Unified all-atom molecule generation with neural fields

We thank the reviewer for the comprehensive review and positive recognition of FuncBind's competitive performance across multiple molecular modalities and its state-of-the-art results in CDR loop generation. We also appreciate the reviewer's acknowledgment of our model's robustness and the benefit of using data augmentation over explicit equivariance constraints. Next, we address reviewers’ weaknesses and questions.

Undefined Terms ("seed," "density field"). Thank you for pointing out the missing definitions. We will clarify these terms in the main paper.

• Seed: Refers to the original binder present in the co-crystal structure.
• Density field: A function that maps 3D coordinates to n-dimensional atomic occupancy values, where n is the number of atom types. This continuous generalization of voxels offers advantages over point cloud representations, including compatibility with expressive neural network architectures, implicit handling of variable atom/residue counts, and an all-atom formulation across modalities.

FuncBind as an extension of FuncMol [16]: While FuncBind builds upon the neural field concept introduced in FuncMol, it proposed several significant and non trivial innovations:

• Structure-conditioned generative model. Unlike FuncMol, FuncBind is explicitly designed as a structure-conditioned generative model, a setting with more practical value than unconditional generation especially for drug discovery.
• Modality-agnosticism. FuncMol focused primarily on small molecules and small MCPs. FuncBind is the first framework to unify all-atom generation across three distinct and challenging modalities (small molecules, MCPs, and CDR loops) within a single model, demonstrating broad applicability and leveraging diverse training data.
• Spatially arranged feature map. We introduce a spatially arranged feature map (Figure 1b) in the latent space, a departure from FuncMol's global embedding. This innovation allows FuncBind to better capture local spatial information, scale to larger molecules, and integrate expressive 3D U-Net architectures for denoising.
• Multi-measurement walk-jump sampling (WJS-m). We provide the first experimental validation of WJS-m in generative modeling applications (Section 3.2.2), demonstrating its effectiveness in improving sampling by effectively decreasing noise levels upon accumulation of measurements, which is a novel contribution in this context. FuncMol was limited to single measurement walk-jump sampling which we observed has lower validity.
• Novel Dataset and Benchmark. The introduction of the MCP dataset and benchmark is a substantial contribution, enabling future research in this understudied area.

2D Molecular validity metrics. Our claim of "high molecular validity" (Lines 192-193) refers to the successful inference of chemically sensible 3D structures and bonds by OpenBabel, which inherently verifies 2D validity. We observed that increasing the number of noise levels, from walk-jump sampling to multi-measurement walk-jump sampling and ultimately to diffusion (approximating infinite noise levels), directly correlates with a higher fraction of molecules passing the OpenBabel filter. In practice, our method achieved around 50% molecular validity performance on CDRs, meaning half of our generated molecules passed the OpenBabel filter. We note that our fast sampling speed ensures that this validity rate does not become a bottleneck for the utility of our method.

Baselines for MCP. You correctly highlight the absence of baselines for macrocyclic peptide (MCP) generation, which is precisely why we introduced a new dataset and benchmark for this challenging modality. MCPs pose significant challenges for generative models due to their non-canonical amino acids, cyclization, and scarce training data. At submission time, no other target-conditioned, structure-based MCP generative models could handle non-canonical amino acids, making direct comparisons impossible. To address this, we now provide a comparison of FuncBind with AfCycDesign [Rettie et al 25a] and RFPeptide [Rettie et al 25b], two very recent generative models that generate MCPs exclusively with canonical amino acids and N-to-C cyclization. As the table below shows, FuncBind achieves better or similar metrics, particularly with lower average ligand RMSDs (2.47 vs 3.08 and 3.99) and interface RMSDs (2.1 vs 3.3 and 5.2). FuncBind also yields the highest proportion of generated samples with docking scores better than the seed (50% vs 7% and 18%). The only metric where FuncBind samples underperformed was the fraction of residues with a Tanimoto similarity greater than 0.5 (0.38 vs 0.39), which was expected as FuncBind has access to a larger set of non-canonical amino acids and sequence lengths unlike the baselines in its sampling process. We encourage future comparisons of MCP models, especially those handling non-canonical amino acids, against FuncBind on this new benchmark.

