ForceFM: Enhancing Protein-Ligand Predictions through Force-Guided Flow Matching
Authors: Huanlei Guo
Song Liu
Bingyi Jing
Venue: NeurIPS 2025 poster ()
Keywords: Molecular Docking; Flow Matching; Energy-Guided Sampling
Primary area: machine_learning_for_sciences
TL;DR: Force-Guided Flow Matching for Molecular Docking

Abstract: Molecular docking is a fundamental technique in structure-based drug discovery, playing a critical role in predicting the binding poses of protein-ligand complexes. While traditional docking methods are generally reliable, they are often computationally expensive. Recent deep learning (DL) approaches have substantially accelerated docking and improved prediction accuracy; however, they frequently generate conformations that lack physical plausibility due to insufficient integration of physical priors. To deal with these challenges, we propose ForceFM, a novel force-guided model that integrates a force-guided network into the generation process, steering ligand poses toward low-energy, physically realistic conformations. Force guidance also halves inference cost compared with the unguided approaches. Importantly, replacing the guiding potential with diverse energy functions-including Vina, Glide, Gnina, and Confscore-preserves or improves performance, underscoring the method's generality and robustness. These results highlight ForceFM's ability to set new standards in docking accuracy and physical consistency, surpassing the limitations of previous methods. Code is available at \url{https://github.com/Guhuary/ForceFM}.

ForceFM: Enhancing Protein-Ligand Predictions through Force-Guided Flow Matching
Huanlei Guo
Song Liu' Bingyi 123+
Department of Statistics and Data Science Southern University of Science and Technology School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen Shenzhen Loop Area Institute
Abstract
Molecular docking a fundamental technique structure- drug discovery, playing critical role in predicting the binding poses of progain-ligaad complexes. While traditional docking methods are generally reliable, they are often compu- tationally expensive. Recent deep learning (DL) approaches have substantially accelerated docking and improved prediction accuracy; however, they frequently generate conformations that lack physical plausibility due insufficient integration of physical priors. To deal with these challenges, we propose ForceFM, a novel force-guided model that integrates force-guided network into the generation process, steering ligand poses toward low-energy, physically realistic conforma- tions. Force guidance also halves inference compared with the unguided approaches. Importantly, replacing the guiding potential with diverse energy cunctions-includdng Vina, Glide, Gnina, and Confscore-press presservsss or improves performance, underscoring the method's generality and robustness. These results highlight ForceFM's ability to set new standards in docking accuracy and physical consistency, surpassing the limitations of previous methods. Code is available at httpps://gt thub. comm/uuuary/Forcee"
Introduction
Molecular docking is critical component of structure- based drug discovery I aiming to predict the predominant binding modes of protein- complexes based on experimentally determined or computationally modeled protein structures and ligands. Traditional docking programs such as AutoDock 4 (2), AutoDock Vina (3) Glide [4. and GOLD [5] use heuristic search algorithms to explore a range of possible ligand conformations. These programs employ scoring functions grounded in physics and chemistry principles to estimate binding strengths and select optimal poses. Despite their effectivvness, these classical methods often involve high computational costs, leading to slow processing and significant resource demands, which limit their applicability in large-scale drug discovery projects. high seghthhouughpt screening scenarios, researchers may need to dock millions of molecules daily. The prohibitive runtime of traditional methods thus significantly constrains their utility in practical pharmaceutical pipelines.
Motivated by the success of deep learning (DL) and geometric learning (GL) in diverse 3D generation tasks in the vision community, recent works have begun to leverage these techniques for molecular docking. This has given rise to two broad categories of DL-based docking approaches. The first category encompasses regression- based models, which directly predict the ligand coordinates in 3D space 16. 7 8 9. The second category relies on generative modeling, producing multiple candidate poses for selection
[10 II [2]. Although these methods significantly improve efficiency
"Corresponding authors: Bingyi Jing (jingby @ sustech.edu.cn).
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Translation Flow
Rotation Flow
Torsion Flow
01
To
C
Co
C.
O
Molecular Docking via Manifold Flow Matching
Conformer generation RDKit
With Intermediate Force Guidance
Improved Energy
RMSD=3.5
Vina Score 10.17 (kcal/mol)
Initialization
RMSD=1.4
Vina Score = 4.18 (kcal/mol)
Figure 1: Overview of ForceFM. The baseline flow matching model operates on translational, rota- tional, and torsional degrees of freedom. By incorporating additional force guidance based on physi- cal principles, ForceFM generates ligands with lower energy. Color scheme: Blue iete--iiiiallztiin... Green ground truth, Red sampled ligand without force guidance, Purple samleed ligand with force guidance.
and accuracy (e.g.. in terms of the root-mean-square deviation, RMSD), notable shortcoming remains: many generated conformations are physically implausible, exhibiting steric clashes or residing in high-energy regions [13], primarily because physical priors under-utilized in the model design.
However, purely data-driven methods often fail to incorporate critical physical constraints, which can lead unphysical poses. real-world drug discovery, low-energy and physically consistent poses are vital. To address this gap and combine the advantages of both traditional physics- based approaches and deep generative methods, we propose novel force called ForceFM. Specifically, ForceFM integrates physics-based priors in the form of guiding force terms derived from multiple scoring functions, including the Vina score 3 Gnina score [14,, Glide score 4. and Confscore [00. By explicitly modeling force-guidance network with these diverse energy functions, our approach steers the generative process toward lower-energy conformations, thereby improving physical plausibility while also improving the sampling efficiency. Moreover, it demonstrates robust generalization blind docking scenarios, showing promising performance on unseen examples. This aligns with the growing demand for generalization in DL-based molecular docking, addressing concerns about overfitting to specific protein or ligand types and broadening its applicability across diverse drug discovery tasks.
flow matching model
In summary, our main contributions are as follows: (1) Innovative Docking Model. We present force-guided flow matching model for molecular docking that integrates deep learning with multiple energy functions (e.g., Vina, Glide, Gnina, Confscore). This hybrid approach combines the flexibility of deep learning with the physical accuracy of energy- based methods, guiding the generative process

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toward low-energy conformations with fewer steps, improving computational efficiency, especially in high- high-throughput screening applications. (2) Comprehensive Benchmark Validations. Extensive experiments on the PDBBind dataset demonstrate that our model outperforms existing methods in both docking accuracy and physical plausibility, consistently generating more realistic ligand poses. Moreover, we evaluate the generalization of our approach across multiple energy functions, confirming its broader applicability in various docking scenarios.
2 Related Works
2.1 Molecular Docking
Molecular docking, or protein-ligand docking, is computational technique for predicting the optimal binding pose of a protein-ligand complex. Traditional approaches, such as AutoDock (2). AutoDock Vina [3] Glide 44, and GOLD [51. use heuristic search algorithms explore possible ligand conformations. These methods rely on physics-based energy functions to evaluate, rank, and refine ligand structures. However, with recent advances, geometric deep learning has emerged as a promising approach for docking predictions. These approaches can be broadly categorized into regression- and sampling-basee -bacd methods.
1) Regression- methods aim to directly predict ligand binding coordinates or refine structures by predicting pairwise atomic distances. Notable methods in this category include EquiBind (6). TankBind [15]. E3Bind
77.. FABind
[]. and KarmaDock [16].
2) Sampling- baasliing- methods generate multiple ligand poses and then optimize select from the sampled conformations 17 TO M.. Although these methods are computationally more demanding than regression bbgre models, they generally yield more accurate predictions.
In addition. Alphafold- achieves huge breakthroughs, but in close-form introduction without details. DeltaDock [18] and HelixDock [19] also obtain competitive results for us. However, they either generate large-scale data with simulators or add external high quality data for the training, which is not fair comparison.
2.2 Guided Generation
In generative modeling, controllable generation essential to align diffusion models with desired outputs. Classifier guidance [20] and classifier-free guidance [21] are prominent approaches that conditionally guide diffusion models, achieving impressive results in applications like text-to-image
22 2
and video generation [24). Recently, Zhou al. (25) adopts an energy-based perspective
to understand the confidence model. FlowAl AB (26) adopts the important physical prior knowledge into the flow model to guide the antibody generation, which not an exact guidance. Lu al. (77 proposed an exact energy guidance policy using a scalar reward function, rather than fixed conditioning, while Wang al. [28] introduced CONFDIFF for protein conformation generation. These advances motivate our proposed exact force guidance strategy, which uses an equivariant network to approximate the intermediate force vector directly.
3 Proposed Method
This section describes our force-guided flow matching framework, ForceFM, which generates physically plausible ligand conformations by integrating physics-based priors into data-driven manifold flow matching approach. Section 3.1 briefly reviews Riemannian Flow Matching, while Section 3.2 introduces our baseline manifold flow matching model that operates on the translational, rotational, and torsional degrees of freedom of ligands. Finally, Section 33 presents our key contribution: force-guided generation strategy that incorporates the different energy function corrective signal to ensure low-energy conformations.
3.1 Preliminaries: Riemannian Flow Matching
Let P(M) represent the space of probability distributions defined on manifold M endowed with a Riemannian metric g. Suppose have data distribution gxx) and prior p(x). We
3

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define a probability path [0,1] + P(M) interpolating between and p1, with corresponding
tangent vector fields (x)) T.M. Flow Matching (FM) 29 30 approximates u, (,(x) by
learned vector field (x), minimizing (f) = E. po (x) - =x(xx]l where || llg is the Riemannian norm and the parameters of Ut- In practice, we use the Conditional Flow Matching (CFM) formulation: (CRFM( = Ex-2((011) I): pı (x [/((x)) - (x(x xx)]( which is easier to compute. Once trained, sampling from the data distribution is performed by integrating the learned ODE 27 Pr (x) = (x())(x)), transforming points from the prior po to
3.2 Baseline: Manifold Flow Matching
To adapt Flow Matching to ligand docking, we note that ligand's pose can be decomposed into three main types geometric transformations [T]: translation, rotation, and torsion angles (internal rotation around rotatable bonds). Each transformation lives on a distinct manifold: Translation in RR, Rotation 50(3) and Torsion angles (5O(2))"" (a hypertorus).
Hence, the ligand pose is represented as _ (C, Tm). where C R 0 SO(3), and [-m, rT. This decomposition naturally leverages the Lie group structures T(3), SO(3), and (0(2) for each respective degree of freedom, aligning well with Riemannian Flow Matching.
3.2.1 Translational Degree of Freedom
To model the translation, we treat the path of the center C₁ as a flow on a Euclidean manifold. We use a vanilla Gaussian flow matching (CFM) approach on this manifold, which employs independent coupling techniques [31 to model the conditional flow:
C = C1 + ()-
where Co ~ (0, o I) is sampled from an isotropic Gaussian (the prior), and C1 is the ground- truth ligand translation. The corresponding CFM objective is
Tar (0) = E..g (x1) (xn) [[ - Ci + Coll.
3.2.2 Rotational Degree of Freedom
To model the probability path of rotation matrix O₂ E SO(3), we adopt 50(3)-CFM
32 as
O =xpo (t logo,
where exp and log are the exponential and logarithmic maps on SO(3), which can be efficiently computed using Rodrigues' formula and the Lic algebra (3). The prior distribution to sample Og is defined as isotropic Gaussian distribution on SO(3) B3 Then the loss is
logo, (Oo)
Lyoi(0 = Er (xx)
(4)
S0(3)
3.2.3 Torsional Degree of Freedom
For a ligand with m rotatable bonds, the torsion angles lie in [-n, T)". For the torus, the manifold is the quotient space In /2 Z, leading to the equivalence relations with period 2n 34 We choose the prior distribution po as the product of standard wrapped normal distribution as:
N
|| ( + 2nd
(T(
I exp
(5)
2
1=1 dEZ
The path TT(To, T)) is then an interpolation on the torus with linear shift to handle 2n periodicities:
34
We approximate the geodesic distance
T/ =(To + 7) mod (2rr) - n,
Me (Th. Ti =( TO + T) mod (2m) - x,
(6)
T. (T6 TI) =To + t us (T/: TI).
The conditional Flow Matching loss is:
Leor (f) E,, a (x1). (xx)) Ue
(xx) (x))) ue ue(TT' T2)

