UniMoMo: Unified Generative Modeling of 3D Molecules for De Novo Binder Design
Authors: Xiangzhe Kong
Zishen Zhang
Ziting Zhang
Rui Jiao
Jianzhu Ma
Wenbing Huang
Kai Liu
Yang Liu
Venue: ICML 2025 poster (2025)
Keywords: Unified Generative Framework
Molecular Binder Design
Drug Discovery
Geometric Latent Diffusion
Primary area: applications->health_medicine

Abstract: The design of target-specific molecules such as small molecules, peptides, and antibodies is vital for biological research and drug discovery. Existing generative methods are restricted to single-domain molecules, failing to address versatile therapeutic needs or utilize cross-domain transferability to enhance model performance. In this paper, we introduce **Uni**fied generative **Mo**deling
of 3D **Mo**lecules (UniMoMo), the first framework capable of designing binders of multiple molecular domains using a single model. In particular, UniMoMo unifies the representations of different molecules as graphs of blocks, where each block corresponds to either a standard amino acid or a molecular fragment. Based on these unified representations, UniMoMo utilizes a geometric latent diffusion model for 3D molecular generation, featuring an iterative full-atom autoencoder to compress blocks into latent space points, followed by an E(3)-equivariant diffusion process. Extensive benchmarks across peptides, antibodies, and small molecules demonstrate the superiority of our unified framework over existing domain-specific models, highlighting the benefits of multi-domain training.

UniMoooo Unified Generative Modeling of 3D Molecules for De Novo Binder Design
Xiangzhe Kong' 12 Zishen Zhang'
Ziting Zhang Rui Jiao
Jianzhu Ma 42 Wenhing Huang" 56 Kai Liu?
Yang Liu 12
Abstract
Peptide
The design of target-specific molecules such as small molecules, peptides, and antibodics is vital for biological research and drug discovery. Exist- ing generative methods are restricted to single- domain molecules, failing to address versatile therapeutic needs utilize cross-domain trans- ferability to enhance model performance. In this paper, we introduce Unified generative Modeling of 3D Molecules (UniMoMo), the first framework capable of designing binders of multiple molec- ular domains using single model. particular, UniMoMo unifies the representations of different molecules as graphs of blocks, where each block corresponds to either a standard amino acid or molecular fragment. Subsequently, UniMoMo utilizes a geometric latent diffusion model for 3D molecular generation, featuring an iterative full-atom autoencoder to compress blocks into la- tent space points, followed by E(3)-equivariant diffusion process. Extensive benchmarks across peptides, antibodies, and small molecules demon- strate the superiority of our unified framework over existing domain- specific models, highlight- ing the benefits of multi-domain training.
LOGAL
Antibody
?
Target Protein
Small Molecule
Figure I. Given the binding site the target protein, our Uni- MoMo capable of generating diverse molecular binders, includ- ing peptides, antihodies, and small molecules.
the resulting bindings ical pathways of interest (Glögl et al., 2024; Wang et al., 2021). Various types of molecules have been exploited for different purposes because their unique biochem- ical properties. For instance, small molccules are ideal for oral administration due to their high absorption effi- ciency (Beck al., 2022), peptides excel in intracellular targeting thanks their cell cell-penetrating capability (Der- akhshankhah & Jafari, 2018), and antibodies are favored for treating severe diseases like cancer because of their high specificity (Basu et al., 2019). The distinct roles of gener-
induce block specific biolog-
these molecular types have led to domain ative models. In particular, for small molecules, research has focused on autoregressive models (Peng al., 2022), liffusion-based approaches (Guan al., 2023a; Schneu- ing et al., 2024), Bayesian flow networks (Qu et al., 2024), and voxel-based representations (Pinheiro et al., 2024). For peptides and antibodies, diffusion models (Iuo et al., 2022; Kong et al., 2024b), iterative refinement (Jin et al., 2021; Kong et al., 2023a;b) and multi-modal flow matching (Li et al., 2024b; Lin et al., 2024c) are prevalent.
1. Introduction
Designing molecules that bind to target proteins is funda- mental task in biological research and drug discovery, as
'Dept. of Comp. Sci. & Tech., Tsinghua University lInttittte for AI Industry Research (AIR), Tsinghua University 'Dept. of Automation, Tsinghua University "Dept. of Electronic Engineer- ing, Tsinghua University 'Gaoling School Artificial Intelligence, Renmin University of China BBiijing Key Laboratory of Research on Large Models and Intelligent Governance "Bytedance Project Voyager Team. Correspondence to: Wenbing Huang <hwen- bing @ 126.com>. Kai Liu Zluuai0024@byytdamm weeebtycaanc.comm.. com>> Yang Liu <liuyang2011 esittsuaa.du..oo edu.en>.
We argue that unified generative framework for all types of molecules offers distinct advantages over the current domain-specitee paradigm. From an application standpoint, such a framework enables the exploration of multiple drugs spanning diverse molecular types for single target, ad- dressing varied therapeutic needs. From a machine learning
Proceedings of the 4nnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
perspective, unified modeling leverages larger and more diverse datasets, better exploiting available data. More- over, this methodology is well founded, as the principles underlying molecular binder design are consistent across dif- ferent molecular types, including interactions with the target protein (Bissantz et al., 2010) and adherence to geometric constraints like bond lengths, angles, and clashes (Lide, 2004), all governed by the same physiochemical rules.
allows the diffusion model to bypass the intra-block depen- dencies within building blocks, focusing instead on global arrangements, with the fine-grained reconstruction of local full-atom details handled by the decoder module of the au- toencoder. Second, by performing the diffusion process in the latent space, with reduced dimensionality and graph size, the model achieves significant improvements in training and inference efficiency.