[Rettie et al 25a] Cyclic peptide structure prediction and design using AlphaFold2 [Rettie et al 25b] Accurate de novo design of high-affinity protein binding macrocycles using deep learning

Sampling time. FuncBind is not tied to any specific score-based sampling methods. In fact, we tried three generative models: single measurement and multi measurement walk jump sampling, and diffusion. All these approaches leverage several sampling steps at the different noise levels (in walk jump sampling, these sampling steps are called “walk”). Despite using several sampling steps (500 for single measurement, 1600 for multi measurement and 256 for diffusion), we still achieve the fastest sampling time, owing to our latent formulation.

MCP dataset complex selection. The 641 MCP-protein complexes are all the complexes we could isolate from the RCSB PDB [19] at the time of data curation.

Adaptability to partial molecular optimization. Yes, our approach is adaptable to partial molecular optimization and fixing specific moieties. In fact, the antibody CDR loop generation task (Section 4.2) is a direct instance of this: it involves generating the CDR loops with a fixed antibody framework dock and epitope. Our model can be directly trained for this type of constrained generative task due to the continuous neural field representation and its ability to capture local information. As mentioned by the reviewer, this inherent flexibility makes FuncBind promising for applications like hit-to-lead optimization, where fine-grained modifications to known binders are critical.

We thank the reviewer for the thoughtful review, particularly for recognizing FuncBind's scalability, its ability to handle complex spatial conditioning, and the significant contribution of our new macrocyclic peptide (MCP) dataset. We are also pleased that you found the paper well-written and the method clear. The reviewer's main concern is about lack of comparison with VoxBind, which we address first, followed by the other remarks.

Comparison of FuncBind and VoxBind. Our core contribution introduces neural fields as a novel representation for structure-conditioned molecular generation, an approach previously unexplored in this context. While VoxBind is a conditional model utilizing discrete voxel grids—the discretized counterpart of neural fields—both methods share benefits like compatibility with powerful denoiser architectures and score-based generative frameworks, and ease of structure-based conditioning. However, the computational and memory costs of voxel representations scale cubically with molecular volume. In practice these models are only applicable to small molecule generation. This is why we did not compare FuncBind vs VoxBind on the CDR/MCP datasets: for the simple reason that VoxBind cannot be trained efficiently in these settings. Our proposed continuous neural field representation directly addresses this fundamental scalability challenge by offering significantly greater memory efficiency. This enabled its application to larger and more complex molecular systems such as MCPs and CDR loops.

This paper reads more like a "we delivered a model"-paper than a scientific methods paper. What are the hypotheses being tested? Why or when are the proposed changes to VoxBind important? What have we learned from this paper? In our work, we show that continuous neural field representation combined with modern computer vision architectures and efficient score-based sampling can effectively generate diverse all-atom molecular systems conditioned on target structures, without relying on modality-specific representations or explicit equivariance constraints. Through FuncBind, we learned that modality-agnosticism is achievable with a single model spanning disparate molecular modalities (small molecules, macrocyclic peptides, antibody CDR loops), demonstrating the power of unified representation. This is highly non-trivial. Furthermore, our results further validate that explicit SE(3) equivariance constraints are not strictly necessary for high structural accuracy when strong data augmentation is employed, as evidenced by our large improvement of prior SE(3) equivariant baselines on the task of CDR loop redesign. This work also provided the first experimental validation of multi-measurement walk-jump sampling (WJS-m) in generative modeling, showing its effectiveness and efficiency for sampling. These learnings provide generalizable principles for potential future molecular design methodologies, moving beyond merely "delivering a model."

Ablation studies we perform some additional ablation studies; first, we ablate the different sampling methods (walk jump sampling, multi measurement walk jump sampling and diffusion). We observe that adding more noise levels (from single measurement walk jump to diffusion) leads to better metrics, especially w.r.t. Strain energy.

We also include a study on the impact of the latent space’s dimension; we observe that more latent dimensions helps the model better perform loop inpainting (both higher uniqueness and metrics on unique samples).

