Bond Energy models the interaction between two bonded atoms i, using an harmonic potential:
E/i bond 2 k(d.; - -d
1
where dıj the bond length between atoms i, j. do the equilibrium bond length, and & the bond force constant.
Harmonic Angle Energy describes the energy cost of deviating from the equilibrium bond angle between atoms j,
k(Oajk 0o)
where Bayk is the bond angle between j, k. Og the equilibrium bond angle, and & is the angle force constant.
Periodic Torsion Energy accounts for dihedral interactions between four atoms i,j, k. using periodic function:
siskl k(1 + cos(neijkr - 7)); tonsion
where Φiski is the dihedral angle between j. k I, n is the periodicity, y is the phase offset, and is the torsional force constant.
Lennard-Jones Energy models van der Waals interactions between atoms i.j using the Lennard- Jones potential:
6
ej 4cg
Oíj dij
ij
dig
where Gj defines the interaction strength, dij is the distance at which the potential is zero, and di is the distance between atoms and j.
Coulomb Energy describes electrostatic interactions between atoms i, using Coulomb's law:
jij
9:96
coulomb
Arspde
where zi, 2j the atomic charges, dy is the distance between atoms and j. and En the permittivity of vacuum (+e 8.85 x 10 10-12f/mb
B.4 Pose Optimization algorithm
The PO algorithm is described in Algorithm S7
We used the Adam optimizer with learning rate of 0.2. The refinement protocol is divided into two main phases, with weights that can vary across iterations to progressively adjust the optimization focus. The two-phase protocol is structured as follows:
Phase 1: Hydrogen-free refinement
Step 1: Focus minimizing internal energy.
Step 2: Reinforce ligand alignment with a focus on shape and pharmacophore overlap.
Step 3: Add steric clashes and internal energy penalties while maintaining overlap improvements.
Step 4: Fine-tune steric clashes and internal energy, with reduced shape weighting.
Phase 2:
refinement
Step /: Focus on internal energy minimization after hydrogen addition.
Step 2: Add shape and pharmacophore constraints for improved fit.
Step 3: Emphasize pocket volume interactions alongside energy adjustments to refine binding.
Step 4: Perform final fine-tuning of both overlap interactions and energetic stability.

---

The weights of the loss terms (Table S2) were empirically tuned using a validation set of ten diverse protein
protein-ligand ligand complexes from the training data. For each term shape similarity, pharmacophoric complementarity, steric clash penalty, and internal energy regularization- we explored multiple weightings. The final values were chosen based on convergence behavior, pose quality, RMSD and alignment performance across the validation set.
Algorithm S7: POSEOPTIMIZZATION
Input: Ligand conformation with coordinates number of optimization steps Reterations learning rate
for Riterations do
Compute loss: Loptim -a SSTS B SPIS
Spucket + ? Ennernal
Update atoms positions
Ir x V VzLoptim
Table S2: Hyperparameters for two-phase pose optimization protocol. All weights were tuned empirically. (x y) means that the weight increase linearly over iterations from y.
Phase
Step
max iterations
8
Y
50
1.0
0.0
0.0
1.0
2
200
(1.0~22..0
(1.0+50.0)
10.0
10.0
Without H
50
30.0
10.0
200.0
(1.0~50.0)
4
200
1.0
50.0
200.0
50.0
25
0.0
0.0
0.0
1.0
2
200
10.0
10.0
25.0
10.0
With H
50
10.0
10.0
150.0
(10.0~25..0)
4
200
10.0
10.0
25.0
10.0
AlignDockBench and training dataset
C.1
AlignDockBench
Table S3: PDB IDs of template and query structures used in AlignDockBenchh
Template PDB ID
Query PDB IDs
IA4G
2QWJ, IINF, IVCI, 4HZW, IINV, 2QW1, IIVB, 1B9S, IXOG, 3K37, IFSE, IFSC, 4MJV, INN,, 5JYY
2BIP
7KSJ, 7KSI, 4W4V, 4WHZ
IUY6
IUYD, 3HZ5, IUYH, SLRI, 1UY9, 7D24, 3FT8. 2H55, 7D22, 1UY8, 2FWZ, 6OLX, IUYI, 4XIR, 1UYF, 4U93, 4XIQ, 6LR9, 1UY7, IUYC, 7D26, 2FWY
3BIZ.
3CR0, 272W, 3B16, 3CQE, 1X8B, 2106, 21N6
2AA2
6W9M, IZUC, 6W9K, 5MWY, 4QL8, 5HCV, IXQ3, 6W9L, 2A31. 20AX, 2AMB, 2Q1V, 1GS4
3QKL
3QKM, 3QKK
3EML
SIUB, 5IUA, 5IU7, 5IU8
3SFF
7ZZW, 3SFH, 7ZZU
3D4Q
3PPK, 3PSB, 3PPJ, 7SHV
21CA
3M6F
3LBK
40Q3, 5LAV, IT4E

---

3BQD
7PRV, 6W9M, 6W9L, 5NFP
3KBA
3HQ5, 3G8O, IZUC
210E
8U37, 8UAK, 2JED
IXOI
2IEG, 27B2
3SKC
4XV1, 4EHG, SITA, 4E4X, 5FD2, 3TV4, 4PP7
3KL6
2J34, 2VVU, 5VOF, 2193, 2Y7Z, 2Y80, 2VVC, 2VWO, 4Y71, IWU1, 2UWP, 2J38, 2UWO, 2141, 2P95, 1IOE, INFW, IIQI, 2UWL, 2120, IIQ.L 2VVV, 2194, 1IQK, 2VWN, IIQN, 2PR3, 4Y79, IIQG, 2CJI, 4Y7A, 2J95, 4Y7B, 2DIJ, 1J17, 4ZH8, IIQH, 4Y76, 3SW2, 2P94
2XCH
3OT8, 2R7B, 2IN6, 2PE1, 2106
IE3G
3GOW, IZUC, 2NW4, 2AAX, 5T8J, 2HVC, 4QL8, 4ZN7, 8EIA 5V8Q ST8E, 21HQ, 2A31, 2AMB, 5V04, SCJ6, 3D90, IXNN, 1GS4
2E1W
IWXZ, IV7A, INDY
3LAN
3LAL, ICIC, 2JLE, ITL3, 3DRP, 3TAM, 3LAK, 4NCG, 2YNG, 8U6E, ICIB, 2WON, IRT1, 8U6P, 7SLR, 8U6C, 4WE1, 2B5J, 1RT2, 8U6B, 3DYA, 8U60, 7SLS, 2BE2, 3LAM, 2YNI, STUQ, 8U6Q, 3T19
3LPB
6VNI
IUYG
2QG2, 2QF6, IUY9, 4CWR, 3HZ5, 8SSV, 4U93, 4R3M, IUYI, 7D24 6N8Y 3B26 7D26 5LRI 7D22 IUYC 2H55 1UYK 3001, 1UY7, LUYD, 3B25, 1UY8, 6LR9, 3FT8, 1UYM, IUYH. 4L91, 6EL5, 2FWY
3BKL
3BKK, 6TTI
IW7X
4JYU, 5PAM, 4X8V, 4ZXY, IYGC, 1WOY, 4YT7, 4JYV, 4YT6, 4NGA, SPAQ, 4NG9, IW2K
IS3B
2VZ2, IGOS, 2C66, 2C64, 2C65, IS3E, SMRL
3F9M
4MLH, 3FRO, 6E0E, 3GOI, 3A0I, 4MLE
2ZEC
3V7T, 2ZA5, 2BM2, 2ZEB
2GTK
3FEJ
3LNI
3N8X. 6COX, 5KIR, 3QMO
2RGP
3W33, 3BEL
3CJO
2FME, 2FL.2, 6HKX, 2FKY, 2G1Q, IYRS, 2FL6
314B
5BVF 3160
1Q4X
3IMY
2VWZ
5MJA, 4YJS, 8BK0, 4YJP, 4P4C, 2VWY, 4G2F
3HMM
6B8Y, 3KCF, IVJY, IPY5, 3FAA, SQTZ, IRW8
5L7H
20AX. 5MWY, 5L7G
2010
3B92
2AZR
2BGE, 7FQU, 2HB1
3FRG
5C2E, 5SHB, 4FCD, 5SF7, 3GWT, 6MSC, 5SHG, SSJF, STKB, 4PMO. SSKF, 3SNI
ILRU
IBSJ
IZW5
40GU, 4DXJ, 3ICZ, 4DWB, 4KPD
3L3M
4RV6, 5XSR, 5A00, 5XST, 2RCW, 618M
IEVE
6TTO, 6EZH, 7D9Q, 6EZG, 7D9P, 7D90, SNAP
3CHP
7AV1
10

---

IFOR
IFOS
3NY8
2YCZ, 7DHI, 5A8E, 6PS1, 4BVN
3KK6
3N8X. 5KIR
3M2W
3FYJ
1L2S
6DPY, IXGJ, IXGI, 4K74, 4IXS, 6DPX
IB9V
3CKZ, 1B9T IVCJ, 3K39, 4DGR
2QD9
6M95, 3ZSH
3NW7
3NW6, 3181
3K5E
IX88, 2FL6, 2FME, 2X7C, 2X7D
1J4H
1J4I
1S3V
IMVT
27DT
2GMX, 27DU
2VT4
6PS1, 5A8E, 2YCZ, 6PS4, 2Y04
ICX2
5KIR
3KC3
3R30
IKVO
IKQU, IJIA
Chaperone
Other
GPCR
Ligase
Transcription Regulstor Isamerase
Oxidoreductase
3,3%
6.6%
1.6%
8.2%
Nuclear Receptor
8.2%
29.5%
Hydrolase
29.5%
Kinase
Figure S6: Overview of protein diversity in AlignDockBench.
C.2 Structure Preparation
Each structure retrieved from the PDB was repaired and protonated using the PDB2PQR program (Dolinsky et al.) 2007 with the AMBER force field. Subsequently, energy minimization was performed using the GROMACS molecular dynamics engine [Van Der Spoel al. 2005 with the
AMBER03 force field in implicit solvent. Small molecules were parametrized using GAFF2 Wang