However, designing a unified generative framework poses significant challenges due to the distinct representation of different molecular types. Small molecules comprise var- ious functional groups assembled in diverse patterns (Qu et al., 2024), while peptides and antibodies are composed of amino acids arranged linearly (Kong et al., 2024b), with antibodies further featuring distinct regions defined by their functional roles (Kong et al., 2023a). A straightforward yet suboptimal approach is to treat all molecules as atomic graphs regardless of distinct types. However, this ignores the intrinsic hierarchical priors of molecular structures (e.g., benzene rings or standard amino acids) and results in high computational complexities for larger systems like peptides and antibodies. Conversely, relying solely on vocabulary of common substructures, without preserving atomic details, lacks transferability, as the shared principles of molecular binder design rely heavily on full-atom geometry. Thus, de- veloping an effective and efficient unified generative frame- work that incorporates both atomic details and hicrarchical priors remains an open and pressing challenge.
We conduct extensive experiments benchmarks of pep- tides, antibodies, and small molecules. The results demon- strate the superiority of our unified framework over the domain-specific models, and also illustrate the benefits of training a unified model with multi-domain molecular data. Furthermore, we showcase the ability of UniMoMo to gener- ate binders targeting the same protein pocket across different molecular types with desired affinity.
2. Related Work
Small Molecule Design Structure-basel drug design (SBDD) has advanced with deep generative models. Early voxel-based methods, like LIGAN (Masuda et al., 2020) and 3DSBDD (Luo al., 2021), predict atom densities and types using VAEs or autoregressive approaches. Equiv- ariant Networks (Satorras et al., 2021) enable direct 3D atomic position generation, as in Pocket2Mol(Peng et al., 2022) and GraphBP (Liu et al., 2022). Diffusion mod- els (Ho et al., 2020) further improved SBDD with meth- ods like TargetDiff (Guan et al., 2023a), DiffBP (Lin et al., 2025), and DiftSBDD (Schneuing et al., 2024). Recent works, including FLAG (Zhang et al., 2023), D3FG (Lin et al., 2024a), and DecompDiff (Guan et al., 2023b), lever- age domain knowledge, while MolCraft (Qu et al., 2024) and VoxBind (Pinheiro et al., 2024) introduce Bayesian Flow Networks (Graves et al., 2023) and walk-jump sam- pling (Frey et al., 2024). Our work relates closely to diffu- sion and fragment- based models, as we employ principal subgraphs (Kong al., 2022) to decompose molecules into blocks within our unified generative framework.
In this paper, we propose Unified generative Modeling of 3D Molecules (UniMoMo), the first framework capa- ble of designing binders across multiple molecular types using single model. Our approach begins by represent- ing 3D molecules as graphs of blocks, where each block corresponds to either a standard amino acid or a molecu- lar fragment (Figure 2). Fragments, extracted from small molecules and non-standard amino acids, are identified us- ing the principal subgraph algorithm (Kong et al., 2022). This representation preserves both the full-atom geometry and the hierarchical structure of building blocks, which are critical for modeling interactions and local geometries (Figure 1). Built upon the unified representations, we lever- age a geometric latent diffusion model for efficient and effective generative modeling. First, an iterative full-atom autoencoder is trained compress each block into a la- tent representation consisting of dindeiinniional hidden state and a spatial coordinate, then reconstruct the full-atom geometries from the latent point cloud with two-stage de- coding. Subsequently, a diffusion model operates in the latent space to generate the E(3)-invariant latent states and the E(3)-equivariant coordinates.
Peptide Design Peptide design has shifted from energy- based sampling (Bhardwaj et al., 2016; Hosseinzadeh et al., 2021) to deep generative models (Li et al., 2024a). PepFlow (Li et al., 2024b) and PPFlow (Lin et al., 2024c) similarly apply multi-modal flow matching over residue types, orientations, Ca positions, and side-chain dihedral angles. PepGLAD (Kong et al., 2024b) employs geometric latent diffusion models to co-design the sequence and full- atom structure of peptides. Additional efforts have explored specific peptide subtypes, such as a-helical peptides (Xic et al., 2024) and D-peptides (Wu et al., 2024). Our work is closely related PepGLAD, leveraging geometric latent diffusion, but with the novel inclusion of iterative design and bond prediction within the full-atom autoencoder.
The architecture design of our model offers the following two key advantages. First, the compressed latent space
2

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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
Antibody Design Antibody design, which mainly focuses on the hampllemmnntatty-eeemmmnnni
and iteratively merges the frequent neighboring nodes into common building blocks such benzene and indole (Ap- pendix A). The resulting vocabulary of blocks, denoted by V. comprises standard amino acids and the extracted princi- pal subgraphs. Consequently, each block in the molecular graph can be assigned with a type s; E V. For better control- lability, we introduce a binary prompt for each block, with indicating the generation of natural amino acids (AAs), and 0 indicating either AAs or molecular fragments. During benchmarking for peptides and antibodies, all blocks are assigned prompt of to enforce AA-only generation. For small molecules, we set the prompt to O, allowing flexible sampling from a broader set of molecular fragments.
Regions (CDRs),
has also evolved from forcefield-based sampling (Adolf-
Bryfoglc et al., 2018) to deep learning (Saka et al., 2021;
Akbar et al., 2022; Martinkus et al., 2024; Jin et al., 2021).
MEAN (Kong et al., 2023a) and DiffAb (Luo et al., 2022)
generate antigen-specific antibodies using iterative decoding or diffusion, while dyMEAN (Kong et al., 2023b) handles full-atom generation in scenarios of unknown antibody dock- ing poses. HERN (Jin et al., 2022) employs hierarchical graphs and auto-regressive decoding, while GeoAB (Lin et al., 2024b) incorporates physical constraints. Other ap- proaches explore pretraining (Wu & Li, 2024; Gao et al., 2023; Zheng et al., 2023), and explicit optimization on ener- gies to enhance performance (Zhou et al., 2024).