Computation. FuncBind's design, as a latent approach with continuous neural fields, inherently scales more efficiently with model size, enabling it to leverage increased computation more effectively. This contrasts with voxel-based methods like VoxBind, which face significant memory constraints that limit their scalability for larger molecules due. Thus, FuncBind's architectural choices are key to its demonstrated scalability and performance. For context, AbDiffuser reports 169M parameters, RFDiffusion ~100M, and VoxBind ~120M.

Runtime. Below is the table of average sampling time per molecule for different methods on small molecules and antibody CDR loops with one A100 GPU. FuncBind achieves preferable runtime than other methods (sometimes by an order of magnitude). We attribute this to the efficient latent representation, to the use of standard architectures (CNN and self-attention layers only) and to the efficiency of score based generative models.

MCP dataset and baselines. You correctly highlight the absence of baselines for macrocyclic peptide (MCP) generation, which is precisely why we introduced a new dataset and benchmark for this challenging modality. MCPs pose significant challenges for generative models due to their non-canonical amino acids, cyclization, and scarce training data. At submission time, no other target-conditioned, structure-based MCP generative models could handle non-canonical amino acids, making direct comparisons impossible. To address this, we now provide a comparison of FuncBind with AfCycDesign [Rettie et al 25a] and RFPeptide [Rettie et al 25b], two generative models that generate MCPs exclusively with canonical amino acids and N-to-C cyclization. As the table below shows, FuncBind achieves better or similar metrics, particularly with lower average ligand RMSDs (2.47 vs 3.08 and 3.99) and interface RMSDs (2.1 vs 3.3 and 5.2). FuncBind also yields the highest proportion of generated samples with docking scores better than the seed (50% vs 7% and 18%). The only metric where FuncBind samples underperformed was the fraction of residues with a Tanimoto similarity greater than 0.5 (0.38 vs 0.39), which was expected as FuncBind has access to a larger set of non-canonical amino acids and different sequence lengths as opposed to these baselines in its sampling process. We encourage future comparisons of MCP models, especially those handling non-canonical amino acids, against FuncBind on this new benchmark.

[Rettie et al 25a] Cyclic peptide structure prediction and design using AlphaFold2 [Rettie et al 25b] Accurate de novo design of high-affinity protein binding macrocycles using deep learning

Minor: "modality-agnostic representation" phrasing. We will revise the current phrasing to clarify that our "modality-agnostic representation" refers to the unified approach of representing diverse molecular structures (small molecules, peptides, proteins, etc) as continuous atomic density fields, rather than using distinct, modality-specific representations (e.g., graphs for small molecules, amino sequences or backbone coordinates for proteins). This allows a single model to be trained across these varied chemical entities (and allows us to trivially model non-canonical amino acids).

We thank the reviewer for the thoughtful review and positive assessment of FuncBind's unified, modality-agnostic approach and its innovative use of neural fields. We appreciate your recognition of our framework's ability to span diverse molecular modalities and its competitive performance against specialized baselines. Next, we address the reviewers' concerns.

Decoding pipeline's reliance on heuristic stages. We acknowledge that our multi-stage decoding pipeline involves heuristic steps. However, the current pipeline, while not fully differentiable end-to-end for bond inference, was a pragmatic choice to enable unified, all-atom generation across diverse molecular modalities, including variable atom/residue counts and non-canonical amino acids. Our competitive results across small molecules, macrocyclic peptides, and antibody CDR loops demonstrate that FuncBind successfully generates high-quality and chemically plausible structures despite these heuristics. Finally, we also mention that many of the small molecule baselines also rely on post-processing heuristics (eg, OpenBabel to infer bonds).

Bond lengths, angles and torsions. While it is not standard to explicitly measure bond lengths, angles, and torsions in the benchmarks we considered, these structural qualities are indirectly evaluated through metrics such as strain energy for small molecules, RMSD and IMP (related to energy) for antibodies. Notably, our diffusion-based variation improved strain energy to a level comparable with VoxBind (166 for FuncBind with diffusion vs 188 for VoxBind), and our original IMP metric remains state-of-the-art by a significant margin. This indicates that our model generates high-quality structures, performing competitively—if not better—than baselines. Furthermore, qualitative assessments reveal consistent peptide and closure bonds in macrocycles. The successful generation of novel, chemically plausible non-canonical amino acids further supports the model’s ability to learn fundamental atomic relationships.