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3.2.4 Baseline Flow Matching Objective
We combine these three losses with respective weights:
L(0) = bar Arot Lrot. + Ator Ltor-
Here, we set At. 1, Arot = Ator 1. After training, sampling is performed by solving the ODE di (x) with Xo drawn from the prior. This baseline approach is purely data-driven, relying on learned distributions of ligand poses, but it does not explicitly ensure low-energy or sterically valid configurations. As we will see, unconstrained flow flow matching can sometimes produce high-energy or overlapping geometries the absence of physical priors.
3.3 Force-Guided Generation
To address the limitations of bascline flow matching and ensure physically valid docking poses, we introduce a force-guided strategy inspired by energy-based diffusion methods [27 (28). Our goal is bias ligand conformations toward low-energy regions of the conformational space by incorporating an additional force term derived from chosen scoring function.
Let q1 (x1) be the distribution generated by our baseline flow model in Section 3.2 and let E (x1) be the energy function for conformation xı given protein y (y is omitted for simplification). We aim to form a Boltzmann-like distribution:
(x x (x1)
where & is an inverse temperature factor controlling the strength of energy guidance. By incorporating this additional energy term. p1 (x1) provides a more accurate estimate and generates ligands that adhere to physical plausibility.
3.3.1 Deriving the Force-Guided Flow
The following theorem suggests force-guided flow from a conditional vector field generate the modified probability distribution.
Theorem 3.1 Given an energy function E1(-) and conditional flow un (x x1) that generates the probability distribution qi (x x1). Assume the guided distribution has the form Pe xc qe (x) exp (x)) and pt. (x x1) == 4e (x x1). Then
log Egi(xi x) [e [e-kEL(xU]] + const,
& (x) Ko
(10)
and the guided distribution (x) will be generated by the flow
Sez qt (x1 x) ue (x x1) exp (-kEi (x1)) dxi
(x(x)
(11)
Sx, 9t (x1 x) exp (-kE, (x1)) dx1
which will generate final distribution p1 (x) xx qi (x) x (x)).
Theorem 3.1 provide method construct the vector field ūr (x) from the conditional vector field un (x x1 and the intermediate energy function & in the closed-form solution. Since we have learned the vector field vxxx), we have the following corollary.
Corollary 3.2 Given an energy function E-(-) and a trained flow vx(x) that generates the probability distribution qt (x). Following the presumption in Theorem 3.1 then the guided distribution Pe(x) x qe (x) exp (x)) is generated by the flow
(x)x (x(x) + rT(
(12)
Sx, (e(x, (x)((xxx)) REE (x.))) and ((xx x1) = Ue (x x, (x).
where (x(
Jx, g. (xi x) exp( [dx
As shown in Theorem 3.1 and Corollary 3.2
incorporating the energy term into the learned flow can be viewed as adding a corrective vector field ry (x) to the baseline vector field vx(x):
xx(x) vx(x) + (x)).
(13)
5

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Algorithm 1:
Training Procedure (Single Epoch) for Force Model
Input:
trained flow network v, energy function (1(), guided network ho foreach 31, y in training set do
Randomly perturb X1 to obtain !!:K
Sample X (Co, Co, TO) ~ po. ((,0 1);
Sample X ~ Px X0, x1) (C
Co. Ci) x pr(O | Ob. 01) x xP((T] To, T));
ex - (xx))
Set w, Σイ=n exp(log 4: (x. xx) k (x:)))
SA.r = We,tr (Ce 0.) Ut Lt,ttr (Xte)
Si,ro = rt O2 0²) vt, ( (x:),
Si, Uor
Tt
ra)
ve (xt):
= |1 xx,)
= misiaal1 1
hho, (xx)
>
Wi 1/3 50(3)
i=
/ (X:)
1 woGr 2::
Update 0 + 0 - Voo..
The correction term (x) accounts for how likely each conformation x, is, weighted by expl-k & (x1)]. In practice, we introduce an additional force network (x) to approximate rx(x). enabling efficient end-to-end training.
Algorithm| [ outlines the single-epoch training procedure. For each training complex (x1.y), we sample K candidate ligand conformations from the random perturbations of and compute weighted residuals Ç based on exp - & (x.)]. The objective is to match hy (xx) to the weighted average of these residuals. Here, the perturbed data is sampled from p1-s(x x1), with 5 (0,0, 0.1) and K is a critical aaper-parameter in our method, as it directly affects the accuracy of the energy landscape estimation during training. A higher K leads to more accurate approximation of this distribution and, consequently, more precise force estimation.
After training, samples can be generated by integrating the modified ODE -x (x(x) + (2), where 17 is a user-defined guidance strength. Larger emphasizes physical energy constraints more strongly, reducing the risk of steric clashes but potentially sacrificing some flexibility.
Experimental Results
4.1 Experiment Settings
Dataset: We utilized protein-ligamt complexes from PDBBind, originating from the Protein Data Bank (PDB) (35. Adopting the time-based splitting in [6), we trained model on 17k complexes up to 2018 and tested on 363 structures in 2019, ensuring no ligand overlaps. This temporal split is favored over molecular scaffold or protein similarity- based methods [36]] 15]. Further details about
the pre-processing steps and construction of heterogeneous graphs are presented in Appendix B
Evaluating metrics: We follow prior works 66 10 and use ligand root-mean-square deviation (RMSD) heavy atomic positions and centroid distance to compare predicted binding structures with ground-truth. The Ligand RMSD) calculates the normalized Frobenius norm of the two corresponding matrices of ligand coordinates. The centroid distance is defined as the distance between the averaged 3D coordinates of the predicted and ground-trute truth bound ligand atoms. In addition, we use the PoseBuster [13 to validate chemical consistency and physical plausibility of the generated ligands.
Implementation Details: All statistics are averaged over three random seeds. We implemented all the models using the open-source Python library Py and e3nn [37], and the experiments were conducted on PC equipped with 4 NVIDIA A 1100-40GB GPUs. The network structures for flow matching model and guidance model are presented in Appendix and the training and inference details with hyper-parameters are listed in Appendix D In the inference stage, to generate initial ligand conformation, we employed the ETKDG algorithm using RDKit, which randomly produces low-energy ligand conformation. we follow common blind docking practice by first predicting

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Ligand RMSD
Centroid Distance
Method
P
% Below
Percentiles,
Belowt
Average
25%
50%
75%
Mean
2A
5 A
25%
50%
75%
Mean
2λ
5À
Runtime (s)
QVINA-W
2.5
7.7
23.7
13.6
20.9
40.2
0.9
3.7
22.9
11.9
41.0
54.6
49
GNINA
2.8
8.7
22.1
13.3
21.2
37.1
1.0
4.5
21.2
11.5
36.0
52.0
146*
SMINA
3.8
8.1
17.9
12.1
13.5
33.9
1.3
3.7
16.2
9.8
38.0
55.9
146
GLIDE
2.6
9.3
28.1
16.2
21.8
33.6
0.8
5.6
26.9
14.4
36.1
48.7
1405*
VINA
5.7
10.7
21.4
14.7
5.5
21.2
1.9
6.2
20.1
12.1
26.5
47.1
205*
EQUIBIND
3.8
6.2
10.3
8.2
5.5
39.1
1.3
2.6
7.4
5.6
40.0
67.5
0.03
TANKBind
2.4
4.0
7.7
7.4
19.3
61.7
0.9
1.7
4.2
5.5
56.5
77.4
0.87
E3Bind
2.1
3.8
7.8
7.2
23,4
60.0
0.8
1.5
4.0
5.1
60.0
78.8
0.44
FABind
1.7
3.1
6.7
6.4
33.1
64.2
0.7
1.3
3.6
60.3
80.2
0.12
FABind+
1.3
2.4
5.3
43.8
73.3
0.5
1.0
2.6
3.5
69.1
86.2
DifiDock
3.6
8.0
7.5
38.4
62.4
1.3
3.2
60.8
79.0
68.1
DiftDock + Vina
1.3
3.2
5.5
3.8
43.5
73.0
0.3
1.2
3.0
4.1
66.1
88.3
45.6
DifiDock + Conf
1.3
3.3
5.5
4.3
42.6
69.1
0.4
1.1
3.1
4.5
65,8
83.2
45.5
DifiDock Gnina
1.3
3.1
4.9
4.2
43.5
70.5
0.4
1.1
2.9
4.4
67.7
86.5
45.5
DiffDock Glide
1.2
3.1
5.7
4.0
45.8
71.2
0.4
1.1
3.2
4.3
67.4
85.7
45.4
Ours
1.3
2.3
5.3
4.2
41.1
73.7
0.5
1.0
2.5
3.1
71.7
89.4
46.9
Ours Vina
4.3
3.8
48.6
78.0
0.9
2.2
76.2
25.3
Ours + Conf
1.2
2.3
5.4
3.3
49.1
76.5
0.3
0.8
2.2
2.2
75.1
92.5
25.1
Ours Gnina
1.2
2.2
5.2
3.1
47.5
75.6
0.4
0.9
2.0
2.4
74.3
91.6
25.1
Ours Glide
1.2
2.1
4.2
3.2
49.5
78.0
0.3
0.9
2.1
1.9
77.1
92.5
25.2
Table PDBBind blind Top-1 self-docking performance. The first quarter contains the results from
traditional docking software, and the second contains recent deep learning-based docking methods The last two lines show the force- grrred results of DifiDock and our baseline model. The symbol "*" means that the method operates exclusively the CPU. The best results shown in bold.
binding pockets with P2Rank (38 and initializing ligand conformations around predicted centers. 40 poses are sampled in the inference stage and they are ranked by using the rank model in (10]
4.2 Molecular Docking Quality Assessment
In our assessment of molecular docking quality, we benchmarked our proposed method against
several well-established methods, including SMINA (39 Quick Vina-W [40]. GLIDE [4, GNINA
14, Autodock Vina 3. EquiBind 6 TANKBind 15 E3Bind 77, DiffDock I0, FABind [8], FABind+ [2]. To demonstrate both the absolute performance of our model and the generality of the proposed force-guided sampling framework, we evaluate two families methods (1) Our base model (Ours) and its energy-gnn -ugdeed variants, and (2) DiffDock with exactly the same guidance procedure, detail for sampling with force guided diffusion model is presented in Appendix[F] This section reports the main results for comparison, the additional results the sensitive analysis guidance strength number of generative samples are presented in appendix
4.2.1 Blind Self-Docking Performance for Seen and Unseen Proteins
Blind self-docking involves docking a flexible ligand to protein without prior knowledge of the binding site, which requires accurate prediction of the ligand's conformation. We observe the notable performance of our ForceFM as shown in Table T By introducing force guidance strategies, both the DiffDock and our baseline models see notable improvements. Specifically, using force guidance results in marked improvement in RMSD and centroid distance metrics. For example, one of the most notable results occurs with Ours + Glide, where the model achieves mean RMSD of 3. 3.2A, a 49.5% success rate below 2A, and impressive 78,0% success rate under the 5À threshold. These figures underscore the positive impact of integrating force guidance on docking accuracy. This model's performance is superior not only in RMSD but also in the overall prediction accuracy when compared to both the baseline models and traditional docking approaches such as Vina and DiffDock. When comparing results across models, it is evident that integrating force-guided strategies (either with Vina, Conf, Gnina, or Glide) improves both the percentile RMSD and the percent below 2Å and