The molecular binder and the binding site of the target protein are denoted as two graphs of blocks, G2 and Gy, respectively. Any optional context, such the framework regions of antibodies, are also included in gy. In this paper, we address de novo binder design, which involves generative modeling of p(9z Gy), namely the conditional distribution of the molecular binder given the context environment. To avoid information leakage of reference binders, the binding site is defined residues within 10Å distance the binder based on Cj atoms, following previous work (Peng et al., 2022; Kong al., 2024b), or based on the center of mass for those blocks without C3 atoms.
Unified Modeling GET (Kong al., 2024a) pioneers the unified modeling of biomolecules for molecular interaction prediction, showcasing zero-shot generalizability. Subse- quent works further explore unified language models (Zheng et al., 2024) and inverse folding models (Gao et al., 2024). Recently, Alphafold 3 (Abramson et al., 2024) achieves groundbreaking accuracy in structure prediction across di- verse biomolecular types. Our work is inspired by GET and Alphafold 3, which highlight the transferability of cross- molecular interactions, but focuses on the more challenging task of de novo molecular binder design.
3.2. Iterative Full-Atom Variational AutoEncoder
3. Method: UniMoMo
We first propose an iterative full-atom variational autoen- coder (VAE), comprising an encoder & and a decoder De (Vincent et al., 2010), to establish a mapping between the full-atom geometries and a compact latent space.
In the following section, we begin by introducing the nec- essary notations and our unified molecular representation in $3.1. Next, we elaborate on the two core components of our UniMoMo: 1) A full-atom variational autoencoder that compresses building blocks into latent points and iteratively reconstructs atom-level details ($3.2); 2) A geometric diffu- sion model that operates within the latent space ($3.3). The overall framework is illustrated in Figure 2.
Encoder The encoder & projects the binder Gn and the binding site Gy into latent point clouds Z, and Zy:
Z, = EG()),
Z, = (G
(I)
where 2g = [(z,,, contains the latent states 2; E Rd
(d = 8 in this paper) and coordinates 2 E R of block i in G.. Both z, and Z, are sampled from the encoded distri- bution N(zz; pt, or)) and (i,;; pu; o;: using the reparam- eterization trick (Kingma, 2013). The latent representation Z, for the binding site follows similar definition. Note that the binder and the binding site are encoded indepen- dently, without access to each other's 's information. Such implementations align with test-time applications where only the binding site Gy. without binder 9r., is input as the condition. To regularize the scale of the latent states z; and coordinates E. we implement Kullback-Libble (KL) diver- gence constraints relative to the prior distributions N(O, I) and N(F, I) (Kong et al., 2024b), where ri represents the center of mass for all atoms in block é:
3.1. Notations and Unified Representation
We represent a molecule as a graph of blocks -= = EV, V- = {(A,, X.) A; E 2d X; E RRxx3), where each block i has n, atoms, with A; and X; representing their element types and coordinates, respectively. E = i * j). where B; and Bij denote intra- block and inter-block chemical bonds, respectively. For simplicity, we use matrix notation here, but the atoms within each block are unordered. To decompose molecules into blocks, we first identify all standard amino acids individ- ual blocks. In other cases, such as non- non-standard amino acids and small molecules, we leverage the principal subgraph al- gorithm (Kong et al., 2022) for decomposition, as illustrated in Figure 2. This algorithm begins with an atom-level graph
((B,,
Lx (i) = A (N I)II diag(a,)))
(2)
+ X2 (FF, ( digg
3

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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
A
Peptide
Encoder
Forward Diffusion
Antibody
A NM X, E au13 B, By
2, Re
4 e
Full-Atom Dacodar
Block Decoder
Denoising Diffusion Eg
Small Molecule
Iterative
Intialization (7,1)
Decoding Block Type
Decoding
Satur
Figure 2. Overview of our UniMo.Mo. (A) Graph of blocks as the unified representation for peptides, antibodies, and small molecules. (B) The proposed unified generative framework for 3D molecular binder design involves iterative full-atom autoencoder and diffusion model implemented in the latent space. The autoencoder compresses the atomic details of each block into single latent points and reconstructs them by first predicting block types for the latent points, followed by iterative generation of the full-atom geometries.
where DKL. denotes the KL. divergence, X and A2 control the strength of regularization for the latent states and coordi- nates, respectively. During training, we further perturb Σ by adding random noise sampled from (0, I) before feeding it into the decoder. This is crucial because the diffusion mod- ule, operating in the latent space, is hard to generate precise locations, which introduces errors in the latent coordinates during the generation process. By incorporating noise dur- ing training in advance, the decoder learns to handle these imperfections effectively with much higher robustness.