---

1e6
2,5
2.0
Frequency
1.5
1.0
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Tanimoto Similarity
Figure S7: Morgan fingerprints tanimoto similarity histogram between AlignDDockenchh and the training set molecules.
et al. 2004] with the ambertools suite [Case al. 2023 and partial charges were assigned using AMI- BCC Jakalian et al. 2002]. The minimization was performed two stages; initially, 5,000 conducted with positional restraints of 10,000 kJ/mol applied to all heavy atoms. In the second stage, another 5,000 steps were performed with restraints of 1,000 kJ/mol-nm² applied the protein backbone and all heavy atoms of the small molecules.
steps (time step 2 fs)
D Experimental details
D.1 Experimental setup
Vina and rDock. Docking simulations were performed as follows: a random conformer of each query molecule was generated using RDKit ETKDGv2 [Riniker and Landrum, 2013) and minimized with MMFF94 forcefields [Halgren| 1996). Protonation states were assigned using the internal proprietary small-molecule protonation model at physiological pH (7.4). Ten docking poses were generated per molecule. In rDock, docking was carried out "dock" mode using the default "STANDARD SCORE" scoring function. For AutoDock Vina, docking was performed with an exhaustiveness parameter set to 15, using the default Vina scoring function.
FitDock and LSalign. To prepare ligand inputs for both FitDock (Yang et al. 2022 and LS-align HHu al. 2018). we generated 10 random conformers per query molecule using the same protocol described above, based on RDKit's ETKDGv2 method followed by MMFF94 energy minimization. Each minimized conformer was exported an individual SDF file, then converted MOL2 format using Open Babel [O'Boyle et al. 2011], with partial atomic charges assigned using the Gasteiger method [Gasteiger and Marsili 1980 For each template query pair, FitDock was provided with the MOL2 representations of both the template and query ligands, as well as the corresponding PDB files of the template and query proteins. LSalign requires only the MOL. ligand files; we used flexible alignment mode with the "-rf" flag enabled, allowing torsions to adjust during superposition. After alignment, we selected the tap-ranked conformer based on each software's primary scoring metric: the "Binding Score" for FitDock, and the "RMSD lb" output for LSalign.
12

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ROSHAMBO. For the ROSHAMBO software [Atwi et al. 2024), the query ligand was provided as single 2D SDF file, from which aligned poses were generated. Shape volumes were modeled using the "Gaussian" option. The resulting poses were ranked according to the "ComboTanimotoo" score, and the highest-scoring pose was retained.
D.2
Supplementary results
D.2.1
Cumulative distribution of RMSD values
In Figure S8
we report the cumulative distribution of RMSD values on AlignDockBench for each
method.
1.0
Fraction of ligands (s RMSD)
0.8
0.6
FMA
FMA-PO
0.4
FMA-PO+
Fitdock
LSalign
0.2
ROSHAMBO
Vina
rDock
0.0
2
6
8
10
RMSD (Å)
Figure S8: Cumulative distribution RMSD values: percentage molecules with RMSD below different thresholds
D.2.2 Redocking experiments
Results for each method in a redocking scenario, where the query ligand is aligned within its own crystal protein, are presented in Table S44 Methods like ROSHAMBO and LSalign, which do not incorporate protein information, have identical performance in both redocking and crossdocking contexts.
Figure 59 compares the performance of pocket-aware methods both crossdocking and redocking scenarios, highlighting the gain of using true protein context for pose accuracy. Traditional docking approaches, such as Vina and rDock, exhibit significant improvements in redocking due to the availability of the correct pocket environment, FMA-PPO- also shows slight performance gain in the redocking scenario whereas FMA-PO shows no notable difference.
D.2.3 Comparison to HarmonicFlow
We compared [MA
to the recent flow-based docking method HarmonicFlow Stärk et al. 2023
using the official settings from the authors' repository. As shown Table S5 FMA significantly outperforms HarmonicFloww both mean RMSD and success rate (< 2 even when reporting HarmonicFlow's best RMSD across the 10 sampled poses. Applying PO HarmonicFlow improves
results but still underperforms [MA highlighting the higher quality of FMA s pose distribution and the benefit of using the template ligand to guide docking.
13

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Table S4: Performance comparison of 3D molecular alignment and docking methods on AlignDock- Bench in redocking scenario. Methods marked with (*) use GPU. For methods that did not align all 369 molecules, percentages are reported as X/Y, where the first value calculated over aligned molecules only, and the second over the total set of 369 molecules.
# of Molecules Aligned
Mean RMSD
% of Molecules with RMSD < 2Å (1)
Method
(Å !)
FMA-PO
369/369
1.86 1.43
68.56
FMA-PO+*
369/369
1,52 = 1.24
82.11
FitDock
292/369
3.27
54.11 42.82
LSalign
368/369
2.54
54.35 54.2
ROSHAMBO*
369/369
2.87
48.51
rDock
369/369
2.79 + 2.93
60.43
Vina
368/369
1.95 + 2.54
75.82 75.61
100
Redocking Crossdocking
Molecules with RMSD < 2 À (%)
60
60
40
20
FMA-PO
FMA-PO+
RtDockk
Vina
rDock
Figure S9: Pose accuracy comparison in redocking and crossdocking scenarios.
Table S5: Comparison to Harmonic Flow
Molecules successful pose generation
Mcan RMSD (Å J)
% of Molecules with RMSD < 2Á (t)
Method
FMA (Top score)
369/369
1.97 1.36
64.77
FMA (Top RMSD)
369/369
1.39 + 0.85
84.55
FMA PO+ (Top score)
369/369
1.62 1.33
77.78
FMA + PO+ (Top RMSD)
369/369
1.11 + 0.85
91.6
Harmonic-Flor (Top RMSD)
356/369
4.47 2,07
2.81/2.71
Harmonic- Flow PO +Top RMSD)
356/369
3.71 & 2.22
19.94/19.24
D.2.4 Discussion about runtime
We analyzed runtime as a function of ligand size for both FMA and PO. As shown in Table S6 PO (2.7 s per pose, run CPU) is slower than FMA (0.84 for 10 poses, GPU). In both cases, runtime increases moderately with the number of heavy atoms and rotatable bonds (Pearson ~0.2), without signs of exponential growth.
Runtime a critical factor for practical applications. Fach molecule processed independently. so scaling across multiple compute instances is straightforward. To illustrate this, we report in Table S7
14

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Table S6: Time, GPU
Average runtime (s)
Pearson correlation with the number of heavy atoms
Pearson correlation with the number of rotatable bonds
Method
FMA*
0.84 (for 10 poses)
0.20
0.23
PO
2.7 (for pose)
0.19
0.23
the estimated runtime and cost of processing various dataset sizes using 100 AWS g4dn. 2xlarge instances in parallel. This setup could be use within a de novo drug design pipeline, where screening around 50,000 molecules is a realistic and relevant scale. For ultra-large virtual screening campaigns (e.g., tens or hundreds of millions molecules), further acceleration and simplification PO would be required. For example, moving to a batched optimization strategy, rather than optimizing one molecule at a time, could significantly reduce total runtime.
Table S7: Estimated runtime (in hours) and cost (USD) using 100 AWS g4dn. 2xlarge instances in parallel for different numbers of molecules.
Number of molecules
50,000
10a
106
Time FMA+PO (h)
0.49
0.98
9.83
Cost FMA+PO ($)
41
82
826
D.3
Quality of predictions
Figure STO reports of the strain energy defined by GenBench3D Baillif et al. (2024), for each method. FMA yields higher strain energies, due to the absence of the PO module. While unrealistic conformations are known limitation of deep learning models [Buttenschoen et 2024), this was one of the key motivations for introducing our PO module, Both FMA-PO and FMA-PO+ reduce strain energy.
Table SS reports the number of molecules exhibiting clashes with protein, per method. FMA suffers from significantly more clashes, due to the absence of pocket conditioning. FMA-PO and FMA-PO+ reduce the number of clashes, confirming the effectiveness of the PO module in improving structural plausibility.
To further evaluate the quality of generated poses, we employed the PoseBusters test suite [Butten schoen et al. 2024]. which checks a range of geometric and chemical criteria to ensure physically plausible ligand conformations within the binding pocket. We observed that some the 369 ground- truth crystallographic query poses from AlignDockBench did not fully satisfy the PoseBusters criteria, particularly the minimum distance to the protein. As a result, we restricted our evaluation to a subset of 263 molecules for which the ground-truth poses passed all PoseBusters checks.
Figure $11 presents, for each method, the percentage of molecules achieving an RMSD below 2 along with the proportion that also satisfies the PoseBusters criteria. Traditional docking methods tend to yield higher proportion of Poseeusters-valid poses. In contrast, purely LB methods like LSalign and ROSHAMBO exhibit substantial drop in valid poses, reflecting context in guiding pose generation. FMA (without PO) shows larger drop in PoseBusters. valid poses compared to (MMA--OO), highlighting the critical role of PO and the importance of sampling multiple initial poses. Nevertheless, FMA--OO- still exhibits 12% drop, primarily due to the minimum distance-to-protein check. This suggests that the method could further improved by incorporating additional pocket-specific constraints assigning greater weight to the pocket score during the PO stage. Additionally, integrating protein context directly into the initial pose generation with the FMA model may enhance the physical plausibility of the generated poses.
importance of protein
15