Ablation studies. We conducted several ablation studies during FuncBind's development. Eg, preliminary experiments led us to select the EDM2 U-Net architecture for our denoiser (over ADM), adapting its conditioning mechanism for 3D tensors.

Below, we investigated various sampling configurations. First, we varied the number of sampling steps, as shown in the tables, as requested. For small molecule generation on CrossDocked, reducing sampling steps (e.g., from 256 to 64) leads to increased strain energy, while most other metrics remain stable, and clashes even improve. For antibody CDR loops, more steps generally improve performance, though uniqueness slightly decreases with increased steps.

Finally we perform an ablation on different sampling methods (walk jump sampling, multi measurement walk jump sampling and diffusion). We observe that adding more noise levels generally leads to better metrics, especially w.r.t. Strain energy.

Components of FuncBind critical for performance. There are two components to performance: 1) a good reconstruction performance and 2) a good denoising performance. As with most papers on latent diffusion, there is a trade-off between these two terms. Based on our experiments, the largest strength of our approach is the use of the latest EDM2 denoiser architecture which can be efficiently reused in this setting (with some adaptation from 2D to 3D data that we made to that network). Moreover, we significantly improved the reconstruction performance of our neural field based auto-encoder by using a spatial latent vector instead of a vector value latent space.

Equivariant baselines. The vast majority of our baselines are recent equivariant diffusion models, e.g. DiffSBDD, Pocket2Mol, Molcraft, DecompDiff, TargetDiff on the small molecules and DiffAb, AbDiffuser on the antibodies.

Empirical results presentation. We apologize for this oversight. In a revised version, we will bold the best numbers in all performance tables to enhance clarity and ease of comparison.

Thanks for the response! I have no further concerns and I am willing to keep my accept score.

Unsubstantiated central hypothesis. We appreciate the feedback regarding our central hypothesis and the call for an ablation study comparing unified and modality-specific models. This analysis is insightful and we have now included an ablation study to directly address this point.

Unified training is inherently challenging, which explains the prior absence of models spanning the three modalities we consider. Our neural-field-based representation, however, made multi-modality training seamless and straightforward; we achieved this by simply conditioning the denoiser on the modality class and applying uniform rebalancing. While performance on individual saturated benchmarks could be further optimized with modality-specific tuning, our primary goal was to establish a robust unified model, not necessarily to achieve state-of-the-art on metrics known to poorly correlate with true binding.

The appeal of multi-modality lies in its potential for positive knowledge transfer, enabling better generalization by leveraging more diverse data and eliminating the need for separate models. Given the distinct nature of our modalities, evaluating this transfer is particularly insightful. To empirically address the reviewer's concern, we trained modality-specific models for small molecule, CDR loop, and MCP generation, and the results are compared against our unified model in the revised manuscript.

Ablation: unified vs. single-modality. We conducted this ablation using similar compute resources and diffusion as the score-based generation method. The comparison considers uniqueness/diversity and performance metrics across modalities:

• CDR loop inpainting: The specialized model shows a drop in sequence design uniqueness, with comparable performance on unique samples. Given uniqueness's importance in library design, the unified model's ability to maintain higher uniqueness is a notable advantage.

For the H3 loop specifically on unique samples:

• Small Molecules (CrossDocked): Metrics remained largely comparable between unified and specialized models, indicating no significant performance degradation from unification.

• Macrocyclic Peptides (MCP): The unified model demonstrated superior performance in key structural metrics (TM-score, lRMSD, iRMSD) and cyclization fraction, with other metrics remaining similar.

In summary, the unified model generally shows a positive to neutral effect on performance across modalities. A key benefit is the improved uniqueness, likely due to mitigating overfitting from a larger, more diverse training set. Furthermore, unification greatly simplifies experimental validation by eliminating the need to train separate models per modality. We note that transfer is likely to have a greater impact between more similar molecular classes (e.g., antibodies and proteins); this is an area for future work.

Performance on benchmarks.