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Ligand RMSD
Centroid Distance Percentiles.
Method
P
% Below
% Below
25%
50%
75%
Mean
2A
5
25%
50%
75%
Mean
2A
5A
QVINA-W
3,4
10.3
28.1
16.9
15.3
31.9
1.3
6.5
26.8
15.2
35.4
47.9
GNINA
4.5
13.4
27.8
16.7
13.9
27.8
2.0
10.1
27.0
15.1
25.7
39.5
SMINA
4.8
10.9
26.0
15.7
9.0
25.7
1.6
6.5
25.7
13.6
29.9
41.7
GLIDE
3,4
18.0
31.4
19.6
19.6
28.7
1.1
17.6
29.1
18.1
29.4
40.6
VINA
7.9
16.6
27.1
18.7
1.4
12.0
2.4
15.7
26.2
16.1
20.4
37.3
EQUIBIND
5,9
9.1
14.3
11.3
0.7
18.8
2.6
6.3
12.9
8.9
16.7
43.8
TANKBind
3,4
5.7
10.8
10.5
3.5
43.7
1.2
2.6
8.4
8.2
40.9
70.8
E3Bind
3.0
6.1
10.2
10.1
6.3
38.9
1.2
2.3
7.6
43.8
66.0
FABind
2.2
3.4
8.3
7.7
19.4
60.4
0.9
1.5
4.7
5.9
57.6
75.7
FABind+
1.7
2.9
8.4
7.2
33.3
63.9
0.8
1.5
4.6
5.4
59.7
77.1
DiffDock
2.8
6.4
16.3
12.0
17.2
42.3
1.0
2.7
14.2
9.8
43.3
62.6
DifiDock Vina
2.6
5.8
12.5
9.7
23.8
49.9
0.9
2.5
12.1
8.9
47.6
70.2
DiffDock + Conf
2.7
5.9
13.2
10.1
20.1
46.4
1.0
2.6
12.4
9.6
48.4
70.5
DifiDock Gnina
2.4
5.4
11.8
9.3
25.1
50.2
0.9
2.5
11.3
9.0
50.5
72.3
DiffDock + Glide
2.5
5.6
12.0
9.5
25.4
49.1
1.0
2.4
11.6
8.9
49.2
71.0
Ours
1.7
3.2
7.3
5.7
31.8
62.8
0.7
1.4
4.0
4.6
63.2
78.3
Ours Vina
1.5
2.7
6.5
4.9
38.6
69.5
1.3
3.5
3.2
70.2
84.9
Ours Conf
1.7
3.2
7.2
5.6
32.7
63.7
0.7
1.4
3.9
4.4
65.2
79.5
Ours + Gnina
1.5
2.8
6.5
4.8
40.1
69.5
0.6
1.2
3.2
3.3
70.2
83.4
Ours + Glide
1.4
2.7
6.6
4.8
39.7
70.3
0.5
1.3
3.5
3.1
71.7
85.2
Table 2: Performance of blind self-docking on unseen receptors.
5Å. The Ours Glide method, for instance, produces some of the best performance, especially with remarkable 77.1% % success rate for predictions within 5 and a 92.5% success rate for predictions within 5Á when including Conf guidance.
In conclusion, incorporating force guidance significantly enhances the performance of self-docking. offering more reliable and accurate predictions for ligand-protedd interactions, especially when there no prior knowledge of the binding site. This approach represents a key advancement the field of computational docking and
interaction prediction.
4.2.2 Blind Self-Docking Performance for Unseen Proteins
This section evaluates the generalization capability of our model on proteins not seen during training. set of
Following the approach of previous studies [8] [2], we assess the model's performance proteins filtered by their UniProt IDs, excluding those encountered during training or validation. The evaluation results, summarized in Table 2 provide an in-depth analysis of the model's performance on these unseen proteins.
Based on the data in Table 2 the force-guided models significantly outperform other methods on unseen proteins. Specifically, the Ours + Glide model achieves the best performance with a 4.8A mean RMSD and success rates of 39.7% at 2Å and 70.3% 5A, surpassing all baseline methods, especially in terms of precision.
4.2.3 PoseBuster Evaluation
In addition conventional metrics, we employed the PoseBuster benchmark (Fig[(() to assess the physical validity of the generated ligand poses, which is crucial for their practical applicability. While standard metries such as RMSD provide spatial alignment evaluations, the PoseBuster benchmark further examines the generated poses for physical and chemical plausibility. It imposes specific criteria, such as avoiding steric clashes and maintaining realistic bond lengths and angles, to ensure that predicted poses biologically viable.

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Sampling Curve
Comparative performance on PoseBuster Benchmark
50
DL-based Method
Percentage of Predictions
Ours with Guidance
DiflDock with Guidance
Fraction with RMSD 24
40
-30
25,21/75 6%
37.5%
27.3%
14,2%
20
10
DiffDock
DiffDock vina
10
Ours
Eqpabbodd
TonkBind
Cofteck
Curg
Vina
armback Ghild
Conf
Difbbok clisd
Guee Vinu
Oas Goine
oses Glide
Ours Vina
oebbor
Gur
15
Number of Sampling Steps
(a) PoseBuster evaluation
(b) Ablation study the number of sampling steps
Figure 2: (a) PoseBuster evaluation: The model with force guidance significantly outperform the model without guidance. (b) Ablation study on the number sampling steps.
Figure 2(a) reveals clear stratification among the evaluated pipelines. The pure deep-learning (DL) baselines methods including "Ours" show poor energetic reasoning, underscoring the pitfalls of relying on geometric alignment alone. Crucially, supplementing both DiffDock and our method with force guidance produces a dramatic jump in physical validity. For DiffDock, the best guidance option (+Glide) lifts the pass rate from 14.3% 25.6% an absolute gain of 1..3% and relative improvement of about 79%. Our method benefits even more: the same Glide-basee boosts performance from 17.5% to 31.4% (+13.9%, also 79% relative). Across all four guidance strategies (Vina, ConfGen, Gnina, Glide), our approach consistently stays 4 4-6% ahead of the corresponding DifiDock variant, establishing a new state-of-the-art with up to 31.4% PoseBuster- compliant predictions. These findings demonstrate that the energetic guidance is indispensable for converting generated poses into physically realistic, drug-like conformations.
refinement
4.2.4 Performance with Number of Sampling Steps.
illustrates the relationship between the number of sampling steps and the fraction of docking results with RMSD < 2Aacross four methods: DiffDock, DiftDock + Vina, Ours, and Ours Vina. The key observation is that energy-based guidance significantly improves the convergence speed and performance of generative sampling. DiffDock alone converges around 20 samples, reaching a plateau in the success rate beyond this point. DiflDock + Vina, which incorporates energy-based sampling. achieves similar performance with steps, converging around 12 steps. The method Ours without force guidance converges slightly faster than DiffDock, around 14 steps. Ours + Vina, combining our generative approach with Vina scoring, shows the fastest convergence, reaching performance plateau at approximately 8.
Figure 2(b)
These results demonstrate that integrating energy-based guidance significantly enhances sampling efficiency, reducing the number of required steps to achieve optimal docking performance.
5 Conclusion
In this work, we introduce ForceFM, a novel porce-guided flow-matching model for protein-ligand docking. By integrating generative model with physical principles, ForceFM addresses key limitations of current state-of-tt of-te-of-the-an art (SOTA) methods, particularly their struggles with physically consistency and structural validity. The incorporation
force-guided network enables ForceFM to significantly outperform existing models in both accuracy and physical plausibility with fewer sampling steps. Extensive experiments on the PDBBind dataset and PoseBuster benchmark demonstrate superior performance, yiclding physically consistent and structurally valid ligand conformations. Additionally,

---

ForceFM shows strong generalization to unseen protein data, making it a versatile and reliable tool for drug discovery and molecular docking.
However, there are still certain limitations. Despite its promising results, ForceFM relies on the energy functions chosen for force guidance, and performance may vary depending the choice of energy function. Furthermore, while the model successfully handles static protein-ligand interactions, does not yet fully account for protein flexibility or the dynamic conformational changes that occur during ligand binding. In addition, while the force-guided network improves physical plausibility and data efficiency, its generalization ability remains constrained by the training data. ForceFM is primarily trained on the PDBBind dataset, which limits its exposure to diverse protein families, binding environments, and rare conformational states. This can affect performance when applied to novel targets or large-scale virtual screening tasks.
In future work, we plan enhance ForceFM by incorporating molecular dynamics simulations capture protein flexibility and the conformational transitions in the protein-ligand complex during binding, and expand training across larger and more diverse datasets. These directions will enhance the model's 's robustness, improve generalization, and allow a more realistic description of protein- ligand interactions.
Acknowledgments and Disclosure of Funding
The authors acknowledge the financial supported by the Natural Science Foundation of China (Grant No. 12371290).
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19

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Appendix
A Proof of Theorem 3.1
Before proof, we need the following lemma:
Lemma A.1 (Theorem 3.1 in (27]) Let qe (xe) be the data-based marginal distribution specific
protein y. Suppose Pt (x, x1) == (xt x1) and pt (xx) qi (xx) e- e-k8,(xx), & (xt) satisfies
for I (ex((x),,orr [0. 1). Then
[c- --ik((x)))
& (x:) log (x.(x)))
(14)
after dropping the constant, and
kEi(xe)) Vx, E (xx) (9)())) [ge (x1 xx) e-)(xkk))))) G (x1,
(15)
killyg en (xe)) (et (xe x1) e e
with G (x1, Xx) = Xx, log (xx) - Vx, log (xt x1)-
Proof of Lemma A.1 Given pl (x1) 91 (x1) (
/ 17 and pa (xt x1)
2: (xt
x1). the
distribution Pz (x,) tollows
/ Pt (xx X1) (xI) = f (xe (x1) ④1 (x1) e (xi())))
(xt)
dxi
Z
(16)
f 4:. (x1 xt (xx)
e-ki)(x1))
e (x)()))
dxi qt (x+) (xi(x))))))
7
Z
Under the assumption that
Pe (xx) = ae (xx) ( kE,(x)),
(17)
then & (xx) satisfies
& (xI) = k log Exs(xx//ee) (o [c-kE,0xi]]
+ log Z.
(18)
k
for 0 < <
The corresponding intermediate force can be derived by
f {e e--kee kC, (x.) Vx (x1 xx) dxi
V Ex (xx)
(19)
ʃ qe (x1 xx) KE, (x1)
The numerator can be derived as
kE (x1) Vx, V (x1 xx) dxi
e (Ei (x1 xx) Vx, log qt. (x1
xx) dxi
f qe (x1 xx) e (x1( Xx, log
ge (xx x1) gi (x1) dxi
(20)
zt (xt)
/ ge (x1
xx) (x1) (vx, log ae (xe x1)
Xx, log ge (xx)) dxi
(e (x)((x)) (x1, xi)
Ex (xx)
where ç xx), = Vx, log (xx) - Vx, log qe (xe x1). Therefore
Vx, & (xx) Ex((x(lx)) (x.) le (xx) (xx,
E (x.) le- REI(x)))
(21)
E Ex((x)) [ge (xe xx) G (x) (x]: kE (x)) [g (x, x1) kx))
20