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12.
10
Strain energy (log scale)
Figure S10: Strain energies of poses across methods (log scale).
Table S8: Number of molecules with protein clashes with the protein, per method.
Method
clash
2 clashes
> 3 clashes
FMA
16
20
FMA-PO
35
9
FMA-PO+
21
Vina
0
0
FitDock
Co-crystallized Ligand
0
0
100
RMSD <2A
Percentage of predictions (%)
RMSD <2Å & PB-Valid
72%
68%
60
55%
52%
49%
49%
40
36%
68%
51%
20
38%
42%
34%
12%
FMA
FMA-PO
FMA-PO+
FitDock
LSalign
ROSHAMBO
Vina
rDock
Figure S11: Percentage of accurate poses (RMSD 2 and Pose valid (PB-valid) poses for each method, evaluated on subset of 263 molecules whose ground-trun -truh crystallographic poses pass the PoseBusters checks.
16

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D.4
Ablation studies
D.4.1 FMA's contribution
We generated candidate poses per method (FMA RDKil-centroid, Vina, LS-align, FitDock-LB), applied PO to each, and selected the top-ranked pose. Results are reported in In Table S9 The RDKit-centroid baseline places a random conformer at the binding-seer center. FMM--OO consistently yields the lowest RMSD among all alternatives, indicating that FMA is the best initialization strategy for PO and that its accuracy is crucial.
Table S9: PO applied to different base alignments. All methods use flexible search mode and identical PO hyperparameters.
# of Molecules Aligned
Mean RMSD (Å 4)
% Molecules with RMSD 2A (1)
Method + PO
FMA PO+
369/369
1.62 + 1.33
77.78
rdkit PO+
369/369
4.63 1.94
10.33
Vina PO+
368/369
1.96 1.87
71,47/71.27
LS LSlalign PO+
357/369
2.31
63.31/61.25
Fitdock LB + PO+
365/369
2.78
52.6/52.03
D.4.2
PO
contribution
evaluate the impact of the PO stage and its objectives pose prediction. [MA exhibits the poorest performance across all metrics, highlighting the importance of the pose refinement. Moreover, including the pocket during PO enhances the quality of the generated poses, evidenced by lower mean RMSD values and higher percentages of accurate alignments for both FM and FMA-PO
In Table STO
Table S10: Ablation studies of PO loss terms on AlignDockBench in a crossdocking scenario.
Mean RMSD
% of Molecules
Method
(Å L)
with RMSD < 2Á (T)
FMA
1.97 1.36
64.77
FMA-PO
1.86 + 1.42
69.38
FMA-PO w/o SSTs
1.98 + 1.38
63.96
FMA-PO w/o Sprs
1,86 + 1.38
67.48
FMA-PO w/o Spockt
1.88 1.41
67.75
FMA-PO w/o Enternal
2.8 + 0.91
13.82
FMA-PO+
1.62 + 1.33
77.78
FMA-PO+ w/o SSTS
1.85 + 1.32
66.67
FMA-PO+ w/o SPTS
1.71 + 1.33
74.25
FMA-PO+ w/o Spocket
1.70 + 1.39
75.61
FMA-PO+ w/o Einternal
2.98 + 1.26
14.09
In Table S11 applied PO
top poses from other methods. PO
consistently reduced RMSD PO also improves chemical plausibility
supporting its general effectiveness as a refinement stage. PO
and geometrical validity demonstrated in Figure (S10 and Table S8
D.4.3 Vina contribution to Swore
We evaluated the influence of the Syin component in the total score Sware by systematically ablating across three key configurations: FMA, FMA-PO(i.e. scoring of FMA poses and PO applied the top-ranked pose), and FM..PO+(Le., PO applied to all poses, and scoring of optimized poses). The
17

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Table S11: Impact of PO on FMA, Vina, LS-align and FitDock LB compared the base aligners alone.
Method
# Aligned
Mean RMSD (À
% RMSD 2Á (1)
FMA
369/369
1.97 = 1.36
64.77
FMA PO
369/369
1.86 # 1.42
69.38
Vina
368/369
3.39 # 2.81
47.28 47.15
Vina + PO
368/369
3.84
52.17 52.03
LS-align
368/369
+
54.35 / 54.20
LS-align + PO
357/369
2.47 + 2.15
59.66/57.72
FitDock LB
366/369
2.93 2.36
49.73/ 49.32
Fitdock LB PO
366/369
2.75 + 2.38
52.88/52.3
results are summarized Table S12 These results indicate that Vina scoring provides limited benefit when applied unoptimized poses (FMA FMA-PO), but can help select better candidates among refined poses (FMA-PO+)). Our method still outperforms all baselines without using the Vina score in Sucore-
Table $12: Vina contribution S
Vina term in Store
Mean RMSD (Å L)
% of Molecules with RMSD < 2Á (1)
Method
FMA
Yes
1.97 + 1.36
64.77
FMA
No
1.96 + 1.35
64.77
FMA-PO
Yes
1,86 + 1.42
69.38
FMA-PO
No
1.81 + 1,40
69.38
FMA-PO+
Yes
1.62 + 1.33
77.78
FMA-PO+
No
1,68 + 1.38
75.61
D.4.4 Impact of the number of generated conformations
We assessed the impact of the number of generated poses with FMA on final pose accuracy. Figure S12 shows the percentage of molecules with RMSD below 2A and 1.5A for the best (i.e., lowest RMSD) pose of afTMA-POaand FMA-POO as a function of the number of sampled poses prior to PPO Performance increases with the number of generated poses, with higher sampling yielding a greater proportion of low RMSD predictions.
Molecules with RMSD 2 (%)
90
les with RMSD 1.5A 189)
80
70
80
60
Melecue
70
FMA
50
FMA
FMA-PO
45
FMA-PO
10
10
Number of Poses
Number of Poses
Figure S12: Effect of the number of generated poses prior to PO on the pose accuracy of FMA--P and PM BlinnDockBench.
18

---

Examples
Template: PDB SQCY Query: PDB 5QCO
Template: PDR 1KVO Query: PDB 1J1A
Template: PDR 1LRU
Softwares
Query: PDB 1G27
FMA-PO
RMSD 0.85
RMSD 0.75 Á
RMSD 0.74 A
FMA-PO+
RMSD 0.72
RMSD 0.73 A
RMSD 0.73 À
FitDock
RMSD 4.15
RMSD 1.41 Á
RMSD 0.62 A
LSalign
RMSD 5.71
RMSD 2.39 A
RMSD 1.49 À
ROSHAMBO
RMSD 2.13 À
RMSD 7.81 À
RMSD 3.53 A
rDock
RMSD
RMSD 8.04 À
RMSD 4.29 À
Vina
RMSD 8.02
RMSD 0.97 Á
RMSD 4.12 À
Figure S13: Comparison predicted binding poses of various ligands using 3D molecular
alignment and docking methods. The crystallized protein and ligand are shown in grey. The first example is based on PDB entry SQCO, corresponding to the human Beta-secretase (BACEI) ), co-crystallized with macrocyclic compound [Parks et al.) 2020). using the PDB entry 5QCY (Parks et al. 2020] as template. The second structure is based on PDB entry 1J1A, corresponding to the pancreatic secretory phospholipase A2 co-crystallized with an inhibitor (Hansford et al. 2003 using the PDB entry IKVO [Cha et al. 1996] as template. The third structure is based on PDB entry polypeptide deformylase from Escherichia coli co-crystallized with an inhibitor [Clements et al.) 2001], using the PDB entry ILRU [Guilloteau et al.) [2022 as template.
1G27, corresponding
The quality of the predicted poses was assessed by computing FeMMDrellativ to the crystallized ligand conformation.
19