• Small molecules: We acknowledge that FuncBind's performance on the highly competitive CrossDocked benchmark is on par with, or slightly behind, leading specialized models like VoxBind. However, achieving this parity while being a unified model capable of tackling significantly larger and more complex modalities like macrocyclic peptides and CDR loops—which VoxBind's discrete voxel representation inherently struggles with due to cubic scaling limitations —is a major achievement for generalizability and viability. Our primary goal was to demonstrate unification without significant performance compromise on individual tasks, rather than solely achieving state-of-the-art on (saturated) benchmarks.
• CDR redesign: We appreciate your recognition of FuncBind's "remarkable and significant advantage in structural fidelity (RMSD)". This is indeed an unqualified win. Our Amino Acid Recovery (AAR) is competitive, and with recent enhancements using a diffusion model, FuncBind now leads on all AAR metrics as shown in the updated table below. Furthermore, our strong IMP (interface energy improvement) scores in the original manuscript, nearly double that of some baselines without explicit minimization, underscore the quality of our generated structures.

• For practical validation beyond in silico metrics, we tested our antibody H3 redesign in the wet-lab using Surface Plasmon Resonance (SPR) in a de novo setting. This yielded a 42% binding rate on a target with a rigid epitope and 4% on a target with a flexible epitope. Further details will be provided in future revisions, pending legal clearance.

MCP baselines. You correctly highlight the absence of baselines for macrocyclic peptide (MCP) generation, which is precisely why we introduced a new dataset for this modality. MCPs pose significant challenges for generative models due to their non-canonical amino acids, cyclization, and scarce training data. At submission, no other target-conditioned, structure-based MCP generative models handled non-canonical amino acids, precluding direct comparisons. To address this, we now compare FuncBind with AfCycDesign [Rettie et al 25a] and RFPeptide [Rettie et al 25b], two models generating MCPs exclusively with canonical amino acids and N-to-C cyclization. As shown below, FuncBind achieves superior or similar metrics, notably lower average ligand RMSDs (2.47 vs 3.08 and 3.99) and interface RMSDs (2.1 vs 3.3 and 5.2). FuncBind also yields the highest proportion of designs with better docking scores (50% vs 7% and 18%). The only underperformance was in Tanimoto similarity (0.35 vs 0.39), expected as FuncBind accesses a larger set of non-canonical amino acids and different sequence lengths as opposed to these baselines. We encourage future comparisons on this new benchmark, especially for models handling non-canonical amino acids.

[Rettie et al 25a] Cyclic peptide structure prediction and design using AlphaFold2 [Rettie et al 25b] Accurate de novo design of high-affinity protein binding macrocycles using deep learning

Technical components. We respectfully disagree that FuncBind is merely an integration of existing methods. Our core contribution is a novel neural field representation specifically for structure-conditioned generation, a previously unexplored area. This enabled us to develop one of the first unified models for generating small molecules, MCPs (with non-canonical AAs), and CDR loops, all conditioned on a target structure, achieving competitive or SoTA results across diverse chemical matter. The unified training, facilitated by this representation, was a direct byproduct of its inherent flexibility.

Unlike the unconditional FuncMol, FuncBind is explicitly structure-conditioned. It introduces significant methodological advancements like replacing FuncMol's vector latent with a spatial latent tensor, which greatly improves performance by enabling U-Net architectures and simplifying structure conditioning. Finally, while FuncBind utilizes established score-based generative models (walk-jump sampling in the initial draft, and diffusion in revision), this is common practice in the field. Our primary aim was not to invent a new sampler, but to propose a new, highly compatible representation for structure-conditioned generation that can seamlessly integrate with any score-based generative framework.

Sampling efficiency. We agree that sampling efficiency is a crucial practical metric. FuncBind demonstrates a significant speed advantage, sometimes an order of magnitude faster than many baselines, as shown in the table below (average time in seconds per molecule on A100).

Unlike FuncBind, these slower models may face more issues with real-world viability where high-throughput generation is critical. While lower sampling time is useful, we prioritize models with demonstrated high experimental binding rates, a benchmark FuncBind has achieved in CDR loop redesign.