---

Proof of Theorem 3.1 Considering the dynamic of probability distribution p. g=(xc)&xxx)
according to the continutty equation, we have
dp, d (x(x) exp (x)E((x)
dt
dt
2
d qx(x), Ixx 9 (x1 x)) exp (-kE (x)) dxi
dt
Z
d Sx, ai (x1, exp (-kE (x1))
(22)
dt
7 d Sxy ae (x xi) (x) exp (-kE (xi))
dt
1
/
d
9 (x x1) (x1) exp (-kE (x1)) dx1.
Z
dt
In addition,
dgi (x x1)
div [qe (x x1) uy (x x1)]
(23)
dt
Plugging the definition of continuity equation dx:(x)
23 into 22 we can obtain that
dt Z x: dt 9 (x xx1) (x1) exp (-KE (x1)) dx1
(x) div lac (x x1) uz (x x 1 (xi) exp (- (x1 dxi
div. Ixx To (x x1) u. (x x exp (-kE (x1) dxi
(24)
2
[x(()) exp (-kE((x))
exp (-kE (x1)) exp (x){((x))
div.
4e (xi x) (x x1)
dxi
2
div (x)
Thus we conclude our proof by showing (x) defined by Equ. distribution sequence (x).
can generate the guided
B Details for Constructing Protein, Ligand Features, and Heterogeneous Graphs
B.1 Protein Representation
For protein representation, we utilize residue levels features. Each amino acid, denoted as n characterized by feature vector h", encoded using ESM2 [4] (esm2_133_óns (133_650M_UiB (000____6_0MU_55DDD) including its residue type. The position of each node, x", corresponds to the Cartesian coordinates of the Co. atom in 3
The total number of protein nodes is represented as NP.
B.2 Ligand Representation
The ligand is represented the atom level, where each atom considered node with features such as atomic number, chirality, degree, formal charge, implicit valence, number of connected hydrogens, number of radical electrons, hybridization type, aromaticity, ring membership, and six ring-sizi indicators, Each atom's spatial coordinates are denoted as z e R3. The total number of ligand nodes given !
B.3
Geometric heterogeneous graph construction
In this work, structures are represented as heterogeneous geometric graphs with nodes representing ligand (heavy) atoms, receptor residues (located in the position of the a-carbon atom), receptor heavy
21

---

atoms. To build the radius graph, we connect nodes using cutoffs that are dependent on the types of nodes they are connecting:
Ligand atoms-Ligand atoms: An edge between two ligand heavy atoms exists if the distance between them is less than 5Á covalent bond exists. We also represent covalent bonds with some initial embedding representing the bond type (single, double, triple, and aromatic).
Receptor residues-Receptor residues: An edge between residual of and of exists if o is among the 24 nearest neighbors of vg within 15A.
Receptor Lesidues-Ligand atoms: It uses a cutoff of 20 a where or (1 t) max + 10 min is the current standard deviation for translation.
All these features (protein, ligand nodes and edges) are concatenated with sinusoidal embeddings of the time. As for the edges, they are concatenated with radial basis embeddings of edge length. These scalar features of each node and edge are then transformed with learnable two-layer MLPs (different for each node and edge type) into set of scalar features with number ns that are used as initial representations by the following layers.
C Network Structures
In this part, we provide a detailed description of the network structures of each stage. We first introduce the core feature extraction module: E3-equivariant graph convolution layer (EGCL).
EGCL: E3-equivariant graph convolution layer
EGCL serves as the foundational module for feature extraction in model, which is build upon Tensor field and e3nn [37]. It operates by utilizing the tensor products of current node features with the spherical harmonic representations of edge vectors to construct messages. These tensor products are weighted according to the edge embeddings and scalar features of the connected nodes. For any node set of nodes G.A. radius graph constructed with target nodes from Gg. The output feature for node is then formulated as follows:
out, BN
Σ bEN.
Y (Fab) Op. hy
(25)
Wa
with viss = (Eab, ha, ha), where N₂ denotes the neighbors of a in Gs. h, and h; are feature vectors, Cab is the edge embeddings of (a, b), and Y (Fat) represents the spherical harmonics of the edge direction vector up to f = 2. The BN symbolizes the equivariant batch normalization. The orders of the output are restricted to maximum of
In addition, &y.. refers the spherical tensor product of irreps with path weights vab. and all learnable weights are contained in V dictionary of MLPs with dropout. This process generates scalar and vector representations for each node, leading to the output feature matrix as described in the following equation:
EGCL(GAA = [out1, .ufg....,,,ty,.
(26)
where NA the number of nodes in GA-
C.1 Baseline Model
Bt stacking EGCLs, at time t, the current perturbed ligand graph is represent as Gigg i x and protein residue graph G, which are shown as follows:
The feature matrices are updated by using the EGCLs,
HJ = ff 10.--.
fp.tin (
(27)
HP
H fog ( ( ) + ( .p-11)
(28)
H1:00
22

---

where the functions / 1,... L here are EGCLs. Finally, after obtaining high-quality features for ligand, these features are utilized to predict the translation, rotation, and torsion vector current time I. Translation and rotation can intuitively represent the linear and angular accelerations of the ligand's s center of mass and the remaining molecular structure, respectively.
The translation and rotation of the ligand are represented as the linear and angular accelerations, respectively, of its molecular structure. Specifically, we aim to produce two output vectors, one each for translation and rotation. These vectors are generated by convolution each ligand atom's 's features with the ligand's center of mass, The process is mathematically expressed as:
Translation and Rotation:
Σ Y (Fea) Sicc ha VV
(29)
aEVi
with tien = (μ (Tea), ha)
where pa-)) indicates radial basis embeddings of the edge length. The output vector v contains 2 odd and 2 even vectors (1 single odd and I even for translation and another 2 for rotation and they are summed). These vectors' magnitudes are fine-tuned using an MLP, which considers their current magnitudes and sinusoidal embeddings of the time. The final translation and rotation vectors are adjusted by multiplying by 1/0rr and Trat, respectively.
Torsion:
The torsional aspect of ligand movement is defined based on its rotatable bonds. Assuming there are m rotatable bonds in ligand, we employ a pseudo-torque layer, akin to the approach in Jing et al. [34] to predict SE(3)-invariant scalars for each rotatable bond.
For rotatable bond g = (go. 91) (go and 9i are two nodes on the bond) and node in the ligand graph Gig. the vectorial components "b and gt denote the magnitude and direction connecting bond g's center and atom b respectively. A convolutional filter Tg. specific to each bond is constructed using:
(f)) @ (f)
(30)
where @ represents the complete tensor product as detailed in [37] and the second term contains the spherical harmonics up to l = 1. This filter is then used to convolve with the representations of every neighbor on a radius graph:
& ((g,b) g rotatable bond, b Vz}
Egb = F (μ (rab)) V(g.b) b) E,
h, 1
Σ Tg (Fab) Dra h
(31)
W
BEN,
with Ygb G (Cgb, h,, hgo + hgg)
Here, N₁, {b (g. b) E }. and F and G are MLPs with learnable parameters. Finally, we produce a single scalar prediction for each bond by using both odd and even representations:
out, Fout ohg evvn))
(32)
where Fout is a two-layer MLP with tanh non- con-linearity and no biases. This is also multiplied by Swrr
C.2 Force Model
The force model has the same structure with baseline model, with smaller network size.
D Training & Inference Details with Hyper-parameters
General Settings: Both baseline model and force model employ the AdamW optimizer with a learning rate of be and weight decay le 4. The learning rate is controlled by cosine annealing scheduler with minimum Ir=le 6. During inference, we use the exponential moving average of weights, updated after each optimization step with decay factor of 0.999.
For manifold flow matching, we actually randomly perturb x, to get Xp. The rotation vector can be obtained in the axis-angle parameterization by sampling a unit vector uniformly and random angle
23

---

omega in [0, T] according to the following distribution.
p(w) - cos(w) ((w),
(33)
where (w) Ei=0 (21 +1 (1)
sin (wol+ ((n(++//)/sin((())) The translation per- turbation kernel is normal with variance tr,mar and torsion is warped normal with variance o torrmaz 0.1, moot = x 2/2, Trot,min T/ 100, Otormaar = n. Otor,min =
Otr.maz 8.0, otr,min
100.
D.1 Details for Baseline Flow Matching Model
Objective: The baseline model aims for producing primitive estimation of ligand position.
Training Protocol:
Training Duration: The model is trained over 2000 epochs on the PDBBind dataset, with batch size of 8 and dropout rate of 0.1.
Model Architecture: The number of edge length embeddings is set to 64. We employ EGCLs (I. = 6), with 60 scalar features (ns) and 12 vector features (nv).
Inference Process: Pockets
identified based on P2Rank [38]. By initializing ligand conformations around the pocket, we can sampling ligands via reverse diffusion. The reverse process is split into 15 time steps.
D.2 Details for Force Model
Training Settings:
Extended Training: The model involves 400 epochs of training, a batch size 8, and dropout rate of 0.1.
Model Complexity: The model includes EGCLS (L = 4), with each EGCL having 48 scalar (ns) and 10 vector (nw) features.
Hyper-parameters: The inverse of the temperature k =
1 1o 1. The number of samples
for expectation approximation in Eqn. h is 40.
[2)
2.8
08
(a) Results vina
(h) Results on RMSD.
(c) Results percentage of RMSD < 2 and those also pass the Posebuster test.
Figure 3: Ablation study 1).
Energy function/software details: We run GLIDE, GNINA, and Autodock Vina with their default settings
Autodock Vina is a well-established tool. Vina score is computed by following https rradthaeoocs..///a/aatttt///tood /
htttl .ttml
Gnina builds on SMINA by additionally using leamed 3D CNN for scoring. We uses Gnina v1.3.2 in this work https : cww. htt///gnna////g htwpaiaaagggnaaaeellaaess//gg/// .... We used the Vina-style scoring function implemented in gnina as score function in table in main text. We conduct additional experiments using GNINA's CNN-based scoring functions (c.g., CNNscore, CNNaffinity) in table 7