Reviews:
[{"review_id": "vBvhlWdeEx", "reviewer": "Reviewer_k1u9", "summary": "This paper proposes FMA-PO, a two-step method for ligand 3D pose prediction using flow matching for initial alignment and differentiable optimization for pose refinement. It introduces a new benchmark (AlignDockBench) and shows competitive results compared to docking and alignment baselines.", "questions": "My main concern is on the insufficient analysis of two components: the alignment module and the pose optimization module.\n\nFrom my perspective, a key open question is whether the proposed neural network-based ligand alignment outperforms traditional alignment strategies. It would be helpful to compare with classical or widely used alignment methods, such as:\n* KCOMBU [1]\n* The shape alignment algorithm used in FitDock [2]\n* Schrödinger’s shape-based alignment approach [3]\nEven if direct benchmarking is not feasible for all of them, some discussion or rationale for the neural approach (e.g., accuracy vs. speed trade-offs) would strengthen the paper.\n\nTo further assess the value of the proposed pose optimization (PO) stage, a simple but informative experiment would be to use the alignment generated by the current method, followed by pose refinement using FitDock's optimization network (or vice versa). This would help evaluate the robustness and modularity of each stage.\n\nMisc:\n*  The paper mentions modules like MHAwithEdgeBias and PointSetAttentionwithEdgeBias but doesn’t explain them in enough detail. Brief architectural or pseudo-code descriptions would help.\n*  Some hyperlinks in the manuscript are invalid or incomplete. Please check and fix them for clarity.\n*  A relevant citation is missing: the authors should consider citing GroupBind [4], which is very relevant to template-guided modeling.\n\nOverall:\n\nWhile the direction of the work is promising, the current version lacks sufficient analysis of its components and omits comparisons to standard baselines. The contributions are somewhat difficult to isolate. With additional analysis and explanation, I would be more inclined to support acceptance in the future.\n\n-----\nReferences:\n\n[1] Kawabata, T., & Nakamura, H. (2014). 3D flexible alignment using 2D maximum common substructure: dependence of prediction accuracy on target-reference chemical similarity.\n\n[2] Yang, X., Liu, Y., Gan, J., Xiao, Z. X., & Cao, Y. (2022). FitDock: protein–ligand docking by template fitting. Briefings in Bioinformatics, 23(3).\n\n[3] Sastry, G. M., Dixon, S. L., & Sherman, W. (2011). Rapid shape-based ligand alignment and virtual screening method based on atom/feature-pair similarities and volume overlap scoring. Journal of Chemical Information and Modeling, 51(10), 2455–2466.\n\n[4] Guan, J., et al. (2025). Group ligands docking to protein pockets. ICLR 2025.", "limitations": "N/A", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Pros:\n\n* Tackles an important problem in drug design: predicting ligand poses in the presence of a known co-crystallized template. \n* Provides a new benchmark dataset, which could be valuable to the community. \n* The proposed method shows good experimental results on challenging cases with low template similarity.\n\nCons:\n*  The FMA module is trained without incorporating protein structural information, yet the benchmark labels are derived from co-crystallized complexes that inherently involve protein context. This discrepancy could introduce bias or limit generalizability. A discussion of this mismatch—and potentially experiments adding protein context into FMA—would be useful.\n*  The proposed method involves two stages: ligand alignment and pose optimization. However, the contribution of each stage to the overall performance is not quantified. I encourage the authors to include ablation experiments to isolate the benefit of each stage.", "was_revised": true, "final_justification": "My concerns are well addressed during the rebuttal period.", "rebuttal": "We thank the reviewer for the feedback and evaluation of our method. We\nprovide detailed answers in the following.\n***\n> No protein structural information in training while the benchmark labels are derived from co-crystallized complexes that inherently\ninvolve protein context. This discrepancy could introduce bias or limit generalizability. A discussion of this mismatch—and potentially\nexperiments adding protein context into FMA—would be useful:\n\n\nIncorporating protein structural information was not part of the\noriginal design of FMA, conceived as a molecular alignment algorithm\nindependent of the receptor context. We acknowledge that using co-crystallized complexes as ground truth introduces an implicit receptor context. However, this setup is\nnecessary to define ground truth aligned ligand pairs, especially in cases involving chemically dissimilar ligands. \n\nWhile the initial formulation of FMA was protein-agnostic, the\nintroduction of the protein pocket during the PO phase represents a\nfirst step toward integrating receptor information. We fully agree with\nthe reviewer that extending FMA to directly incorporate receptor context\nis a promising research direction. We are actively developing and\ntraining such a version of the model and consider this an exciting\navenue for future work. In the revised manuscript, we will expand the\ndiscussion section to better emphasize this perspective and acknowledge\nthe potential benefits of explicitly integrating protein structure into\nFMA.\n\n***\n\n> Is the proposed neural network-based ligand alignment outperforms traditional alignment strategies ?\n\n- **KCOMBU.** We evaluated `fkcombu` on AlignDockBench using the same\n  protocol as FitDock and LS-align: 10 conformers per ligand were\n  aligned independently, and the best pose (lowest total energy\n  `Etotal`) was selected. We tested both alignment modes, **Atom\n  Matching** (`-E A`) and **Volume Overlap** (`-E V`), using flexible\n  search (`-S F`) and providing the protein structure (`-P`).\n\n- **FitDock.** In addition to the SB mode of FitDock (v1.0.9) already\n  included in our benchmark, we also ran the LB mode to directly compare\n  its ligand-based alignment against FMA.\n\n- **Schrödinger’s Shape-Based Alignment.** Unfortunately, we could not\n  include Schrödinger’s molecular alignment software in our benchmark,\n  as it is proprietary and not publicly available.\n\nIncluding FitDock, LS-align, ROSHAMBO, and now KCOMBU offers a\nmeaningful comparison with state-of-the-art shape-based alignment\nstrategies. We report both the alignment performance and execution time\nof each method in table 1. Among these,\nthe volume overlap mode of `fkcombu` achieved slightly higher success\nrates than FitDock and LS-align, but was still substantially\noutperformed by FMA. This highlights the benefit of developing a neural\napproach to molecular alignment. These results and the corresponding\ndiscussion will be included in the revised manuscript.  \n  \n\n ***\n### Table 1: Comparison of Ligand Alignment Methods on AlignDockBench  \n\n| **Method**         | N Aligned Molecules | Mean RMSD (Å ↓)      | % of Molecules with RMSD < 2Å (↑) | Avg. Runtime (s) |\n|:---|:--:|:--:|:--:|:--:|\n| FMA*           | 369/369             | 1.97 ± 1.36     | 64.77                         | 0.83             |\n| LSalign            | 368/369             | 2.54 ± 2.00      | 54.35 / 54.2                  | 5.67             |\n| ROSHAMBO*      | 369/369             | 2.87 ± 2.09      | 30.35                         | 4.90             |\n| FitDock LB         | 365/369             | 2.68 ± 2.26      | 54.52 / 53.93                 | 15.24            |\n| FitDock SB         | 313/369             | 2.93 ± 3.73      | 53.67 / 45.53                 | 19.71            |\n| fkcombu AM         | 365/369             | 3.46 ± 2.83      | 38.63 / 38.21                 | 31.95            |\n| fkcombu VO          | 321/369             | 2.72 ± 2.26      | 56.07 / 48.78                 | 48.98            |\n\n\\* denotes GPU-accelerated methods.\n***\n\n>The contribution of each stage to the overall performance is not\nquantified. I encourage the authors to include ablation experiments to\nisolate the benefit of each stage:\n\n\nWe performed ablation studies on AlignDockBench to quantify the\ncontribution of each stage:\n\n1.  **FMA’s contribution (Table 2):**\n    We generated 10 candidate poses per method (FMA, RDKit‑centroid,\n    Vina, LS‑align, FitDock‑LB), applied PO to each, and selected the\n    top‑ranked pose. The RDKit‑centroid baseline places a random\n    conformer at the binding‑site center. FMA-PO+ consistently yields the\n    lowest RMSD among all alternatives, indicating that FMA is the best\n    initialization strategy for PO and that the accuracy of the inital conformation is crucial.\n\n2.  **PO’s contribution (Table 3):**\n    PO consistently reduced RMSD when applied to top poses from other\n    methods, supporting its general effectiveness as a refinement stage.\n    PO also improves chemical plausibility and geometrical validity (see response to reviewer Pn5y - Table 1, 2).\n\n3.  **FMA followed by other methods (Table 4):**\n    Using FitDock, Vina or rDock on FMA outputs degraded performance, likely\n    due to their inability to correct all-atom distortions introduced by\n    FMA. In contrast, PO is designed for full atomic refinement and is\n    better suited to correct such issues.\n\nWe will include these results and the related discussion in the revised\nmanuscript.