atoms in different blocks are also predicted based on the spatial neighborhood (distance below 3,5 of atoms:
b/j.pg = Softmax(MLP + 11,
(6)
where big,gg represents the type of chemical bond (e.g., sin- gle, double, triple, none) between the p-th atom in block and the q-th atom in block j. Furthermore, h H, [p] and क = [![r] denotes the hidden states and coordi- nates of the p-th atom in block i, respectively. MLP de- notes a 3-layer multi-layer perceptron with SiLU activa- tion (Hendrycks Gimpel, 2016), the input of which is the summation of ht and h to enable commutativity. Bond prediction is restricted to spatially neighboring atoms within 3.5A, determined by the distance d'y,n = || T"), While potential inconsistency between predicted bonds and distances exists, they could be easily distinguished and dis- carded (Appendix G). The reconstruction loss includes cross entropy (CE) for block types and bond types, as well as the mean square error (MSE) for vector fields:
Decoder The decoder De reconstructs the full-atom geom- etry of the binder in two stages: decoding block types and reconstructing atomic coordinates. First, the decoder pre- dicts the block types } for the latent points of the binder using both 3, and Zyy yielding the atom types and chemical bonds within each block via a vocabulary lookup:
{ss} (2x
A, B, Lookup(s,, V), (3)
where 8;, A,, and B; denote the decoded block type, the atom types, and the chemical bonds of block i, respectively. Next, the atomic coordinates are reconstructed in an iterative manner by structure module, similar a light-weight flow matching process (Lipman et al., 2023):
Lrec (1) = CF(p((e),
+ EIJU(O.1)
CE(p(65 p(b P(blipa)))
(7)
{HH, V = Deo (1(A,, B,, X()), Zz, Zy, Gys t), x = X +AVV
(4)
MSE v..)}
+ ELJU(U,))
(5)
where Hi and V are the atomic hidden states and the vector fields for each atom in block i. The time variable t decreases from 1.0 to 0.0 with step size At = 0.1 in this paper, totaling 10 iterations. At = 1.0, the initial coordinates X are sampled from a Gaussian distribution NE,, I) for each block The chemical bonds between
where p(s:). p(b) and V denote the ground-truth block types, bond types, and vector fields, respectively. To encourage better reconstruction of the interactions and local geometries, we also implement a pair-wise distance loss Caist on the neighborhood for each atom. As the geometries are still in chaos on large time values, we only implement

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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
this loss when 1 < 0.25:
where a' I (1 - 3²), and 8 is the noise scale con- forming the cosine schedule (Nichol & Dhariwal, 2021). Given the initial state ui. the state at any time & can be directly sampled as:
(iis((,t)) E (pEAA()))ENGG)) 1d'/.g "gppyl
(8)
EPEA; [N((p)
(iis(t)= 110010,,)(4ec0..2 tt)
(9)
ii Valu + V1 C'EC,
(13)
where MM(p) = (6. 9) L2 < 6.00 denotes all atoms within 6A distance to the p-th atom in block in the ground- truth structure. To make the latent point cloud of the binding site Gy more informative, we also implement the KL diver- gence and reconstruction loss on 5% of the binding site residues. Denoting these randomly selected residues as Gy. we have the overall objective for the autoencoder as follows:
where E; ~ (O, The reverse diffusion process re- constructs the data distribution by iteratively removing the noise (Ho al., 2020), which is modeled as:
Po( Z 2,) = N (t) -o (2z 2,), 3'T, (14)
6o 60 2, (i])
100 1u0(22 2n)
(15)
Va
(i) + Lree(() + Adia (1)
CAE =
Σ USG.US,
(10)
where a' 11 3t, and Eg is the denoising network also implemented with the equivariant transformer (Jiao et al., 2024), but with only one latent point in each block. The training objective for the diffusion model minimizes the MSE between the predicted noise and the actual noise added during the forward process (Eq. 13), which is given as:
19. Gg
where Auis balances the contribution of the distance loss.
Both the encoder and the decoder are parameterized by an equivariant transformer (Jiao et al., 2024). with details in Appendix F. Training employs teacher forcing, where the structure module receives ground-truth atom types A, and intra-block bonds Bi, and, with 50% probability, inter-block bonds Bij. During inference, full-atom structures and inter- block bonds are generated simultaneously and refined in cycle with the generated
CLW = E.-U(L..T Σ, ||c
co co( 2,, 2),001 (16)
where |Z4] indicates the number of nodes in the latent point cloud z The overall training and sampling algorithms are included in Appendix D, with discussions on the equivari- ance in Appendix E. It is worth noting that implementing diffusion model in the latent space circumvents iterations over full-atom geometries, and thus tremendously reduce the computational cost for training and sampling.
an additional encoding-decodingg inter-block bonds also as inputs. Time values are randomly sampled at each training step, with the inputting coordinates X interpolated between initial Gaussian sampled coordi- nates X and ground-trutt coordinates X Detailed train- ing and sampling algorithms are provided in Appendix B. We provide additional discussions and ablation studies the design choices of the VAE in Appendix C.
4. Experiments
We evaluate our UniMoMo three categories of molecular binders: peptides, antibodies, and small molecules. For pep- tides, we use PepBench and ProtFrag datasets (Kong et al., 2024b) with 4,157 protein- peptide complexes and 70,498 synthetic samples for training, and 114 complexes for vali- dation. Testing conducted on the LNR dataset (Kong et al., 2024b), comprising 93 protein-peptide complexes (Tsaban et al., 2022) with peptide lengths of 4-25 residues. For antibodies, in line with literature (Luo et al., 2022; Kong et al., 2023a). we use SAbDab (Dunbar et al., 2014) entries deposited before September 24th for training and validation, while 60 antigen-antibody complexes from RAbD (Adolf- Bryfogle et al., 2018) are reserved for testing. After filtering for sequence identity above 40% with the test set (Kong et al., 2023a), the training and validation datasets consist of 9,473 and 400 entries, respectively. For small molecules, we adopt Crossdocked20200 and its established splits (Peng et al., 2022), with 99,900 complexes for training and 100 complexes for testing. Additionally, 100 complexes are randomly sampled from the training set for validation.