---

ConfScore 10 is computed using version 1.1 https:// www.settt.....oeo.eoee.eeee..o /
DiffDck/releases/dmmlo.ooo http:a//wwv....ffooooooooooooooe
Glide is strong heavily used commercial docking tool.
P2Rank v2.3 used for pocket identification
releases/ Veleases/dommloa// bttpaad//..//pp/ 3/p2rank____.... 2.3. 1..3.am. tar gz
E
Additional Experimental Results
In this part, addition ablation studies are conducted for hyper parameter tuning, All these experiments conducted by using force-guided model with energy function Vina score.
E.1 Number of Samples for Expectation Estimation
Percentiles.
% Belowt
K
Mean
2Å
5 Á
5
7.5
37.1
62.7
10
7.0
39.5
65.3
20
6.3
41.2
71.3
40
5.3
42.3
72.5
60
5.2
42.9
73.2
80
5.2
43.0
73.5
Table 3: Flexible blind Top-1 delf-docking performance. Comparative results the number of samples K for expectation estimation.
In this part, for computation efficiency, the model trained only for 100 epochs. By fixing k 1 and 1, we train the force model by setting K E {5, 10, 20, 40, 60, 80). The results are shown in Table The metrics evaluated include the mean RMSD and the percentages below specific thresholds. While K 80 achieves the best performance across all metrics, the improvements between K = 40 and 80 are negligible compared to the computational cost increasing K. Considering the balance between computational efficiency and model performance, K = 40 is selected the optimal choice. This value provides a good trade-off, offering near-peak performance with significantly reduced computation compared to K 80.
To
E.2 Guidance Strength
In this part, by fixing k = 1o and K = 40, we evaluate the effect of 1) by setting 0.1 to 1.2 with step 0.1. The results are presented in Figure 3 It can be observe that as 1) increases up to 1.0. both the vina score and mean RMSD decrease, the percentage of ligand atomic RMSD less than 2 as well as the proportion of ligands passing the PoseBuster tests, improve. Thus, we choose = 1.
E.3
Role of P2Rank for Pocket Identification
As noted in prior work
predicting binding pockets can significantly reduce the conforma-
tional search space and improve the efficiency and accuracy of docking models. In this work, we adopt P2Rank estimate the binding site center and initialize the ligand around it-this aligns with standard practice in blind docking evaluation.
To ensure fair comparison and factor out the influence of P2Rank, conducted additional experiments. Since FABind g and FABind+ [12] incorporate built-in pocket prediction modules, we added a DiffDock P2Rank baseline for direct comparison. As shown the table integrating P2Rank improves the mean RMSD and centroid distance significantly, with minimal change in the &RMSD < Ammerri--indicattiiii more precise pose sampling near the true binding site, even if the top-ranked pose isn' always within the strict 2Athreshold. More importantly, we find that our method robust small perturbations in the predicted pocket location. To evaluate sensitivity, injected Gaussian noise with increasing variance (o = to 10 Å) into the P2Rank- P2Rank-predicted pocket center
25

---

Table 4: Effect of pocket prediction (P2Rank) on DiftDock (Top-1, PDBBind).
Method
Mean RMSD |
% RMSD=2A1
Mean Centroid +
% Centroid
DiffDock
7.5
38.2
5.5
60.8 67.3
DiffDock + P2Rank
5.4
37.6
3.5
before ligand initialization. As shown below, performance remains stable across all noise levels up to o = A, with only minor degradation at o 10 A, comparable to results without P2Rank at all.
Table 5: Sensitivity to pocket-center noise (Gaussian, Å).
Method / Setting
Mean RMSD |
% RMSD=2A1
Mean Centroid L
% Centroid
Ours (no noise)
4.2
41.1
3.1
71.7
0=1
4.2
41.2
3,0
72.3
o=2
4.5
41.7
3.1
71.4
o=3
4.3
41.5
3.1
71.7
o=5
4.4
41.5
3,2
70.9
0=10
4.8
39.8
3.8
66.1
w/o P2Rank
4.8
39.4
3.7
66.9
E.4
Post-Minimization Ablation
critical question whether the improvements from our force-guided framework stem from genuine integration during generation or could be replicated by post-hoc energy minimization of poses generated by standard model. To this end, we conducted additional ablation experiment, where we took the top-1 poses generated by both DiffDock (w or w/o force model) and our baseline model ("Ours"), and applied energy minimization using AutoDock Vina's local optimizer (without re-docking). The results are summarized in the table It can be observed that:
Energy minimization dramatically improves PoseBuster scores, increasing them from 14-24% to over 40%. This confirms that poor physical plausibility is largely due to local geometric distortions (e.g.. clashes, bad bond angles) that minimization can fix.
However, minimization has limited impact on RMSD it slightly reduces mean RMSD but does not significantly improve the percentage of poses below 2Á. some cases, RMSD even increases slightly, likely because the minimizer pulls the ligand away from the crystal pose while optimizing internal energy.
Combining force-guided generation with minimization yields the best of both worlds: 45.8% PoseBuster pass rate, significantly outperforming any other combination.
Table 6: Post-hoe Vina minimization model variants (Top-1, PDBBind).
Method
Mean RMSD +
RMSD<2A f PoseBuster
DiftDock DifiDock Mini
7.5
38.2
14.3
7.0
37.9
40.3
DifiDock + Vina
3.8
43.5
24.6
DiffDock Vina + Mini
3.9
42.8
42.5
Ours
1.7
41.1
17.5
Ours Mini
1.8
40.8
43.1
Ours + Vina
1.1
48.6
29.7
Ours Vina + Mini
1.2
46.2
45.8
26

---

E,5 GNINA scoring function
We have conducted additional experiments on PDBBind testset using CNNscore and CNNaffiniyy the guiding potentials in our force- force-guided guided framework. The results summarized below. This confirms that our method is not only compatible with classical physics-based scoring but also benefits from data-driven, deep learning- carning-based energy models that capture complex sirein-liggad interaction patterns.
Table 7: Performance of the force-guided framework using different scoring functions for GNINA.
Method
Mean RMSD 4
% RMSD=2Á f
Mean Centroid +
% Centroid
GNINA Affinity
3.1
47.5
2.4
74.3
GNINA CNNscore
3.2
46.3
2.5
72.9
GNINA + CNNaffinity
3.1
48.6
2.3
75.8
E.6 DockGen Cross-Domain Benchmark
For the generalization assessment, stronger OOD evaluation desirable. better assess generalizability of our method in a realistic cross-docking scenario, we evaluate our model-trained solely on the PDBBind dataset-on the DockGen test set. This setup provides a test of cross-domain generalization. The results are shown follows in table 8 Our results show that when integrating our plug-and-play force guidance module with the baseline model, there a significant improvement compared the baseline model on this challenging OOD benchmark. This demonstrates that our method not only enhances docking accuracy but also improves robustness to structural and functional shifts across the proteome.
Table 8: DockGen cross-domain evaluation (train: PDBBind only).
Method
Mean RMSD 4
% RMSD<2Á f
Mean Centroid +
% Centroid 1
FABind
19.1
1.3
18.1
14.2
FABind+
18.5
1.5
16.9
16.1
DiffDock
16.2
5.3
14.5
21.4
DiffDock Vina
12.5
7.1
10.9
25.7
DiffDock + Conf
13.4
6.9
12.5
24.6
DiffDock Gnina
12.9
7.2
11.2
25.3
DiffDock + Glide
12.6
7.2
11.9
26.6
Ours
14.5
6.5
14.1
23.2
Ours + Vina
12.3
8.1
10.4
26.8
Ours Conf
12.5
7.9
11.6
25.4
Ours + Gnina
13.1
7.6
12.1
26.9
Ours Glide
12.2
8.1
10.3
27.8
E.7
Visual Quality Assessment
In Figure 4 present comparative visual analysis involving model with Vina force guidance (Red), FABind+ (Purple), and the actual Crystal Structure (Green) of ligands for PDBIDs 6oy I and 6uvv. This side-by-side comparison highlights the positioning accuracy of our model relative to FABind+.
Notably, although FABind+ achieves similar RMSD performance for 6oy1, the energy of the generated ligand is extremely high, as indicated by the Vina score. This high energy suggests that generated conformation is chemically unstable, common issue with many DL-based methods that lack sufficient physical guidance. In contrast, the ligand generated by our gurce- model has much lower Vina score, indicating more stable and physically plausible conformation. As for 6uvv,
27

---

FABind+ generates an incorrect ligand conformation, which further emphasizes the robustness of our method.
In summary, our model not only demonstrates superior RMSD performance but also generates ligands that chemically stable and biologically relevant. These ligands accurately replicate crucial hydrogen bond interactions with protein residues. This visual assessment clearly highlights the enhanced precision and adaptability of our model in generating ligands with physical plausibility.
Ground Truth
FABind+
Ours
(a) PDBID: 6oy1
(b) PDBID: 6uvv
FABind+: RMSD 2.62, Vina Score 19.73
FABind+:
RMSD 7.71, Vina Score 13.0
ForceFM:
RMSD 1.62, Vina Score
ForceFM:
RMSD 0.72, Vina Score 5.43
Figure 4: Comparative visualization of generated ligands for PDBIDs 6oy1 and 6uvv, displayed from left to right. The color coding is as follows: Our model with force guidance (Red), FABind+ (Purple), and the actual Crystal Structure (Green). RMSDs and Vina scores are provided, highlighting the precision and accuracy of our method generating low-energy ligand conformations with improved physical plausibility.
F Implementing Detail for Training/Inference DiffDock with Energy Guidance
First of all, it needs to point that the time index for prior and data distribution for diffusion model and 0 while flow matching perform it in the reverse way.
Let Po (xp yy = (xo y) -Eg(kaaa)))
We are able to sampling from po by the reverse-time SDE
with the score function:
x. log (x,,y) so (x,, y, t) AV & (x,,y)
(34)
where (x, y, L) denotes the given score model, Vx, & (x: is the intermediate force guidance. Lemma A.I provides the precise force function time thereby advancing our understanding of the intermediate energy function. Thus, similar to ForceFM, an additional force network is proposed to approximate V Vx,& y).
Training process. We first employ the given score model to generate ligand candidates from Yo (Xp y), which then used to train independent intermediate force network h. y, t)- For each protein-ligand pair (X) we first sample K ligand conformations x (1:K) ~ 4o (Xo y and perturb the data time according to the forward SDE. We define the intermediate force loss function ffrre (1)) as
((o.v)) (x,,,,) - Σ Sis (xx)) xx,y 1=1
11
(35)
(x
((() (r) -kE (x/0) (10) x)
where wi
and xx) Xx,y)
Vx, log qt (xt
y)
Σk a (x112(6) )) -ke (-8))>)
(4) Xx, log qe (x x y) The latter component of Eqn. signifies the precise value of the in- termediate force at time t, where Vx, log (x, y) is the estimated by the given score model
28

---

Algorithm 2: Training Procedure (Single Epoch) for Force Model
Input: Training pairs ((xo:))} score model so (X,, y: t), energy &o (+), intermediate force network hig (xt, t)
for each Xo. y do
t ~~ u(0, 1);
X, ~ qt. (xx xo); # perturb data
(1:K)
X
(Xg y):
for 1,.., K do
L
x xx,)) s0 (xx, 1) V Plog ge
(1)
(x: xx y):
Ex((x!) xx. y)u (x 3) k50 (x)
E, qe (x11x(0) )) -k50 (x0")>)) x)
lll (Xe: - 11
ming L.
(8) 8e (X,y 8) and Vx, log di Xx Xg y is the tractable perturbation kernel on the product space defined by transition, rotation and torsion. The force-guided training process is summarized in Algorithm
29