\n***\n### Table 2:  FMA’s contribution\n\n| **Method + PO** | N Aligned Molecules | Mean RMSD (Å) ($\\downarrow$)  | % of Molecules with RMSD $<$ 2Å ($\\uparrow$) |\n|:---|:--:|:--:|:--:|\n| FMA + PO+ | 369/369 | 1.62 ± 1.33 | 77.78 |\n| rdkit + PO+ | 369/369 | 4.63 ± 1.94 | 10.33 |\n| Vina + PO+ | 368/369 | 1.96 ± 1.87 | 71.47/71.27 |\n| LS-align + PO+ | 357/369 | 2.31 ± 2.07 | 63.31/61.25 |\n| Fitdock LB + PO+ | 365/369 | 2.78 ± 2.41 | 52.6/52.03 |\n***\n### Table 3: PO’s contribution   \n\n| **Method** | N Aligned Molecules | Mean RMSD (Å $\\downarrow$) | % of Molecules with RMSD $<$ 2Å ($\\uparrow$) |\n|:---|:--:|:--:|:--:|\n| FMA | 369/369 | 1.97 ± 1.36 | 64.77 |\n| FMA + PO | 369/369 | 1.86 ± 1.42 | 69.38 |\n| Vina | 368/369 | 3.39 ± 2.81 | 47.28 / 47.15 |\n| Vina + PO | 368/369 | 3.24 ± 2.85 | 52.17 / 52.03 |\n| LS‐align | 368/369 | 2.54 ± 2.00 | 54.35 / 54.20 |\n| LS-align + PO | 357/369 | 2.47 ± 2.15 | 59.66/57.72 |\n| FitDock LB | 366/369 | 2.93 ± 2.36 | 49.73/ 49.32 |\n| Fitdock LB + PO | 366/369 | 2.75 ± 2.38 | 52.88/52.3 |\n***\n### Table 4: FMA followed by other methods \n\n| **Method** | N Aligned Molecules | Mean RMSD (Å $\\downarrow$) | % of Molecules with RMSD $<$ 2Å ($\\uparrow$) |\n|:---|:--:|:--:|:--:|\n| FitDock LB | 366/369 | 2.93 ± 2.36 | 49.73/ 49.32 |\n| FMA + FitDock LB | 366/369 | 3.00 ± 2.30 | 44.69 / 44.44 |\n| FitDock SB | 313/369 | 2.93 ± 3.73 | 53.67 / 45.53 |\n| FMA + FitDock SB | 302/369 | 3.52 ± 4.56 | 46.69 / 38.21 |\n| Vina | 368/369 | 3.39 ± 2.81 | 47.28 / 47.15 |\n| FMA + Vina | 333/369 | 3.55 ± 2.64 | 39.04 / 35.23 |\n| rDock | 369/369 | 4.52 ± 3.28 | 34.42 |\n| FMA + rDock | 356/369 | 4.89 ± 2.95 | 27.53 / 26.56 |\n\n***\n\n> Misc \n\n- All algorithmic pseudocodes specific to our model are provided in\n  Appendix A2 and A3. However, the modules\n  `MHAwithEdgeBias` and `PointSetAttentionwithEdgeBias` are directly\n  taken from the *Neural Plexer* architecture \\[1\\]. Their detailed\n  pseudocodes are already available in the original Neural Plexer paper,\n  specifically as Algorithm S3 (`MHAwithEdgeBias`) and Algorithm S8\n  (`PointSetAttentionwithEdgeBias`). In the revised version of the\n  manuscript we will explicitly indicate the origin of these modules and\n  where their full descriptions can be found. Should the reviewer find\n  it helpful, we could additionally include the corresponding\n  pseudocodes in our supplementary material.\n\n- We will carefully review all hyperlinks in the manuscript to ensure\n  that they are valid and complete.\n\n- We thank the reviewer for bringing this work to our attention. It will\n  be included in the revised manuscript.\n  \n***\nReferences \n\n\\[1\\] Qiao, Z., Nie, W., Vahdat, A., Miller III, T. F., &\nAnandkumar, A. (2024). State-specific protein–ligand complex structure\nprediction with a multiscale deep generative model. Nature Machine\nIntelligence, 6(2), 195-208."}, {"review_id": "3hBP9PWqf4", "reviewer": "Reviewer_XzAP", "summary": "The paper introduces a two-stage framework called FMA-PO, which combines a flow-matching-based model for template-guided ligand pose generation with a differentiable pose refinement module. The method aligns a 2D query molecule to a 3D reference ligand using flow matching, and then refines it based on shape, pharmacophore, internal energy, and optional pocket information. The authors release AlignDockBench, a benchmark dataset specifically for template-based pose generation, containing 369 protein-ligand pairs with co-crystallized templates. This is a valuable contribution on its own, as template-based evaluations are often missing in public datasets.", "questions": "All mentioned in \"Strengths And Weaknesses\"", "limitations": "All mentioned in \"Strengths And Weaknesses\"", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "- The model design is clean and modular. The use of a harmonic prior and graph-based encoding of atom and fragment features allows smooth integration into the FM formulation. This feels like a natural extension of recent works like FlowDock and DiffDock, but with the added benefit of using template ligands instead of receptor pockets.\n\n- The differentiable optimization step is thoughtfully designed. It balances pharmacophore similarity, shape matching, and internal energy terms, which are all differentiable with respect to coordinates. The ability to optionally incorporate protein pocket info is a nice touch and makes the model flexible across use cases.\n\n- Empirical results on AlignDockBench show consistent improvements over several baselines, including FitDock, LS-align, and traditional docking tools like Vina and rDock. The paper reports both mean RMSD and % of poses under 2Å, which are standard and appropriate.\n\n- The improvement in low-similarity and high-flexibility regimes is especially noteworthy. Most alignment tools tend to fail in these settings, and the method's robustness here makes it practically useful.\n\n- The FMA-PO+ variant, where all samples are refined before ranking, offers stronger performance but at the cost of runtime. This tradeoff is acceptable, and it's good that the authors report both variants.\n\n- One thing that's missing is a comparison to recent flow-based or diffusion-based methods like HarmonicFlow or SE(3)-FM. These are the most relevant generative baselines for 3D generation, and even a small subset comparison would help contextualize FMA's performance.\n\n- The use of a Vina-based score in the final scoring function (Sscore) might be a bit confusing, given that Vina was also used as a baseline. It would be good to clarify if this introduces any advantage or bias when comparing methods.\n\n- The paper notes that all runs were done on T4 GPUs and provides runtime comparisons, which is appreciated. Still, there's no mention of how model performance scales with ligand size, does runtime blow up with more rotatable bonds or heavy atoms?\n\n- The benchmark design seems solid, but it would be great to release a few more challenging cases or outlier visualizations, especially where the method succeeds but others fail. This would highlight the strengths of the alignment stage more clearly.", "was_revised": true, "final_justification": "[Final Thoughts]: I will maintain my score.", "rebuttal": "We thank the reviewer for the feedback and evaluation of our method. We provide detailed answers in the following.\n***\n\n> A comparison to recent flow-based or diffusion-based methods like\nHarmonicFlow or SE(3)-FM is missing:\n\n\nWe directly compared FMA to HarmonicFlow using the official settings from the authors’ repository. As shown in Table 1, FMA significantly outperforms HarmonicFlow in both mean RMSD and success rate (% of Molecules with RMSD $<2$Å), even when reporting HarmonicFlow’s best RMSD across the 10 sampled poses. Applying PO to HarmonicFlow improves results but still underperforms FMA, highlighting the higher quality of FMA’s pose distribution and the benefit of using the template ligand to guide docking.\n***\n### Table 1: Comparison to HarmonicFlow\n\n| **Method**                        | N Aligned Molecules | Mean RMSD (Å ↓)     | % of Molecules with RMSD < 2Å (↑) | \n|:----------------------------------|:-------------:|:----------------:|:----------------:|\n| FMA (Top score)                   | 369 / 369     | 1.97 ± 1.36      | 64.77            |\n| FMA (Top RMSD)                    | 369 / 369     | 1.39 ± 0.85      | 84.55            |\n| FMA-PO+ (Top score)           | 369 / 369     | 1.62 ± 1.33      | 77.78            |\n| FMA-PO+ (Top RMSD)            | 369 / 369     | 1.11 ± 0.85      | 91.60            |\n| HarmonicFlow (Top RMSD)          | 356 / 369     | 4.47 ± 2.07      | 2.81 / 2.71      |\n| HarmonicFlow + PO$+$ (Top RMSD)  | 356 / 369     | 3.71 ± 2.22      | 19.94 / 19.24    |\n\n\n***\n\n> The use of a Vina-based score in the final scoring function (Sscore) might be a bit confusing, given that Vina was also used as a baseline. It would be good to clarify if this introduces any advantage or bias when comparing methods.\n\nLike most pose generation methods, our approach outputs multiple candidate conformations, which necessitates a scoring function to rank and select the final pose. Each baseline method we compare against uses its own internal scoring mechanism for this selection, as the Vina score for Vina. We opted for a simple scoring function based on shape overlap, pharmacophore similarity, and Vina’s docking score. The inclusion of the Vina score was motivated by the desire to introduce a structure-based component into the selection process, thereby accounting for receptor–ligand interactions. We evaluated the influence of the $\\mathcal{S}\\_\\text{Vina}$ component in the total score $\\mathcal{S}\\_{\\text{score}}$ by systematically ablating it across three key configurations: FMA, FMA-PO, and FMA-PO$+$. The results are summarized in Table 2.\n\n- For FMA, removing $\\mathcal{S}\\_\\text{Vina}$ has no impact on performance.\n\n- For FMA-PO (i.e., scoring of FMA poses and PO applied to the\n  top-ranked pose), removing $\\mathcal{S}\\_\\text{Vina}$ slightly improves mean\n  RMSD.\n\n- In the FMA-PO$+$ configuration (i.e., PO applied to all poses, and\n  scoring of optimized poses), we observe a modest but consistent\n  contribution from $\\mathcal{S}\\_\\text{Vina}$ : removing it reduces the $RMSD<2$Å\n  success rate from $77.78\\%$ to $75.61\\%$.\n\nThese results indicate that Vina scoring provides limited benefit when\napplied to unoptimized poses (FMA or FMA-PO), but can help select better\ncandidates among refined poses (FMA-PO$+$). Our method still outperforms\nall baselines without using the Vina score in\n$\\mathcal{S}_{\\text{score}}$. In future work, we plan to develop a\ndedicated learned scoring module integrated directly into FMA via a\nconfidence prediction head, to further improve pose selection. We will\nclarify this point more explicitly in the revised version of the\nmanuscript.