ForceFM: Enhancing Protein-Ligand Predictions through Force-Guided Flow Matching

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.

W1: Methodological novelty modest.

We 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.

Importantly, 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…

We 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.

W2/Limitations: Dataset splitting / additional benchmarks.

Thank 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.

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 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.

W3: Typos

All reported typos fixed; we also ran Grammarly and LanguageTool.

Q1: Time & space overhead.

Thank 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.

Train:

• 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.
• 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.

Inference:

• 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.
• 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.

Looking 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.

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.

W1: Emphasize guidance module over baseline FM.

We 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.

W2: Runtime fairness: different step counts.

We 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.

Looking 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.

W3: GNINA score ambiguity.

We 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.

Q1: Missing $\sigma_{tr, max}$ and $m$ definitions.

We 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.

In addition, for improved clarity, the number of rotatable bonds $m$ will be in the main text when the term is first introduced.

Q2: Missing algorithm details: randomly perturb and hyper-parameter $k$

We thank the reviewer for pointing out missing this important detail.

• Perturbation. It is set at the noise level at $\sigma_{max}/10$. Then perturbing the ligand via random translation, rotation and torsion.
• 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.

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.

W1. Limited Core Novelty Due to Reliance on Energy Functions

We 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).

Importantly, 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…

We 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.

W2/W3/Q1. Hyperparameter Tuning and Lack of Ablation Studies

The ablation study for $k$ and $\eta$ is presented in Appendix E, with following principle.

• 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.
• 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.

In 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.

W4/Q3: Limited Baseline Comparison

Thank 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.

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 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.

Q2: Inference efficiency

We 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.

Looking 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.

Q4: Practical utility.

Yes, 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.

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.

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.

Although 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.

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.

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.

W1/Q1. Generalization claims overstated; time‑split and UniProt filtering are insufficient.

Thank 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’.

For 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.

W2/Q2. Method is pocket‑based, hence not blind docking. Sensitivity to pocket definition.

We 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.

To 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.

More 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.

These 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.

Q3. Is graph rebuilt after each update?

Yes; edges are recomputed every step to guarantee geometric consistency and they are used as features in the neural network.

Q4. Table 2 says “flexible” although receptor is rigid.

We 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.

Q5. Could post‑minimization deliver same gains?

Thank 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.

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 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.
• Combining force-guided generation with minimization yields the best of both worlds: 45.8% PoseBuster pass rate, significantly outperforming any other combination.

Q6. Vina does not measure internal strain—wording.

Thank 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.

[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.

[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.

[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.