Reviews:
[{"review_id": "jV4bB1EohK", "reviewer": "Reviewer_y7e8", "summary": "The paper describes an approach to integrate energy functions into a flow matching model for molecular docking.  The energy function is introduced through a force network that does not require ground truth forces, just energies, for training. The evaluations show this approach results in better, more realistic docked poses. The approach is effective across multiple energy functions and model architectures. Claims to generalizability are problematic, however.", "questions": "How does the method perform in a more realistic cross-docking scenario?\n\nHow sensitive is the model to the initial pocket definition?\n\nIs the graph structure updated with each iterative update (since the distances between nodes will change)?\n\nWhy does table 2 say it is for flexible docking? Nothing in the text indications flexible docking (moveable receptor) is being performed.\n\nThe importance of integrating the force network into training isn't evaluated.  If one simply performed minimization on the generated poses using the evaluated tools, would you see similar improvements in accuracy?\n\nVina does not measure the chemical stability of a conformer, only of its interaction - please be careful with your language.", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths.  This is a good idea. The force network provides a general approach for integrating an arbitrary energy function.  The evaluations convincingly show that including force matching is beneficial. If it weren't for the unsupported claims about generalizability, this would be a solid paper.\n\nThe effect of force guidance on the number of sampling steps needs is an interesting observation.\n\n\nWeaknesses.  The claims to generalizability are overstated and the evaluations do not support the claims. It is true the approach generalizes to multiple energy functions and other generative models (DiffDock), but the paper claims they address \"concerns about overfitting to specific protein or ligand types.\"  No practitioner of molecular docking would agree that time splits are a useful approach to measure  generalization or that simply filtering by Uniprot identifiers is sufficient to remove train/test information leakage.  \nPlease review https://arxiv.org/html/2402.18396v1 for a more rigorous and reasonable approach for accurately assessing generalization.\n\n\nThe model does not actually perform blind docking, but instead uses P2Rank to identify pockets and then does pocket-based docking. A more sensible comparison would be to do pocket-based docking across the board to factor out the influence of P2Rank.", "was_revised": true, "final_justification": "With the additional evaluations presented during rebuttal, the paper now makes a compelling case for the utility of the method for molecular tasks.  They make a compelling argument that their model generalizes and is effective.", "rebuttal": "We sincerely thank reviewer for your careful evaluation and constructive feedback. The insightful comments and thoughtful suggestions have greatly helped us improve the quality and clarity of this manuscript. We have carefully considered each comment and made corresponding revisions to address the concerns raised. We believe that the manuscript has been significantly strengthened through this process, and we are grateful for the time and expertise the reviewer have generously shared. \n\n**W1/Q1. Generalization claims overstated; time‑split and UniProt filtering are insufficient.** \n\nThank you for your insightful feedback. We’ll carefully check the language. The statement like ‘concerns about overfitting to specific protein or ligand types’ will be revised as ‘improve the generalization ability of model’. \n\nFor the generalization assessment, we agree that stronger OOD evaluation is desirable. To better assess the generalizability of our method in a realistic cross-docking scenario, **we evaluate our model—trained solely on the PDBBind dataset—on the DockGen test set.** This setup provides a test of cross-domain generalization. The results are shown as follows. Our results show that when integrating our plug-and-play force guidance module with the baseline model, there is a significant improvement compared to the baseline model on this challenging OOD benchmark. This demonstrates that our method not only enhances docking accuracy but also improves robustness to structural and functional shifts across the proteome. \n\n| Method | Mean RMSD | % RMSD < 2 | Mean Centroid Distance | % Centroid Distance < 2 |\n| --- | --- | --- | --- | --- |\n| FABind | 19.1 | 1.3 | 18.1 | 14.2 |\n| FABind+ | 18.5 | 1.5 | 16.9 | 16.1 |\n| DiffDock | 16.2 | 5.3 | 14.5 | 21.4 |\n| DiffDock + Vina | 12.5 | 7.1 | 10.9 | 25.7 |\n| DiffDock + Conf | 13.4 | 6.9 | 12.5 | 24.6 |\n| DiffDock + Gnina | 12.9 | 7.2 | 11.2 | 25.3 |\n| DiffDock + Glide  | 12.6 | 7.2 | 11.9 | 26.6 |\n| Ours | 14.5 | 6.5 | 14.1 | 23.2 |\n| Ours + Vina | 12.3 | **8.1** | 10.4 | 26.8 |\n| Ours + Conf | 12.5 | 7.9 | 11.6 | 25.4 |\n| Ours + Gnina | 13.1 | 7.6 | 12.1 | 26.9 |\n| Ours + Glide | **12.2** | **8.1** | **10.3** | **27.8** |\n\n**W2/Q2. Method is pocket‑based, hence not blind docking. Sensitivity to pocket definition.**\n\nWe appreciate the reviewer’s insightful comment regarding the role of pocket prediction in our method. As noted in prior work [1, 2, 3], predicting binding pockets can significantly reduce the conformational search space and improve the efficiency and accuracy of docking models. In this work, we adopt **P2Rank** to estimate the binding site center and initialize the ligand around it—this aligns with standard practice in blind docking evaluation. \n\nTo ensure a fair comparison and factor out the influence of P2Rank, we conducted additional experiments. Since **FABind [2]** and **FABind+ [3]** incorporate built-in pocket prediction modules, we added a **DiffDock + P2Rank** baseline for direct comparison. As shown in the table below, integrating P2Rank improves the mean RMSD and centroid distance significantly, with minimal change in the %RMSD < 2\\AA metric—indicating more precise pose sampling near the true binding site, even if the top-ranked pose isn’t always within the strict 2\\AA threshold.\n\n| Method | Mean RMSD | % RMSD < 2 | Mean Centroid Distance | % Centroid Distance < 2 |\n| --- | --- | --- | --- | --- |\n| DiffDock | 7.5 | 38.2 | 5.5 | 60.8 |\n| DiffDock + P2Rank | 5.4 | 37.6 | 3.5 | 67.3 |\n\nMore importantly, we find that our method is **robust to small perturbations in the predicted pocket location**. To evaluate sensitivity, we injected Gaussian noise with increasing variance ($\\sigma$ = 1 to 10 \\AA) into the P2Rank-predicted pocket center before ligand initialization. As shown below, performance remains stable across all noise levels up to $\\sigma$ = 5 \\AA, with only minor degradation at σ = 10 \\AA—comparable to results without P2Rank at all.\n\n| Method | Mean RMSD | % RMSD < 2 | Mean Centroid Distance | % Centroid Distance < 2 |\n| --- | --- | --- | --- | --- |\n| Ours | **4.2** | 41.1 | 3.1 | 71.7 |\n| $\\sigma$=1 | **4.2** | 41.2 | **3.0** | **72.3** |\n| $\\sigma$=2 | 4.5 | **41.7** | 3.1 | 71.4 |\n| $\\sigma$=3 | 4.3 | 41.5 | 3.1 | 71.7 |\n| $\\sigma$=5 | 4.4 | 41.5 | 3.2 | 70.9 |\n| $\\sigma$=10 | 4.8 | 39.8 | 3.8 | 66.1 |\n| W/o P2Rank | 4.8 | 39.4 | 3.7 | 66.9 |\n\nThese results suggest that our model does **not rely heavily on precise pocket localization**, likely due to the random initialization of ligand conformations and the iterative refinement process in the diffusion framework. Even when initialized far from the true site, the force guidance module helps steer the ligand toward plausible binding regions. \n\n**Q3. Is graph rebuilt after each update?**\n\nYes; edges are recomputed every step to guarantee geometric consistency and they are used as features in the neural network. \n\n**Q4. Table 2 says “flexible” although receptor is rigid.**\n\nWe appreciate the reviewer for highlighting this imprecision. This label was inadvertently adopted from the original reporting style in the FABind[2]/FABind+[3] papers, which used the term to describe their experimental setup. To avoid misinterpretation, we will revise the table header to **\"PDBBind Docking Performance\"**, which more accurately reflects our evaluation protocol. \n\n**Q5. Could post‑minimization deliver same gains?**\n\nThank you for the insightful feedback. We fully agree that a critical question is whether the improvements from our force-guided framework stem from **genuine integration during generation** or could be replicated by **post-hoc energy minimization** of poses generated by a standard model. To this end, we conducted a additional ablation experiment, where we took the top-1 poses generated by both **DiffDock (**w or w/o force model**)** and **our baseline model (\"Ours\")**, and applied **energy minimization using AutoDock Vina's local optimizer** (without re-docking).  The results are summarized in the table below.\n\nIt can be observed that:\n\n- **Energy minimization dramatically improves PoseBuster scores**, increasing them from ~14–24% to **over 40%**. This confirms that **poor physical plausibility is largely due to local geometric distortions** (e.g., clashes, bad bond angles) that minimization can fix.\n- **However, minimization has limited impact on RMSD** — it slightly reduces mean RMSD but does not significantly improve the percentage of poses below 2\\AA. In some cases, RMSD even increases slightly, likely because the minimizer pulls the ligand away from the crystal pose while optimizing internal energy.\n- **Combining force-guided generation with minimization yields the best of both worlds**: **45.8% PoseBuster pass rate**, significantly outperforming any other combination.\n\n| Method | Mean RMSD | % RMSD < 2 | PoseBuster |\n| --- | --- | --- | --- |\n| DiffDock | 7.5 | 38.2 | 14.3 |\n| DiffDock + Mini | 7.0 | 37.9 | 40.3 |\n| DiffDock + Viina | 3.8 | 43.5 | 24.6 |\n| DiffDock + Vina + Mini | 3.9 | 42.8 | 42.5 |\n| Ours | 1.7 | 41.1 | 17.5 |\n| Ours+ Mini | 1.8 | 40.8 | 43.1 |\n| Ours+ Viina | 1.1 | 48.6 | 29.7 |\n| Ours+ Vina + Mini | **1.2** | **46.2** | **45.8** |\n\n**Q6. Vina does not measure internal strain—wording.** \n\nThank you for pointing out this issue. You are absolutely right that Vina’s scoring function does not model ligand internal strain. Instead, it provides an empirical docking score that heuristically approximates protein–ligand binding affinity. To improve scientific precision, we will revise the original phrase “**chemical stability**” to “**empirical binding affinity score**,” and carefully review the manuscript to ensure all related terminology aligns with domain conventions. \n\n[1] Guo H, Liu S, Lou Y, et al. Diffdock-site: A novel paradigm for enhanced protein-ligand predictions through binding site identification[C]//NeurIPS 2023 Generative AI and Biology (GenBio) Workshop. 2023. \n\n[2] Pei Q, Gao K, Wu L, et al. Fabind: Fast and accurate protein-ligand binding[J]. Advances in Neural Information Processing Systems, 2023, 36: 55963-55980. \n\n[3] Gao K, Pei Q, Zhang G, et al. Fabind+: Enhancing molecular docking through improved pocket prediction and pose generation[C]//Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 1. 2025: 330-341."}, {"review_id": "iwkJj6nMnT", "reviewer": "Reviewer_5rW8", "summary": "This paper introduces ForceFM, a novel force-guided flow matching model for protein-ligand docking. The method first trains a purely data-driven flow matching model, and then trains a separate guidance model to apply force-guided corrections based on an energy function. By injecting physics-based knowledge into an advanced generative model, ForceFM is designed to favor conformations that are lower in energy and more chemically plausible. The model is built on sound principles and features an elegant design. Experimental results demonstrate that ForceFM significantly outperforms existing methods in both accuracy and the validity of its generated poses, while also showing strong generalization capabilities. The work has high potential for practical applications.", "questions": "This is good work, and I commend the authors for their contribution. I have a couple of questions to help contextualize the results:\n\n1.\tThe two hyperparameters, the energy weight k during training and the guidance strength η during inference, appear to be crucial for the model's performance. How were their final values chosen, and what trade-offs were considered? I would recommend adding an ablation study to clarify their impact and justify the selection.\n2.\tGiven that the model consists of two trained components, what is its inference efficiency? It would be valuable to report the inference time and, if possible, compare it with the baselines to better assess its practical applicability.\n3.\tAre there other relevant baselines that could be considered for comparison? A broader comparison would help to better position the performance of ForceFM within the field.\n4.\tCould you further elaborate on the practical utility of the model?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1.\tThe paper is exceptionally well-written. It provides a comprehensive and lucid exposition of the underlying principles.\n2.