\n***\n### Table 2: Vina contribution to $\\mathcal{S}_{\\text{score}}$\n\n| **Method**    | Vina in $\\mathcal{S}_{\\text{score}}$ | Mean RMSD (Å ↓)     | % of Molecules with RMSD < 2Å (↑) |\n|:-------------|:-------------------------------:|:---------------:|:----------------:|\n| FMA          | Yes                             | 1.97 ± 1.36     | 64.77            |\n| FMA          | No                              | 1.96 ± 1.35     | 64.77            |\n| FMA-PO       | Yes                             | 1.86 ± 1.42     | 69.38            |\n| FMA-PO       | No                              | 1.81 ± 1.40     | 69.38            |\n| FMA-PO$+$    | Yes                             | 1.62 ± 1.33     | 77.78            |\n| FMA-PO$+$    | No                              | 1.68 ± 1.38     | 75.61            |\n***\n\n\n> There’s no mention of how model performance scales with ligand\nsize—does runtime increase with more rotatable bonds or heavy atoms? \n\n\nWe analyzed runtime as a function of ligand size for both FMA and PO. As shown in Table 3, PO (2.7 s per pose, run on CPU) is slower than FMA (0.84 s for 10 poses, run on GPU). In both cases, runtime increases moderately with the number of heavy atoms and rotatable bonds (Pearson correlation ≈ 0.2), without signs of exponential growth.\n\nWe will include runtime vs. ligand size plots in the revised manuscript to better illustrate these trends (not shown here due to NeurIPS figure restrictions).\n\n***\n### Table 3 : Runtime\n| Method | Average Runtime (s)               | Pearson correlation w/ the number of heavy atoms | Pearson correlation w/ the number of rotatable bonds |\n|:-----------|:--------------------------:|:------------:|:----------------:|\n| FMA (GPU)    | 0.84 (for 10 poses)        | 0.20         | 0.23             |\n| PO  (CPU)       | 2.7 (for 1 pose)           | 0.19         | 0.23             |\n***\n\n\n\n> The benchmark design seems solid, but it would be great to release a few more challenging cases or outlier visualizations, especially where the method succeeds but others fail:\n\n\nWe fully understand the reviewer’s interest in seeing additional challenging or outlier cases, especially those where our method demonstrates superior robustness. We initially believed that the three examples provided in Figure S9 would adequately serve this purpose.\nThese include:\n\n- An alignment case involving a macrocyclic compound,\n- A very flexible ligand with 47 heavy atoms and 17 rotatable bonds,\n- A metalloprotein-ligand complex where the ligand is coordinated to a metal atom.\n\nEach of these was selected to highlight specific and difficult alignment challenges, and where our method still performs successfully. We will enrich the supplementary material with additional examples."}, {"review_id": "Kmz4yWi8dx", "reviewer": "Reviewer_Pn5y", "summary": "This paper introduces a FM-based method for template-based ligand docking. First, authors formulate the ligand conformer generation task conditioned on the template 3D structure with flow matching. Next, authors propose the pose optimisation (PO) algorithm that refines the generated pose using shape and colour similarity and additional pocket constraints. Authors evaluate the method on a newly curated  benchmark AlignDockBench and show that the proposed method outperforms other structure-based and ligand-based approaches.", "questions": "1. My main concern is about the quality of the generated molecules. While I agree that the ultimate metric in this task is RMSD, I believe that the high quality of the designed conformations is the necessary condition to meet - even before computing RMSD. Besides, the proposed PO has multiple objectives some of which are directly connected to the molecule quality (i.e., steric clashes and strain energies). Based on this, I have two comments:\n - (1.1) In my opinion, the work would benefit a lot from an additional subsection where the authors focus on the quality metrics of the generated poses: i.e. what are the distributions of strain energies for FMA and FMA-PO? how do they compare with the reference molecules and with other methods? same for steric clashes. For future work I would also recommend to look at GenBench3D (https://arxiv.org/abs/2407.04424) - I find it very neat for measuring the 3D quality of generated molecules.\n - (1.2) I see that in the Appendix authors report PB-validity values and they are not very high. I would suggest to focus on these problems and incorporate additional terms in the refinement objective that would improve these values.\n\n2. The proposed PO consists of four terms but I found ablation studies only for the pocket term. I would suggest to do ablation studies for all four to clearly understand the importance of each of them.\n\n3. How strong is contribution of S_Vina in the final S_Score?\n\n4. How is pharmocophoric complementarity between protein and ligand computed? For example, a hydrogen bond between protein and ligand would be represented by a pair of \"complementary\" pharmacophores. But depending on the relative orientation of these pharmacophores a hydrogen bond may or may not exist.\n\n5. Why is protein pocket input always labeled as optional? To me pocket looks like an essential component for this task.\n\n6. How were the weights in Table S2 tuned?", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "- Strengths: clear formulation and presentation, new benchmark, good results (in terms of RMSD).\n- Weaknesses: apparently low quality of the generated structures and insufficient ablation studies (see Questions).", "was_revised": true, "final_justification": "My concern about the quality of the generated molecules was addressed and I am happy to raise my score.", "rebuttal": "We thank the reviewer for the feedback and evaluation of our method. We\nprovide detailed answers in the following.\n***\n> Q1.1 : What are the distributions of strain energies and steric clashes ?\n\nTo comply with NeurIPS policies, we cannot include figures in the\nresponse, but we have prepared several plots that will be added to the\nrevised manuscript.\n\n- Table 1 reports the strain energy, as defined by GenBench3D, per quantiles for each\nmethod. FMA yields higher strain energies, due to the absence of the PO\nmodule. While unrealistic conformations are a known limitation of deep\nlearning models \\[PoseBusters\\], this was one of the key motivations for\nintroducing our PO module. Both FMA-PO and FMA-PO+ reduce strain energy compared to FMA.\n\n- Table 2 reports the number of molecules\nexhibiting clashes with protein, per method. FMA suffers from\nsignificantly more clashes, due to the absence of pocket conditioning.\nFMA-PO and FMA-PO+ reduce the number of clashes, confirming the\neffectiveness of the PO module in improving structural plausibility.\n\n***\n\n### Table 1: Strain energy (kcal/mol) quantiles across methods.\n\n| **Method**             | **10%** | **25%** | **50%** | **75%** | **90%** | \n|:-----------------------|:-------:|:-------:|:-------:|:-------:|:-------:|\n| FMA                    |   55    |   82    |   157   |   400   |  1465   |\n| FMA-PO                 |   17    |   24    |   37    |   61    |   214   |\n| FMA-PO+                |   16    |   21    |   32    |   48    |   107   |\n| Vina                   |    8    |   15    |   26    |   45    |   70    |\n| FitDock                |   24    |   32    |   57    |   97    |   306   |\n| Co-crystallized ligand |   11    |   14    |   20    |   29    |   41    |\n***\n\n\n### Table 2: Number of molecules with protein clashes per method.\n\n| **Method**             | **1 clash** | **2 clashes** | **≥ 3 clashes** |\n|:-----------------------|------------:|--------------:|---------------------:|\n| FMA                    |          37 |            16 |                   20 |\n| FMA-PO                 |          35 |             9 |                    7 |\n| FMA-PO+                |          21 |             6 |                    2 |\n| Vina                   |           1 |             0 |                    0 |\n| FitDock                |           7 |             5 |                    4 |\n| Co-crystallized Ligand |           0 |             0 |                    0 |\n\n\n***\n\n> Q1.2 : Incorporate additional terms in the refinement objective that would improve PB-validity.\n\nWe first correct a typo in the manuscript: PB‑validity for FMA‑PO was\nincorrectly reported as 39%; the correct value is 51% (see Figure S6,\nAppendix D).\n\nAs pointed out, improving PB‑validity is crucial. We found most failures\nstem from protein clashes, so we added a Vina‑style repulsive clash\npenalty to the PO objective:\n\n$$\n\\text{InterRepulsiveTerm} = \\log\\left(\\sum\\_{\\substack{(i,j) \\\\\\\\  d\\_{ij} < r^{\\\\text{vdw}}\\_{ij}}} \\frac{1}{d\\_{ij}^6} - \\sum\\_{\\substack{(i,j) \\\\\\\\ d\\_{ij} < r^{\\text{vdw}}\\_{ij}}} d\\_{ij}\\right)\n$$ \nwhere $d\\_{ij}$ is the interatomic distance between ligand atom $i$ and pocket atom $j$, and\n$r^{\\text{vdw}}\\_{ij}$ the sum of van der Waals radii of the two atoms.\n\nA single additional refinement step with this term alongside internal\nenergy reduces clashes (see Table 3) and moves outputs toward more\nphysically plausible conformations.\n***\n### Table 3: Number of molecules with protein clashes, before and after clash optimization in PO.\n\n| **Method** | **1 clash** | **2 clashes** | **≥ 3 clashes** |\n|:---|---:|---:|---:|\n| FMA-PO | 35 | 9 | 7 |\n| FMA-PO w/ clash opt. | 6 | 8 | 6 |\n| FMA-PO+ | 21 | 6 | 2 |\n| FMA-PO+ w/ clash opt. | 4 | 3 | 5 |\n\n\n***\n\n> Q.2: The proposed PO consists of four terms but I found ablation studies only for the pocket term. I would suggest to do ablation studies for all four to clearly understand the importance of each of them.\n\nWe provide ablation results for all four components of the PO objective\nin Table 4.  In addition, Table 5 compares the number of protein clashes between FMA-PO+  and its FMA-PO+ without the pocket . These results will be included and discussed in the final manuscript to\nclarify the role of each component.