3.3. Geometric Latent Diffusion Model
The autoencoder simplifies the complicated molecular data, reducing it to compressed latent representations, which are well suited to learn the conditional distribution p(Zzz zz,) with a diffusion model. Prior to applying the diffusion pro- cess, the latent coordinates are normalized by subtracting the center of mass of the binding site latent point cloud 2, and divided by an empirical scale factor of 10.0 (Luo al., 2022). The forward process incrementally adds Gaussian noise to the latent data from t 0 to t = T, transition- ing the data distribution into the isotropic Gaussian prior (O, I). The reverse process gradually denoises this distri- bution, reconstructing the original data from t = T to = O. Denoting the intermediate state of block at time step t as it = [2], I. we have the forward process defined as:
q( q tे = N(ui /1 1 - 3r. - I), q | x.))= -N((t's Var -., (1-a² a²) I') (12)
(11)
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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
Table 1. Results for novo peptide design.
Recovery C-RMSD
Empirical Energy
Rationality
Diversity
Model
AAR
L-RMSD
AG
IMP
Clashin
Clasheu
JSD
JSD
Soq.
Struet.
Reference
-37.25
0.31%
0.88%
REDiffusion
34.68%
4.69
1.88
-13.47
5.38%
0.06 %
13.58%
0.273
0.798
0.155
0.616
PepFlow
35.47%
2.87
1.79
-21.71
15.22%
2.72%
4.62%
0.240
0.693
0,530
0.507
PepGLAD
38.62%
2.74
1.60
-23.12
18.28%
1.82%
1.66%
0,474
0.398
0.687
0.698
UniMaMo (single)
37.59%
2.48
1.48
-28.72
29.03%
1.53%
0.94%
0.390
0.365
0.626
0.629
UniMoMo (all)
39.45% %
2.19
1.27
-34.35
40.86 %
0.45%
0.93%
0.205
0,180
0.617
0.573
For ablation, we include two variants of UniMoMo in the tables throughout this section: one trained exclusively on domain-speciffe data (single) and the other on all datasets (all). Note that UniMoMo (all) employs the same model weights across benchmarks for different molecular binders, demonstrating its ability to generalize effectively across diverse molecular domains. Other ablations are in Ap- pendix H. In the tables, the best one is marked in bold, with the second best underlined. For small molecules, the third best is also underlined, following the conventions in CBGBench (Lin et al., 2024d).
paras et al., 2022) and full-atom relaxation with Rosetta (Al- ford et al., 2017). For fair comparison, we restrict it to one cycle, as additional cycles optimize Rosetta energy, con- ferring an unfair advantage over other models in physical metrics. Domain-specific models include PepFlow (Li et al., 2024b) and PepGLAD (Kong et al., 2024b), which imple- ment multi-modal flow matching and latent diffusion for generating the sequences and the full-atom structures.
Results Table 1 demonstrates that our UniMoMo signifi- cantly outperforms the baselines in terms of recovery, em- pirical energy, and rationality. with comparable diversity. Higher recovery metrics (AAR, C-RMSD, and L-RMSD) indicate a greater likelihood of recovering the reference se- quences and binding structures. UniMoMo surpasses the baselines by a large margin in pyRosetta binding energy (Al- ford al., 2017), reflecting more realistic interaction pat- terns. Additionally, reduced clash rates and JSD values for dihedral angles demonstrate superior local geometry mod- cling with higher rationality. Although diversity decreases slightly due to the fidelity-diversity trade-off, it remains com- parable to baselines. Notably, the comparison of all-domain UniMoMo with the single-domain UniMoMo reveals clear enhancements across nearly all metrics, particularly binding energy and dihedral angle JSD, highlighting the advantages of leveraging data from multiple domains.
4.1. Peptide
Setup We employ the following metrics. Amino Acid Recovery (AAR) measures the proportion of generated residues matching the reference peptide. While multiple implementations exist (Luo et al., 2022; Kong et al.. 2023a; 2024b; Li et al., 2024b), we adopt the most commonly used one in bioinformatics (Needleman Wunsch, 1970; Henikoff& & Henikoff, 1992), with discussion Appendix I. As AAR is regarded unreliable (Kong al., 2024b), we only include it for completeness. Complex RMSD (C-RMSD) computes the RMSD of Ca atoms between generated and reference peptides after aligning by the target protein, while Ligand RMSD (L.RMMD) is similarly defined with align- ment on the peptide itself. AG and IMP measure the bind- ing energy calculated by pyRosetta (Alford et al., 2017), and the percentage of target proteins where generated peptides can outperform native binders. Clash, and Clash denote residue-level clashes within the peptide, and between the peptide and the target protein, respectively, defined by Ca atoms below 3.6574X (Ye et al., 2024). .SDpbb and JSD,c calculate Sensen-Shannor divergence between dihedral an- gle distributions of generated peptides and the dataset, for backbone (bb) and sidechain (sc) angles discretized into 10-degree bins (Dunbrack Jr & Cohen, 1997). Diversity calculates the ratio of unique clusters to total generations, with sequence identity above 40% and RMSD below 2 as clustering thresholds. For each target protein in the test set, we generate 100 peptides per model for evaluation.
4.2. Antibody
Setup We define Complementtriy--Deeemmiin Regions (CDRs) using the Chothia numbering system (Chothia & Lesk, 1987). following Luo et al. (2022). This system, based on structural alignment statistics, offers advantages over the conventional sequence- based IMGT numbering sys- tem (Lefranc et al., 2003). Specifically, the IMGT system vulnerable to simple unigram patterns, which can artificially achieve high amino acid recovery (AAR) of 39% (Kong et al., 2023b), while the identified pattern only yield 23 % AAR under the Chothia system, alleviating this issue. For evaluation, we use conventional metrics (AAR, RMSD, IMP) and rationality metrics for CDRs (Clasha Clashout- JSDpb- JSDge). as previously defined. Moreover, since some baselines adopt predictive implementations (Kong et al., 2023a:b), we also report AAR, RMSD, and IMP across candidates for each complex, with 1, 10, 100.