\tThe proposed model is elegantly designed and methodologically sound.\n3.\tThe model demonstrates state-of-the-art performance and shows significant promise for practical applications.\n\nWeaknesses:\n1.\tThe core novelty appears somewhat limited, as the method's success is heavily contingent upon the availability of a high-quality energy function.\n2.\tThe need to carefully tune two key hyperparameters may limit the model's broader applicability and future potential.\n3.\tThe paper lacks a thorough analysis or ablation studies for its key hyperparameters.\n4.\tThe experimental comparison could be more comprehensive, as the set of baselines is somewhat limited.", "was_revised": true, "final_justification": "The author's response addressed my concerns.", "rebuttal": "We sincerely thank reviewer for your careful evaluation and constructive feedback. The insightful comments and thoughtful suggestions have greatly helped us improve the quality and clarity of this manuscript. We have carefully considered each comment and made corresponding revisions to address the concerns raised. We believe that the manuscript has been significantly strengthened through this process, and we are grateful for the time and expertise the reviewer have generously shared. \n\n**W1. Limited Core Novelty Due to Reliance on Energy Functions**\n\nWe acknowledge the reviewer’s observation regarding the reliance on external energy functions. However, we emphasize that the core novelty of ForceFM lies not in the energy functions themselves, but in the development of a generalizable, plug-and-play energy guidance module, that enables *exact, differentiable, and efficient* guidance using arbitrary energy functions (e.g., Vina, Glide, Gnina, ConfScore). \n\nImportantly, our framework decouples the energy evaluation from the generative model, making it highly flexible and broadly applicable. Beyond molecular docking, ForceFM can be readily adapted to other tasks such as de novo drug design, conformation generation…\n\nWe believe that by providing a robust and modular interface between black-box energy functions and diffusion / flow matching models, it offers a meaningful contribution to the AI and computational chemistry communities, enabling more effective and controllable generation across a wide range of applications.\n\n**W2/W3/Q1. Hyperparameter Tuning and Lack of Ablation Studies**\n\nThe ablation study for $k$ and $\\eta$ is presented in Appendix E, with following principle. \n\n- **Energy weight** $k$ **(training):** We set $k$=1/10 based on preliminary experiments to ensure the energy term neither dominates nor vanishes in the Boltzmann-weighted distribution. This value balances data fidelity and physical realism. Extremely high $k$ leads to mode collapse, while low $k$ reduces physical guidance.\n- **Guidance strength** $\\eta$ **(inference):** We selected $\\eta$=1 after an ablation study on the validation set (now included in Appendix E.2, Figure 3), which shows that higher $\\eta$ improves energy and RMSD up to a point, beyond which numerical instability arises. $\\eta$=1 offers the best trade-off between pose quality and sampling stability.\n\nIn addition, it need to be emphasized that by combining the guidance strength $\\eta$, the final generated distribution is $p_1({x}) \\propto q_1({x}) \\exp (-k \\eta \\mathcal{E}_1({x}))$. Theoretically we can set any value for $k$ and determine $\\eta$ according to the validation set. \n\n**W4/Q3: Limited Baseline Comparison**\n\nThank you for your insightful feedback. We agree that including other relevant baselines is desirable. To better assess the generalizability of our method in a realistic cross-docking scenario, **we evaluate our model—trained solely on the PDBBind dataset—on the DockGen test set.** This setup provides a test of cross-domain generalization. \n\nThe results are shown as follows. Our results show that when integrating our plug-and-play force guidance module with the baseline model, there is a significant improvement in success rate on this challenging OOD benchmark. This demonstrates that our method not only enhances docking accuracy but also improves robustness to structural and functional shifts across the proteome. \n\n| Method | Mean RMSD | % RMSD < 2 | Mean Centroid Distance | % Centroid Distance < 2 |\n| --- | --- | --- | --- | --- |\n| FABind | 19.1 | 1.3 | 18.1 | 14.2 |\n| FABind+ | 18.5 | 1.5 | 16.9 | 16.1 |\n| DiffDock | 16.2 | 5.3 | 14.5 | 21.4 |\n| DiffDock + Vina | 12.5 | 7.1 | 10.9 | 25.7 |\n| DiffDock + Conf | 13.4 | 6.9 | 12.5 | 24.6 |\n| DiffDock + Gnina | 12.9 | 7.2 | 11.2 | 25.3 |\n| DiffDock + Glide  | 12.6 | 7.2 | 11.9 | 26.6 |\n| Ours | 14.5 | 6.5 | 14.1 | 23.2 |\n| Ours + Vina | 12.3 | **8.1** | 10.4 | 26.8 |\n| Ours + Conf | 12.5 | 7.9 | 11.6 | 25.4 |\n| Ours + Gnina | 13.1 | 7.6 | 12.1 | 26.9 |\n| Ours + Glide | **12.2** | **8.1** | **10.3** | **27.8** |\n\n**Q2: Inference efficiency**\n\nWe appreciate the reviewer’s question regarding the inference efficiency of ForceFM. We note that the force-guidance network is intentionally designed to be **much smaller than the baseline model** (e.g., fewer layers and reduced feature dimensions), minimizing its impact on latency and memory usage. In our work, we would like to clarify that while the per-step computational cost of the full ForceFM (baseline + force model) is approximately **1.3× that of the baseline model alone**, this additional cost is more than offset by a significant reduction in the number of sampling steps required to achieve high-quality results. \n\nLooking ahead, we also envision opportunities to further optimize training and deployment. For instance, instead of training a separate force model, one could incorporate the guidance signal via **parameter-efficient fine-tuning techniques such as LoRA (Low-Rank Adaptation)** applied directly to the baseline model. This would drastically reduce training costs and eliminate any additional inference cost, while still enabling effective energy-based guidance. \n\n**Q4: Practical utility.**\n\nYes, ForceFM shows strong potential for real-world application in drug discovery, particularly in structure-based virtual screening and hit refinement. **First, ForceFM is inherently compatible with widely adopted scoring functions such as Vina, Glide, and Gnina.** This design allows ForceFM to be seamlessly integrated into existing docking workflows as a plug-and-play module, requiring minimal changes to current pipelines. For example, it can be used downstream of coarse docking to refine ligand poses and improve their physical plausibility. \n\n**Second, the model’s force-guided generation mechanism consistently produces conformations that are not only low in energy but also chemically realistic.** These high-quality poses are more reliable for downstream prioritization, such as rescoring, clustering, or initiating free energy calculations, thereby enhancing the efficiency and confidence of lead identification. \n\n**Finally, ForceFM is computationally efficient.** Despite incorporating an additional guidance network, its inference time is significantly reduced—nearly halved compared to unguided diffusion models—making it feasible for mid-to-large scale virtual screening. \n\nAlthough our current paper focuses on benchmarking performance, we are actively collaborating with experimental researchers on the AI-driven design of coronavirus methyltransferase inhibitors. **In this real-world setting, ForceFM is integrated into both the hit finding and lead optimization stages, where it provides high-quality, energetically favorable binding poses that serve as input to alchemical free energy workflows (both ABFE and RBFE).** These physically plausible initial conformations accelerate FEP convergence and improve the reliability of binding affinity predictions.\n\n**More broadly, ForceFM serves as a critical bridge between generative molecular design and physics-based scoring.** In our current pipeline, ligand candidates generated by a deep generative model (e.g., language-based or diffusion-based de novo design) are passed through ForceFM for docking pose generation, ensuring that only physically meaningful and synthetically accessible molecules are prioritized for further evaluation. The system is further enhanced with active learning strategies that iteratively retrain the generative model based on feedback from docking, ForceFM-based refinement, and FEP predictions. This closed-loop integration highlights ForceFM’s role not only as a docking engine, but also as a structure-quality filter and physics-informed sampler that improves both the efficiency and scientific rigor of end-to-end AIDD workflows."}, {"review_id": "upglOWwec1", "reviewer": "Reviewer_vfGj", "summary": "This paper proposes a novel protein-ligand docking framework named ForceFM. The method is based on the Flow Matching generative model and innovatively incorporates a force-guided network, which leverages multiple classical energy scoring functions (such as Vina, Glide, etc.) as physical priors to guide the ligand conformation generation process. Extensive experiments demonstrate that this approach outperforms current state-of-the-art methods in terms of docking accuracy, physical realism, and sampling efficiency.", "questions": "1. The methodology section suffers from missing definitions for key parameters, which hinders reproducibility.\n    - The variance $\\sigma_{tr, max}^{2}$ for the initial translational sampling (Section 3.2.1) is introduced in the formula, but its numerical value is not provided anywhere in the paper or its appendices.\n    - While the meaning of m in $SO(2)^m$ (the number of rotatable bonds) is mentioned in the supplement, it would benefit from a more direct definition in the main text when the term is first introduced (Section 3.2) for improved clarity.\n\n2. As the core algorithm, the description of Algorithm 1 lacks important details.\n    -  The \"randomly perturb `x_1`\" operation is not specified, leaving the nature and magnitude of the perturbation ambiguous.\n    - Furthermore, the hyperparameter `K` (the number of perturbation samples) is critical to this algorithm. While its choice is justified in an appendix, its importance warrants at least a brief mention of its value and purpose in the main text to ensure the methodology is self-contained.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Pros:\n\n1.  The core idea of this work—integrating a learnable, explicit force-guided network into the flow matching framework—is novel and significant. It directly addresses the critical issue of insufficient physical plausibility in generated conformations, a common limitation of current deep learning-based docking methods.  \n\n2.  The experimental results are compelling. ForceFM demonstrates outstanding performance in docking accuracy (RMSD) on both standard test sets and unseen proteins. Notably, in the PoseBuster physical validity test, the introduction of the force-guided approach significantly improves the pass rate.  \n\n3. ForceFM can flexibly integrate various energy/scoring functions (Vina, Glide, Gnina, Confscore) and has successfully applied this strategy to another well-known model, DiffDock, achieving performance improvements. This strongly validates the method's generality and robustness.\n\n\n\nCons:\nWhile the work presents significant contributions, its credibility is hampered by several weaknesses in methodological rigor, transparency, and clarity of presentation. I strongly recommend that the authors address the following points in a revision:\n\n1. The paper's primary contribution appears to be the development of a generalizable, plug-and-play energy guidance module. However, the novelty of the underlying baseline model (a flow-matching approach for ligand docking) is somewhat limited. The application of flow-matching models to molecular generation and docking is an active area of research, and the proposed baseline shares conceptual similarities with other recent works. It is suggested that the authors reframe their contribution to more heavily emphasize the guidance module, which is arguably the more significant and novel aspect of this work.\n\n2. The comparison of average runtimes in Table 1 is a significant point of concern regarding methodological fairness.\n - Inconsistent Sampling Steps: The paper does not explicitly state whether the sampling steps were held constant when comparing the baseline models (e.g., DiffDock, 'Ours') with their force-guided counterparts. Section 4.2.4 suggests that different step counts were used, corresponding to the convergence point of each model.\n\n3. Ambiguous Treatment of Guidance Functions.