\n***\n### Table 4: Ablation study of PO loss terms\n\n|                                              | Mean RMSD (Å ↓)     | % of Molecules with RMSD < 2Å (↑) |\n|:---------------------------------------------|:-----------:|:-----:|\n| FMA                                          | 1.97 ± 1.36 | 64.77 |\n| FMA-PO                                       | 1.86 ± 1.42 | 69.38 |\n| FMA-PO w/o $\\mathcal{S}_{STS}$                | 1.98 ± 1.38 | 63.96 |\n| FMA-PO w/o $\\mathcal{S}_{PTS}$                | 1.86 ± 1.38 | 67.48 |\n| FMA-PO w/o $\\mathcal{S}_{\\text{pocket}}$      | 1.46 ± 1.41 | 67.75 |\n| FMA-PO$+$ w/o $\\mathcal{E}_{\\text{internal}}$ | 2.8 ± 0.91  | 13.82 |\n| FMA-PO$+$                                    | 1.62 ± 1.33 | 77.78 |\n| FMA-PO$+$ w/o $\\mathcal{S}_{STS}$             | 1.85 ± 1.32 | 66.67 |\n| FMA-PO$+$ w/o $\\mathcal{S}_{PTS}$             | 1.71 ± 1.33 | 74.25 |\n| FMA-PO$+$ w/o $\\mathcal{S}_{\\text{pocket}}$   | 1.70 ± 1.39 | 75.61 |\n| FMA-PO$+$ w/o $\\mathcal{E}_{\\text{internal}}$ | 2.98 ± 1.26 | 14.09 |\n\n***\n\n### Table 5: Number of molecules with protein clashes\n\n| **Method** | **1 clash** | **2 clashes** | **≥ 3 clashes** |\n|:---|---:|---:|---:|\n| FMA-PO+ | 21 | 6 | 2 |\n| FMA-PO+ wo/ pocket | 36 | 10 | 10 |\n\n***\n\n\n\n> Q.3 : How strong is contribution of S_Vina in the final S_Score?\n\nWe evaluated the influence of the $S\\_\\text{Vina}$ component in the total\nscore $\\mathcal{S}\\_{\\text{score}}$ by systematically ablating it across\nthree key configurations: FMA, FMA-PO(i.e., scoring of FMA poses and PO\napplied to the top-ranked pose), and FMA-PO$+$(i.e., PO applied to all\nposes, and scoring of optimized poses). The results are summarized in\nTable 6. These results\nindicate that Vina scoring provides limited benefit when applied to\nunoptimized poses (FMA or FMA-PO), but can help select better candidates\namong refined poses (FMA-PO$+$). Our method still outperforms all\nbaselines without using the Vina score in $\\mathcal{S}\\_{\\text{score}}$.\n***\n\n### Table 6: Vina contribution to $\\mathcal{S}\\_{\\text{score}}$ \n\n|                                 |Vina in $\\mathcal{S}\\_{\\text{score}}$  |Mean RMSD (Å ↓)| % of Molecules with RMSD < 2Å (↑) |\n|:--------------------------------|:---:|:-----------:|:-----:|\n| FMA                             | Yes | 1.97 ± 1.36 | 64.77 |\n| FMA                             | No  | 1.96 ± 1.35 | 64.77 |\n| FMA-PO                          | Yes | 1.86 ± 1.42 | 69.38 |\n| FMA-PO                          | No  | 1.81 ± 1.40 | 69.38 |\n| FMA-PO+                      | Yes | 1.62 ± 1.33 | 77.78 |\n| FMA-PO+                      | No  | 1.68 ± 1.38 | 75.61 |\n\n\n\n***\n\n> Q.4 : How is pharmocophoric complementarity between protein and ligand computed? For example, a hydrogen bond between protein and ligand would be represented by a pair of \"complementary\" pharmacophores. But depending on the relative orientation of these pharmacophores a hydrogen bond may or may not exist.\n\nThe concept of pharmacophoric complementarity in our pose optimization\n(PO) process is implemented by maximizing the overlap between\ncomplementary pharmacophoric Gaussians in the presence of an internal\nenergy term and a steric clash penalty. Specifically, the Hydrogen Bond\nDonors (HBD) includes an explicit hydrogen atom, and the Hydrogen Bond\nAcceptors (HBA) is a complementary features, as Cation and Anion\nfeatures are.\n\nIn our PO approach, the geometry of hydrogen bonds is oriented by the\ncombined effect of the three key components:\n\n- **Pharmacophoric Gaussian placement:** A Gaussian sphere labeled as an\n  HBD is placed on the hydrogen atom of a donor group. The PO\n  optimization maximizes the overlap between this donor Gaussian and a\n  complementary HBA Gaussian from the pocket (via the $S_{\\text{PTS}}$\n  term), reducing the donor–acceptor distance and favoring the\n  near-linear X–H$\\cdots$X geometry.\n\n- **Internal energy regularization:** An internal energy term based on\n  GAFF2 is used in the PO loss and maintains chemically plausible\n  geometries, in particular the C–X–H angles, and the distance between the heavy atoms.\n\n- **Steric clash penalty:** The  $-S\\_{\\text{PTS}}$ term between ligand and pocket penalizes excessive Gaussian overlap, preventing the system from favoring unrealistic geometries.\n\n***\n> Q.5 : Why is protein pocket input always labeled as optional?\n\nThe protein pocket provides valuable structural information and is used\nin PO when available. However, in many real-world drug discovery\nsettings, such as ligand-based virtual screening or *de novo*\ngeneration, the protein structure is not always known or used. To\nsupport these scenarios, we designed FMA and FMA-PO to remain effective\nwithout pocket input. The *optional* label reflects this flexibility and\nbroad applicability across both structure-based and ligand-based\nworkflows.\n***\n> Q.6 : How were the weights in Table S2 tuned?\n\nThe weights of the loss terms were empirically tuned using a validation\nset of ten diverse protein–ligand complexes from the training data. For\neach term—shape similarity, pharmacophoric complementarity, steric clash\npenalty, and internal energy regularization—we explored multiple\nweightings. The final values were chosen based on convergence behavior,\npose quality, and RMSD across the validation set."}, {"review_id": "8i9YE01suC", "reviewer": "Reviewer_9yAh", "summary": "The authors introduce a two-step approach for molecular pose generation. Given a template (such as the crystalized version of a ligand), they use flow matching to generate an initial guess for conformations. In a second step, this is then optimized with a differentiable approach that includes biochemical properties (such as the energy) and can also include the binding pocket if the aim is docking. This approach can be seen as a hybrid of a structure-based and ligand-based method. They also introduce a benchmark for template-based docking with broader and more realistic settings.", "questions": "1. The authors reported standard deviations in their main results (table 1), however, they are often quite large and it is not particularly clear whether their method is actually better. It seems like FMA-PO+ is more robust and shows to have a smaller standard deviation. Could you report the actual distributions, e.g., the CDF showing how many ligands have an RMSD of < x? This would make it easier to compare the methods and quantify the results. \n\n2. It was not particularly clear to me how the flow matching sampling works in detail. From figure 2 it seems like the crystallized ligand is used as a conditioning of the NNET that is present across all $t$. However, if this is the case, what target distribution are you using during training? \n\n3. How does each part of your method (i.e., flow matching and refinement) contribute to the overall results? Did you test whether samples generated with your flow matching also improves other energy-based refinement algorithms such as VINA? \n\n4. In Appendix D.5.1 you compared your method with and without pocket information. In table S5, it seems like FMA-PO with pocket seems to perform worse when having pocket information. I would have assumed the score to be better. Could you explain or do you have an intuition for this discrepancy?", "limitations": "For the most part, the authors have adequately discussed the limitations of their work. However, I would have like more discussion about the runtime and whether the performance could be improved for the method to be suitable for large screens.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "The ideas presented in the paper are discussed and demonstrated in detail and an extensive appendix is provided containing a variety of technical details. Generally, the paper is well written and easy to follow, however it took some time to understand the specific flow matching setup they were using and how the model is conditioned on the template. Improving figure 1 might go a long way in making the paper more accessible and easier to digest.\n\nThe main issue I see with the paper is that it is lacking a bit of focus. They introduce three (relatively independent) parts: A flow matching model, a refinement procedure, and the benchmark dataset. While the flow matching part itself is not particularly novel, combining it with the refinement procedure demonstrates improvements is. However, it is not particularly clear / discussed enough how much the flow matching vs refinement contributes to the results. Discussing this in more detail (maybe both parts are equally needed), could help distilling the focus of the work.\n\nApart from that, the authors have discussed their work in detail and especially the discussion in section 5 helps to put the results into context.", "was_revised": true, "final_justification": "In the initial submission, the paper lacked a clear focus. It was difficult to assess which components of the proposed method were driving the observed improvements, or whether all parts were necessary. Additionally, their main results just included RMSD values with certain cutoffs, without any cumulative distributions reported. This made it challenging to fully evaluate the performance.\n\n\nHowever, with thanks to the comments from the authors, the new results now include additional comparisons, including ablations with existing methods such as VINA or more detailed results. The authors have also adequately addressed critical points raised by the other reviewers, such as the addition of steric clashes which is important to study.\n\nGiven these improvements and the thorough responses to the key concerns raised during the review process, I am increasing my score to 4. I believe the paper is now above the acceptance threshold.", "rebuttal": "We thank the reviewer for the feedback and evaluation of our method. We\nprovide detailed answers in the following. To clarify the FM\narchitecture and conditioning, we prepared a detailed FMA pipeline\nfigure, which will be included in the final manuscript (can’t include\nfigure here due to NeurIPS policy).\n***\n> Q1 : Could you report the actual distributions, e.g., the CDF showing how many ligands have an RMSD of < x? \n\nPer the suggestion, we report RMSD CDFs in\nTable 1; the corresponding plot will appear\nin the final manuscript.\n***\n### Table 1 : Cumulative distribution of RMSD values: percentage of molecules with RMSD below different thresholds.