Baselines We adopt the following baselines. RFDiffu- sion (Watson al., 2023) generates peptide backbones fol- lowed by cycles of inverse folding with ProteinMPNN (Dau-
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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
Baselines We evaluate our approach against the follow- ing baselines. MEAN(Kong et al., 2023a) uses multi- channel equivariant graph neural network with iterative refinement for decoding CDR sequences and structures. DyMooN(Kong et al., 2023b) extends MEAN to full-atom structures and scenarios with unknown antibody framework docking poses. DiLu et al., 2022) applies diffusion models amino acid types, C. coordinates, and residue ori- entations. G(in et al., 2024a) incorporates heteroge- neous residue-level encoder and energy-informed geometric constraints for generating realistic structures.
4.3. Small Molecule
Setup We evaluate the results using the CBGBench frame- work (Lin al., 2024d), which assesses models across four categories: substructure, chemical property, geometry, and interaction. Substructure metrics calculate JSD and MAE between the generated and reference distributions of atoms, rings, and functional groups. Chemical property metrics include QED, SA, LogP, and LPSK. Geometry metries fo- cus on JSD for bond lengths and angles, as well as atomic and molecular clash rates. Interaction metries evaluate Vina energy in score, minimization, and dock modes, along with interaction type distributions between molecules and proteins. Models are ranked within each category, with ranks converted to scores using the formula (N - -rank), where N is the total number of models. The overall score is a weighted sum of scores across categories, the higher, the better. Detailed descriptions are available in Appendix J.
Table 2. Results of recovery for antibody design on CDR-H1.
Model
#Gencration
AAR
RMSD
IMP
Predictive
MEAN dyMEAN GeoAB-R
29.13%
1.87
6.67%
31.65%
8,21
11.86%
32.04%
1.67
6.67%
Generative
1
24.60%
2.77
10.34%
Table 4. Overall comparisons for de novo small molecule design.
DiffAb
100
10
38.42%
49.74%
2.08
1.46
34.48%
60.34%
Model
substruct. 0.2
0.2
Interact.
0,4
Geum.
0.2
Weighted Score
Rank
29.74%
1.73
6.67%
LIGAN
1.13
1.40
4.27
1.25
8.05
6
GeoAB-D
38.20%
1.58
20.00%
3DSBDD
1.13
1.50
2.23
0.70
5.67
9
GraphBP
0.17
1.50
0.37
0,10
2.13
14
100
45.96%
1,50
40.00%
Mocket2Mol
0.73
2.83
5.52
20, 44%
2.71
15.00%
TargetDiff
1.27
1.50
3.50
1.70
8:47
5
UniMoMo (single)
10
39.04%
1.90
35.00%
DifSBDD
0.77
1.75
1.20
0.95
4.67
100
48.78 78%
1,39
63.33%
DiTBP
FLAG
0.70
0.27
1.10
1.40
2.10
1.40
0.60
1.35
4,10
4.82
13
21.44%
2.52
13.33%
D3FG
1.47
1.80
UniMoMo (all)
10
42.05%
1.44
41.67%
DecompDiff
1.90
1.30
2.50
1.50
8.00
7
100
52.34%
1.04
65.00%
MoCRAFFT
1.93
1.55
3,93
2.20
9.62
VorBind
1.53
2.00
3.83
2.00
9.37
UniMoMo (singla)
2.23
2.15
2,70
1.95
9.09
Table 3. Results of rationality for antibody design on CDR-H3.
UniMoMo (all)
3,47
Model
Clasha
Clasha
ISDa.
JSD
Table 5. Substructure analysis for de small molecule design.
Reference
MEAN
0.96%
0.08%
0.16%
0.02%
0.529
Model
ISD
Alom Type
MAE
ISD
Ring Type
MAE
Functional Group
JSD
MAE
Rank
dyMEAN
1.02%
2.98%
0.542
0.702
LIGAN
0.1167
0.8690
0.3163
0.2201
0.3468
0:0378
8:33
3DSBDD
0,0868
0.5444
0.3188
0.3682
000454
GeoAB-R
0.59%
0.11%
0.529
GraphBP
0.1642
1.2266
0.5061
0.4382
0.6259
0.0705
13.17
DiffAb
0.31%
0.25%
0.268
Rackei2Mol
0.0916
1.0497
0.3550
0.3545
0.2061
B.6622
10:33
GeoAB-D
0.75%
0.07%
0.430
DiTSBDD
TargtDDif
0.0829
0,1533
0.6316
0.2399
0.3855
0,2345
0.1559
0.5520
0.2876
0.3441
0.0700
5:17
UniMoMo (single)
0.25%
0.06%
0.278
0.284
DitIPP
0,2591
1.5891
0.4531
0.4068
0.5346
0.0670
UniMoMo (all)
0.18%
0.03%
0.224
0.221
FLAG
0.1052
1.7665
0.2452
0.3370
0.3654
0.0666
10.50
D3PG
0,3545
0.8154
0.1369
0.2214
0,2511
0:0515
6.67
DecumpDift
0,0431
0.3197
0.2431
0.2006
0.1915
0.0018
Results Table 2 demonstrates that our UniMoMo achieves the best performance on generating native-like CDRs. While predictive models show strong ainle-ggenerate recovery, generative models like UniMoMo demonstrate a clear advan- tage as the candidate pool increases, achieving higher recov- ery of the native sequences and structures. With 100 genera- tions, UniMoMo surpasses all baselines on IMP, achieving better binding energy than native CDRs in 65% of com- plexes. Table 3 further shows that UniMoMo generates realistic geometries with lower clash rates and much more accurate dihedral angle distributions compared to baselines. Notably, compared to the variant of UniMoMo trained on antibody data only, it is evident that UniMoMo can learn transferable knowledge from other domains to improve the quality of the generated interactions and geometries, leading to better recovery and rationality.