\nThe paper's treatment of guidance functions, particularly GNINA, as simple \"black boxes\" can be problematic. As noted, GNINA is a hybrid method integrating classical scoring functions and a CNN-based model. The paper does not specify which component or version of the GNINA score was used. This lack of specificity makes it difficult to attribute the performance gains to a particular type of physical or learned prior. A more detailed description of the exact scoring function used for each guidance type would allow for a more nuanced understanding of why certain functions perform better than others.", "was_revised": true, "final_justification": "I have read the rebuttal and the discussion with authors (and other reviewers/AC). I will maintain the rating at 4. To be clear, I think this is a strong paper for the borderline category. The concept is sound and the results are promising. However, my reservations about the limited evidence on runtime fairness and the generalization of the guidance attribution keep me from being confident enough for a 5. It remains a borderline paper, but one that I lean towards accepting.", "rebuttal": "We sincerely thank reviewer for your careful evaluation and constructive feedback. The insightful comments and thoughtful suggestions have greatly helped us improve the quality and clarity of this manuscript. We have carefully considered each comment and made corresponding revisions to address the concerns raised. We believe that the manuscript has been significantly strengthened through this process, and we are grateful for the time and expertise the reviewer have generously shared. \n\n**W1: Emphasize guidance module over baseline FM.**\n\nWe thank the reviewer for your constructive feedback. We now highlight the **guidance theorem (Thm 3.1) and corollary** as the primary contribution (§3, Abstract).  Baseline FM details are moved to appendix to de‑emphasize novelty claim. This guidance theorem is general and can be used as a plug and play module in other models. The experiment results also support this main contribution, as we use this mechanism to both DiffDock and our baseline flow matching model. \n\n**W2: Runtime fairness: different step counts.**\n\nWe appreciate the reviewer’s concerns about average runtimes. We note that the force-guidance network is intentionally designed to be **much smaller than the baseline model** (e.g., fewer layers and reduced feature dimensions), minimizing its impact on latency and memory usage. In our work, the per-step computational cost of the full ForceFM (baseline + force model) is approximately **1.3× that of the baseline model alone.** We’ll report the time using same inference steps in the revised manuscript. \n\nLooking ahead, we also envision opportunities to further optimize training and deployment. For instance, instead of training a separate force model, one could incorporate the guidance signal via **parameter-efficient fine-tuning techniques such as LoRA (Low-Rank Adaptation)** applied directly to the baseline model. This would drastically reduce training costs and eliminate any additional inference latency, while still enabling effective energy-based guidance. \n\n**W3: GNINA score ambiguity.**\n\nWe appreciate the reviewer for your constructive feedback. The default parameters are used for every energy function. We’ll specify the parameter for these energy functions in the revised manuscript. \n\n**Q1: Missing $\\sigma_{tr, max}$ and $m$ definitions.**\n\nWe thank the reviewer for pointing out missing these important hyper-paprameters. $\\sigma_{tr, min}=0.1$, $\\sigma_{tr, max}=8$, $\\sigma_{rot, min}=\\pi / 100$, $\\sigma_{rot, max}=\\pi / 2$, $\\sigma_{tor, min}=\\pi / 100$, $\\sigma_{tor, max}=\\pi$. We’ll check other hyper-paprameters to ensure the manuscript is self-contained. The code will be released in github. \n\nIn addition, for improved clarity, the number of rotatable bonds $m$ will be in the main text when the term is first introduced. \n\n**Q2: Missing algorithm details: randomly perturb and hyper-parameter $k$**\n\nWe thank the reviewer for pointing out missing this important detail. \n\n- **Perturbation.** It is set at the noise level at $\\sigma_{max}/10$. Then perturbing the ligand via random translation, rotation and torsion.\n- **Perturbation samples $K$**. $K$ is a critical hyperparameter in our method, as it directly affects the accuracy of the energy landscape estimation during training. In our approach, at each training step, we sample $K$ candidate ligand conformations from the perturbation  and use them to estimate the **local energy landscape** around the current state. This estimation is crucial for computing the intermediate force target, which guides the force network to learn how to steer the generation process toward low-energy regions. Specifically, we use these samples to approximate the Boltzmann-weighted expectation under the energy-augmented distribution $p_1(x_1) \\propto q_1(x_1) \\exp\\bigl[-k \\mathcal{E}_1(x_1)\\bigr]$. A higher $K$ leads to a more accurate approximation of this distribution and, consequently, more precise force estimation."}, {"review_id": "iVcvMKlGk5", "reviewer": "Reviewer_WTRm", "summary": "The authors introduce ForceFM, a force-guided flow matching model for intrinsic molecular docking. Energy functions guide ForceFM's sampling of ligand structural conformations, yielding notably more accurate poses than (comparable) baseline methods. This work highlights how physics-based knowledge can be incorporated into generative flow models to enhance prediction efficacy.", "questions": "How much time and space complexity does the authors' proposed energy term integration add on top of their base network architecture and sampling algorithm?", "limitations": "The authors' current benchmarks do not evaluate robust protein-ligand interaction generalization beyond the PDBBind training set. Including additional benchmark datasets (besides the PoseBench Benchmark set) would alleviate this concern.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Points of strength:**\n1. The authors are among the first to demonstrate theoretically and empirically the strength of combining physics-based knowledge and generative flows for molecular docking.\n2. The authors' empirical results for ForceFM are promising.\n3. The authors compare their method to several well-known baselines using well-known benchmarks.\n\n**Points for improvement:**\n1. The authors' methodological novelty is noted yet modest. The main contribution of this work seems to be in theoretically characterizing how to guide generative flow models with additional energy-based terms. Otherwise, the rest of the network architecture is nearly identical to DiffDock (and its flow-based successors such as PepFlow [1]).\n2. The authors' benchmarks could be made more rigorous concerning dataset splitting and out-of-distribution evaluation. For instance, the PDBBind 2020 dataset splits of EquiBind [2] (which the authors use in this work) are well-known yet unfortunately do not control for protein-ligand interaction similarity with a high degree of stringency. The PoseBusters Benchmark dataset is better in this regard, but it is still not perfect. The authors should also consider evaluating their method on more recent protein-ligand interaction benchmarks such as DockGen [3] to more rigorously characterize the generalizability of their proposed method.\n3. There are a few typos in the paper that should be corrected. A grammar checker should be able to screen these out rather quickly.\n\n**References:**\n\n[1] Li, J., Cheng, C., Wu, Z., Guo, R., Luo, S., Ren, Z., ... & Ma, J. Full-Atom Peptide Design based on Multi-modal Flow Matching. In Forty-first International Conference on Machine Learning.\n\n[2] Stärk, H., Ganea, O., Pattanaik, L., Barzilay, R., & Jaakkola, T. (2022, June). EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction. In International Conference on Machine Learning (pp. 20503-20521). PMLR.\n\n[3] Morehead, A., Giri, N., Liu, J., & Cheng, J. Deep Learning for Protein-Ligand Docking: Are We There Yet?. In ICML 2024 AI for Science Workshop.", "was_revised": true, "final_justification": "The authors have resolved my concerns regarding data splitting, methodological novelty, and time/memory complexity.", "rebuttal": "We sincerely thank reviewer for your careful evaluation and constructive feedback. The insightful comments and thoughtful suggestions have greatly helped us improve the quality and clarity of this manuscript. We have carefully considered each comment and made corresponding revisions to address the concerns raised. We believe that the manuscript has been significantly strengthened through this process, and we are grateful for the time and expertise the reviewer have generously shared. \n\n**W1: Methodological novelty modest.**\n\nWe thank the reviewer for your constructive feedback. We now highlight the **guidance theorem (Thm 3.1) and corollary** as the primary contribution (§3, Abstract).  We emphasize that the core novelty of this work is the development of a generalizable, plug-and-play energy guidance module, that enables exact, differentiable, and efficient guidance using arbitrary energy functions (e.g., Vina, Glide, Gnina, ConfScore). The baseline FM details are moved to appendix to de‑emphasize novelty claim. \n\nImportantly, our framework decouples the energy evaluation from the generative model, making it highly flexible and broadly applicable. Beyond molecular docking, ForceFM can be readily adapted to other tasks such as de novo drug design, conformation generation…\n\nWe believe that by providing a robust and modular interface between black-box energy functions and diffusion / flow matching models, it offers a meaningful contribution to the AI and computational chemistry communities, enabling more effective and controllable generation across a wide range of applications.\n\n\n\n**W2/Limitations: Dataset splitting / additional benchmarks.** \n\nThank you for your insightful feedback. We agree that including other relevant baselines is desirable. To better assess the generalizability of our method in a realistic cross-docking scenario, **we evaluate our model—trained solely on the PDBBind dataset—on the DockGen test set.** This setup provides a test of cross-domain generalization. \n\nThe results are shown as follows. Our results show that when integrating our plug-and-play force guidance module with the baseline model, there is a significant improvement in success rate on this challenging OOD benchmark. This demonstrates that our method not only enhances docking accuracy but also improves robustness to structural and functional shifts across the proteome. \n\n| Method | Mean RMSD | % RMSD < 2 | Mean Centroid Distance | % Centroid Distance < 2 |\n| --- | --- | --- | --- | --- |\n| FABind | 19.1 | 1.3 | 18.1 | 14.2 |\n| FABind+ | 18.5 | 1.5 | 16.9 | 16.1 |\n| DiffDock | 16.2 | 5.3 | 14.5 | 21.4 |\n| DiffDock + Vina | 12.5 | 7.1 | 10.9 | 25.7 |\n| DiffDock + Conf | 13.4 | 6.9 | 12.5 | 24.6 |\n| DiffDock + Gnina | 12.9 | 7.2 | 11.2 | 25.3 |\n| DiffDock + Glide  | 12.6 | 7.2 | 11.9 | 26.6 |\n| Ours | 14.5 | 6.5 | 14.1 | 23.2 |\n| Ours + Vina | 12.3 | **8.1** | 10.4 | 26.8 |\n| Ours + Conf | 12.5 | 7.9 | 11.6 | 25.4 |\n| Ours + Gnina | 13.1 | 7.6 | 12.1 | 26.9 |\n| Ours + Glide | **12.2** | **8.1** | **10.3** | **27.8** |\n\n**W3: Typos**\n\nAll reported typos fixed; we also ran Grammarly and LanguageTool.\n\n**Q1: Time & space overhead.**\n\nThank you for the question regarding the computational complexity of integrating the energy term in our framework. The integration of the force-guided component in ForceFM introduces additional, but manageable, time and space overhead during both training and inference. Below, we break down the complexity based on our experimental setup. \n\nTrain:\n\n- **Memory (Space) Overhead**: Due to its smaller size, the force model requires approximately **50% of the GPU memory** used by the baseline model during training.\n- **Time Overhead**: Training the force model takes about **1/3 the time** of training the baseline model. This is because it is trained in a staged manner (after the baseline is fixed), with fewer epochs (400 vs. 800) and benefits from a smaller network size.\n\nInference: \n\n- **Per-Step Computational Cost**: The forward pass of the combined model takes approximately **1.3× the time and memory** of the baseline model alone, due to the additional forward pass of the smaller force network.\n- **Overall Inference Time**: Despite the higher per-step cost, **the total inference time is reduced** because force guidance enables faster convergence. As shown in Figure 2(b), ForceFM reaches optimal performance in roughly **half the number of sampling steps** compared to the unguided baseline. This leads to a net **improvement in end-to-end efficiency**.\n\nLooking ahead, we also envision opportunities to further optimize training and deployment. For instance, instead of training a separate force model, one could incorporate the guidance signal via **parameter-efficient fine-tuning techniques such as LoRA (Low-Rank Adaptation)** applied directly to the baseline model. This would drastically reduce training costs and eliminate any additional inference latency, while still enabling effective energy-based guidance."}]

Author rebuttal:

Meta-review: This paper introduces ForceFM, a novel framework that integrates a force-guided module into flow matching generative models for protein-ligand docking.

ForceFM presents a compelling advance in structure-based drug discovery by bridging generative modeling with physics-informed guidance. While some methodological and presentation issues were raised, the authors responded constructively and convincingly. The paper is technically solid and well-motivated. All the reviewers are positive about the paper. I recommend acceptance.
Decision: Accept (poster)