\n\n\n| **Method** | \\<0.5 Å(%) | \\<1.5 Å(%) | \\<2.0 Å(%) | \\<3.0 Å(%) | \\<4.0 Å(%) | \\<8.0 Å(%) |\n|:-----------|:----------:|:----------:|:----------:|:----------:|:----------:|:----------:|\n| FMA        |     0      |     40     |     60     |     90     |     90     |    100     |\n| FMA-PO     |     10     |     50     |     70     |     80     |     90     |    100     |\n| FMA-PO+    |     10     |     60     |     80     |     90     |     90     |    100     |\n| FitDock    |     0      |     40     |     50     |     70     |     70     |    100     |\n| LSalign    |     0      |     30     |     50     |     80     |     80     |    100     |\n| ROSHAMBO   |     0      |     30     |     50     |     70     |     80     |    100     |\n| Vina       |     0      |     40     |     50     |     60     |     70     |     90     |\n| rDock      |     0      |     20     |     30     |     50     |     50     |     80     |\n\n\n***\n\n> Q2 : It was not particularly clear to me how the flow matching sampling works in detail. From figure 2 it seems like the crystallized ligand is used as a conditioning of the NNET that is present across all t. However, if this is the case, what target distribution are you using during training?\n\n**(i) Training dataset construction.** Training requires well‑defined\n(template, query) pairs with ground truth alignment. Each pair consists\nof two different ligands co‑crystallized with the same protein (same\nbinding site). Ground‑truth alignment is defined via protein\nsuperposition: we compute a rigid‑body alignment between the two\nreceptors (Kabsch on C$_\\alpha$ of the binding site), and apply the\nresulting rotation/translation to all atoms of the query complex. This\nplaces both complexes into a common coordinate frame. The transformed\ncoordinates of the query ligand define the target pose for training,\nwhile the transformed coordinates of the template ligand serve as\nconditioning. Please see section 3.4 for training set construction\ndetails.\n\n**(ii) Conditioning on the template ligand.** Conditioning occurs at two\nlevels (See Appendix A3):\n\n- \\(a\\) The encoder processes a joint graph over the 2D molecular graphs\n  of the query and the template, including cross-ligand edges. This\n  joint representation allows the query encoding to attend to the\n  chemical and topological features of the template.\n\n- \\(b\\) The vector‑field network processes the fixed 3D coordinates of\n  the template along with the current (noisy) coordinates of the query\n  at time $t$ when predicting velocity $v_t$ of the query.\n\n**(iii) Flow‑matching training.** We minimize the following objective :\n$$\n\\mathcal{L}=\\mathbb{E}\\_{t\\sim\\mathcal{U}(0,1),\\\\\\ \\mathbf{x}\\sim\\rho\\_t} \\big\\\\\\|\\mathbf{v}\\_\\theta(t,\\mathbf{x}\\mid \\text{template})-\\mathbf{v}\\_t(\\mathbf{x})\\big\\\\\\|^2\n$$\nwhere $\\mathbf{v}\\_\\theta(t,\\mathbf{x}\\mid \\text{template})$ is the\nlearned velocity used to denoise the query at time $t$ conditioned on\nthe template, and $v\\_t$ the analytical velocity mapping the initial\ndistribution to the target one:\n$$\n\\mathbf{v}\\_t(\\mathbf{x}) =  \\mathbf{x}\\_1-\\mathbf{x}\\_0  + \\frac{1-2t}{2\\sqrt{t(1-t)}} \\mathbf{z},\n\\quad \\mathbf{z}\\sim\\mathcal{N}(0,\\mathbf{I}),$$ with $\\mathbf{x}\\_0$ a\nharmonic prior conformation of the query and $\\mathbf{x}\\_1$ the query’s\ncrystal ground‑truth pose.\n\n**(iv) Sampling.** At inference we draw an initial harmonic pose of the\nquery $\\mathbf{x}\\_0$ centered on the template, and integrate the learned\nveolcity with a deterministic Euler solver from $t{=}0\\to1$ (30\nuniform steps), yielding the final pose at $t{=}1$:\n$$\n\\mathbf{x}\\_{t+\\Delta t} = \\mathbf{x}\\_t +\\\\mathbf{v}\\_\\theta\\big(t,\\mathbf{x}\\_t \\mid \\text{template}\\big) \\Delta t\n$$\n***\n> Q3 : How does each part of your method (i.e., flow matching and refinement) contribute to the overall results? Did you test whether samples generated with your flow matching also improves other energy-based refinement algorithms such as VINA?\n\nWe performed ablation studies on AlignDockBench to quantify the\ncontribution of each stage:\n\n1.  **FMA’s contribution (Table 2):**\n    We generated 10 candidate poses per method (FMA, RDKit‑centroid,\n    Vina, LS‑align, FitDock‑LB), applied PO to each, and selected the\n    top‑ranked pose. The RDKit‑centroid baseline places a random\n    conformer at the binding‑site center. FMA+PO consistently yields the\n    lowest RMSD among all alternatives, indicating that FMA is the best\n    initialization strategy for PO and that its accuracy is crucial.\n\n2.  **PO’s contribution (Table 3):**\n    PO consistently reduced RMSD when applied to top poses from other\n    methods, supporting its general effectiveness as a refinement stage.\n    PO also improves chemical plausibility and geometrical validity (see response to reviewer Pn5y - Table 1, 2).\n\n3.  **FMA followed by other optimizers (Table 4):**\n    Using FitDock, Vina or rDock on FMA outputs degraded performance, likely\n    due to their inability to correct all-atom distortions introduced by\n    FMA. In contrast, PO is designed for full atomic refinement and is\n    better suited to correct such issues.\n\nWe will include these results and the related discussion in the revised\nmanuscript.\n***\n### Table 2: FMA’s contribution \n\n| **Method + PO** | N Aligned Molecules | Mean RMSD (Å) ($\\downarrow$)  | % of Molecules with RMSD $<$ 2Å ($\\uparrow$) |\n|:---|:--:|:--:|:--:|\n| FMA + PO+ | 369/369 | 1.62 ± 1.33 | 77.78 |\n| rdkit + PO+ | 369/369 | 4.63 ± 1.94 | 10.33 |\n| Vina + PO+ | 368/369 | 1.96 ± 1.87 | 71.47/71.27 |\n| LS-align + PO+ | 357/369 | 2.31 ± 2.07 | 63.31/61.25 |\n| Fitdock LB + PO+ | 365/369 | 2.78 ± 2.41 | 52.6/52.03 |\n***\n### Table 3: PO’s contribution.  \n\n| **Method** | N Aligned Molecules | Mean RMSD (Å $\\downarrow$) | % of Molecules with RMSD $<$ 2Å ($\\uparrow$) |\n|:---|:--:|:--:|:--:|\n| FMA | 369/369 | 1.97 ± 1.36 | 64.77 |\n| FMA + PO | 369/369 | 1.86 ± 1.42 | 69.38 |\n| Vina | 368/369 | 3.39 ± 2.81 | 47.28 / 47.15 |\n| Vina + PO | 368/369 | 3.24 ± 2.85 | 52.17 / 52.03 |\n| LS‐align | 368/369 | 2.54 ± 2.00 | 54.35 / 54.20 |\n| LS-align + PO | 357/369 | 2.47 ± 2.15 | 59.66/57.72 |\n| FitDock LB | 366/369 | 2.93 ± 2.36 | 49.73/ 49.32 |\n| Fitdock LB + PO | 366/369 | 2.75 ± 2.38 | 52.88/52.3 |\n***\n\n### Table 4: FMA followed by other methods.\n\n| **Method** | N Aligned Molecules | Mean RMSD (Å $\\downarrow$) | % of Molecules with RMSD $<$ 2Å ($\\uparrow$) |\n|:---|:--:|:--:|:--:|\n| FitDock LB | 366/369 | 2.93 ± 2.36 | 49.73/ 49.32 |\n| FMA + FitDock LB | 366/369 | 3.00 ± 2.30 | 44.69 / 44.44 |\n| FitDock SB | 313/369 | 2.93 ± 3.73 | 53.67 / 45.53 |\n| FMA + FitDock SB | 302/369 | 3.52 ± 4.56 | 46.69 / 38.21 |\n| Vina | 368/369 | 3.39 ± 2.81 | 47.28 / 47.15 |\n| FMA + Vina | 333/369 | 3.55 ± 2.64 | 39.04 / 35.23 |\n| rDock | 369/369 | 4.52 ± 3.28 | 34.42 |\n| FMA + rDock | 356/369 | 4.89 ± 2.95 | 27.53 / 26.56 |\n\n***\n\n> Q4 : In Appendix D.5.1 you compared your method with and without pocket information. In table S5, it seems like FMA-PO with pocket seems to perform worse when having pocket information. I would have assumed the score to be better. Could you explain or do you have an intuition for this discrepancy?\n\nThank you for pointing this out. After reviewing the\nablation study table, we found an error in Appendix D.1, Table S5. The\nvalue reported as **1.456** for the *Mean RMSD* of FMA-PO (without\npocket) was actually the *Median RMSD*. The correct *Mean RMSD* is\n**1.884**. With this correction, incorporating the protein pocket yields\na slight improvement rather than a degradation, which aligns with our\nexpectations. You can also find the number of molecules with protein clashes for FMA-PO+ with and without pocket in the response to reviewer Pn5y - Table 5.\n***\n> Discussion about the runtime.\n\nWe agree that runtime is a critical factor for practical applications.\nBecause each molecule is processed independently, scaling across\nmultiple compute instances is straightforward.\n\nTo illustrate this, we report in\nTable 5 the estimated\nruntime and cost of processing various dataset sizes using 100 AWS\n`g4dn.2xlarge` instances in parallel. This setup can be use\nwithin a de novo drug design pipeline,  where screening\naround 50,000 molecules is a realistic and relevant scale. For\nultra-large virtual screening campaigns (e.g., tens or hundreds of\nmillions of molecules), further acceleration and simplification of PO\nwould be required. For example, moving to a batched optimization\nstrategy, rather than optimizing one molecule at a time, could\nsignificantly reduce total runtime.\n\n***\n### Table 5:  Estimated runtime (in hours) and cost (USD) using 100 AWS `g4dn.2xlarge` instances in parallel for different numbers of molecules.\n\n| **Number of molecules** | 50,000 | 10^5 | 10^6|\n|:------------------------|:----------:|:----------:|:----------:|\n| Time FMA+PO (h)         |    0.49    |    0.98    |    9.83    |\n| Cost FMA+PO (\\$)        |     41     |     82     |    826     |"}]

Author rebuttal:

Meta-review: This paper outlines the molecular pose generation, guided by templates. This is an important task in computer aided drug-design, where given a known co-crystallized ligand:target complex, the aim is to generate new candidate ligands informed by this information. The authors present a two-tiered approach to this: one for generation and the second for refinement. While reviewers critiqued the initial submission for unclear statement of design choices and limited ablations among other things, following the rebuttal and discussion period, all reviewers agreed that this work passes the acceptance threshold since it presents a first two-tiered and neural approach to the task at hand, and due to the modularity, it is likely that the individual components of the model can be adopted in other contexts.
Decision: Accept (poster)