MelCRAFT
0.1196
0.0477
VoxBand
0,0942
0.3564
0,2401
0.0301
0,1055
0.0761
6.35
LiMoMo (single)
0,0552
0.2795
0.1252
0.0976
0.1562
0.0175
2.83
UniMaMa (xill)
0,0280
0.2108
0.1073
0.0726
0.3356
0,0161
Baselines We evaluate our method against a variety of baselines, including autoregressive models such as Pocket2Mol (Peng et al.. 2022), GraphBP (Liu et al., 2022), and 3DSBDD (Luo et al., 2021). Diffusion- based models, the most prevalent approaches, include TargetD- iff (Guan et al., 2023a), DecompDiff' (Guan et al., 2023b), DitBB (Lin al., 2025), and DifTSBD (Schneuing et al., 2024). Fragment- based methods include FLAG (Zhang et al., 2023), which performs one-shot generation, and D3FG (Lin et al., 2024a), which auto-regressively gener- ates and connects motifs. Voxel-based methods, which leverage voxel grids and convolutional neural networks, in- clude LIGAN (Masuda al., 2020) and VoxBind (Pinheiro
7

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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
et al., 2024). We further compare against the state-of-the- art model MolCRAFT (Qu et al., 2024), which utilizes the Bayesian Flow Network (Graves et al., 2023) for generation.
autoencoder. As shown in Table 4, UniMoMo achieves the highest overall ranking score due to its consistent superiority across the comprehensive evaluation aspects. Importantly, the inclusion of multi-domain data significantly enhances performance in each aspect, indicating that UniMoMo is capable of learning a broader spectrum of property-structure relationships from all types of molecules. This could pre- vent biases seen in single-domain models, which helps the model generalize better and avoid overfitting to specific chemical spaces, therefore results in a model with better overall performance.
Table 6. Results of chemical properties for de novo small molecule design. LogP between -0.4 and 5.6 are all reasonable (Lin et al., 2024d), without preference to higher or lower values.
Model
QED
LogP
SA
LPSK
Rank
LIGAN
0,46
0.56
0.66
4.39
7.00
3DSBDD
0.48
0.47
0.63
4.72
6.00
GraphBP
0.44
3.29
0.64
4,73
6.50
Pocket2Mol
0.39
2.39
0.65
4.58
7.75
Targe:Diff
0.49
1.13
0.60
4.57
6.50
DinSBDD
0.49
-0.15
0.34
4.89
5.25
DimBP
0.47
5.27
0.59
4.47
8.50
4.4. Different Binders for G Protein- Couple Receptor
FLAG
0,41
0.29
0.58
4.93
7.00
D3FG
0.49
1.56
0.66
4.84
2.75
DecompDiff
0,49
1.22
0.66
4,40
5.00
MoICRAFT
0.48
0.87
0.66
4.39
6.25
VoxBind
0.54
2.22
0.65
4.70
4.00
UniMoMo (single)
0.53
1,36
0.68
4.69
3.25
UniMoMo (all)
0.55
1.55
0.70
4.68
2.75
Target
Protein
Table 7. Geometry analysis for de novo small molecule design.
Static Geometry
Clash
Model
Rank
JSDm
JSDaA
Ratio.a
Ratio
LIGAN
0.4645
0.5673
0.0096
0.0718
7.75
3DSBD
0,5024
0.3904
0.2482
0.8683
10,50
GmahBBP
0,5182
0.5645
0.8634
0.9974
13.50
Pocke22Mll
0.5433
0.4922
0.0576
0,4499
10,50
TargetDiff
0,2659
0.3769
0.0483
0.4920
5.50
DinSBDD
0,3501
0.4588
0,1083
0.6578
9.25
Peptide
Antibody AG 65.75
Small Molecule Vina Score -6.04
DiffBP
0.3453
0.4621
0.0449
0.4077
7.25
27.49
FLAG
0,4215
0.4304
0.6777
0,9769
11.00
D3PG
0,3727
0.4700
0.2115
0.8571
10.50
0.00
DecompDiff
0.2576
0.3473
0.0462
0.5248
5.00
8.00
0.0
MoICRAFT
0,2250
0.2683
0.0264
0.2691
3,00
VoxBind
0,2701
0.3771
0,0103
0.1890
4.00
UniMoMa (single)
0,3362
0.4166
0.0042
0.0715
4.25
UniMoMo (all)
0.3223
0.3848
0.0040
0.0708
3,00
Rosatta Score
0.00
Rosetta
-331
Vinta Score
Results Table 4 presents the overall ranking scores, with detailed evaluations summarized in Tables 5, 6, 7, and Uni- MoMo achieves the best fidelity to substructure distributions (Table 5), excelling in JSD and MAE for atom types, rings, and functional groups, which is due to the block-level uni- fied representation that effectively captures frequent motifs, such as aromatic rings and functional groups (Kong et al., 2022). The chemical property evaluation in Table 6 reveals the exceptional performance of our UniMoMo in gener- ating drug-like (QED, Bickerton et al. (2012)) molecules with superior synthetic accessibility (SA, Ertl & Schuffen- hauer (2009)). The geometry analysis in Table 7 highlights strength of UniMoMo in producing molecular binders with minimal steric clashes and well-distributed bond lengths and angles. In Table 8, UniMoMo exhibits competitive Vina docking scores and interaction profiles closely resem- bling the reference distribution, suggesting its capability of forming stable and meaningful interactions with target proteins. These results reflect higher structural rationalities, indicating that UniMoMo learns meaningful atom- level ge- ometric constraints with iterative decoding in the full-atom
Figure 3. Different types of binders generated by UniMoMo on the same binding site on GPCR (PDB ID: 8U4R). The distribution of Rosetta interface energy is calculated for 100 generated peptides and antihodies. And Vina score is used for evaluation of the 100 generated small molecules. The orange box on the molecular topology graph highlights structure similar to the side chain of Arginine, while the red boxes denote amide connections.
G protein-coupled receptors (GPCRs), the largest protein family in humans, are among the most prominent drug tar- gets (Yang et al., 2021). We employ UniMoMo to generate peptide, antibody, and small molecule binders targeting the same binding site on a GPCR (PDB ID: 8U4R). Figure shows UniMoMo produces candidates with strong in silico binding affinities, assessed by Rosetta (Alford al., 2017) and Vina (Trott& & Olson, 2010), and realistic geometries without requiring relaxation by physical forcefields. The showcased small molecule is particularly interesting, reveal- ing two intriguing phenomena: 1) Interaction patterns from amino acids: The small molecule mimics the side chain of Arginine (orange box), one of the standard amino
8

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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
Table 8. Results interaction analysis for de novo small molecule design.
Vina Score
Vina Min
Vina Dock
PLIP Interaction
Model
Rank
E
IMP (%)
IMP (96)
E
IMP (%)
MPBG (%)
LBE
JSD
MAE
JSD
MAEpp
LJGAN
-6.47
62.13
-7.14
70.18
-7.70
72.71
4.22
0.3897
0.0346
0.0905
0.1451
0.3416
3,33
3DSBDD
3.99
9.18
0,3839
0,0392
0.0934
0.1735
0.4231
GraphBP
0.00
1.67
4.57
10.86
-30.03
0.3200
0,0462
0.1625
0.2101
0.4835
13,08
Pocket2Mol
-.23
31.06
-6.03
38.04
-7.05
48.07
-0.17
0.4115
0.0319
0.2455
0.1535
0.4152
6.92
Tifge
-571
38.21
-6.55
47.09
-7.41
51
5.38
0.3537
0.0198
0.0600
0.1757
0.4687
DiASBDD
12.67
-2.15
22.24
-5.53
29.76
-23.51
0.2920
0.0333
0.1461
0.1777
0.5265
11.00
DifiB
8.60
19:68
-7.34
49.24
6,23
0,348
0.0249
0.1430
0.1256
0.5639
8.75
FLAG
0.04
3.44
-3.65
11.78
-4.64
0.3319
0.0170
0.0277
0.2762
0.3976
10.50
D3FG
3.70
28.9
-8.85
0,4009
0.0638
0.0135
0,4641
DecompDiff
-5.18
19.66
-6.04
34,84
-7.10
48.31
-1.59
0,3460
0.0215
0,0769
0.1848
0.4369
7.75
MoCCAAF
-6.15
54.25
-6.99
56.43
-7.79
56.22
8.38
0,3638
0.0214
0.0780
0.1868
0.4574
4.17
VoxBind
-6.16
-7.68
52.91
9.89
0.3588
0.0257
0.0513
0.1850
0.4606
UniMoMo (single)
-5.50
26.37
-5.96
38.21
-7.19
49.60
2.15
0.3521
0.0175
0.0447
0.2372
0,4706
7.25
UniMoMo (all)
-5.22
30.40
-6.08
39.23
-7.25
51.59
7,50
0.3473
0.0135
0.0173
0.2012
0.4277
5.33
acids, to form hydrogen bonds with the target protein. 2) Local geometries from peptides and antibodies: To fit in the large pocket originally designed for antibodies, Uni- MoMo effectively generates wide-spanning scaffolds with amide connections (red boxes) typically seen in peptides and antibodies. The above findings highlight the strong general- ization of our UniMoMo across diverse classes molecular binders, with successful attempts to leverage cross-domain knowledge of molecular interactions and local geometries. Examples other targets are included in Appendix K. Fur- ther analysis reveals an interesting self-adaptive mechanism in block size selection, which depends on the number of blocks designated for generation on the same binding site, with details in Appendix L.
Acknowlegements
This work is jointly supported by the National Key R&D Program of China (02.2022 ural Science Foundation of China (No. 61925601, No. 62376276, No. 62276152), and Beijing Nova Program (20230484278).
the National Nat-
Impact Statement
Our work presents a novel framework for unified genera- tive modeling of 3D molecules, offering significant value to both academic research and industrial applications. From an academic perspective, demonstrate that unified model- ing across different molecular types is not only feasible but also beneficial, as it enables the model to learn transferable knowledge on molecular interactions and geometries. This groof-of-concep is meaningful for addressing the scientific problem of binder design with computational tools, paving the way for more powerful models that can leverage diverse datasets more effectively. From an industrial standpoint, this work exemplifies the potential to design multiple dis- tinct drugs for the same target protein, addressing varied medical needs by leveraging different molecular formats. In summary, this research has profound implications for accelerating drug discovery and expanding the horizons of molecular binder design. We do not identify any specific societal concerns requiring additional attention at this time.
5. Conclusion
We introduce UniMoMo, the first unified framework for generative modeling of molecular binders. Molecules are represented as block-based graphs, with each block corre- sponding to a standard amino acid or a molecular fragment identified via the principal subgraph algorithm. UniMoMo employs full-atom geometric latent diffusion process, com- bining an iterative autoencoder encode blocks latent points with diffusion modeling in the compressed space. Ex- tensive benchmarks across peptides, antibodies, and small molecules confirm its superiority, illustrating enhanced per- formance via the integration of data from diverse molecular categories. The application to a GPCR further highlights its ability to transfer interaction patterns and geometries across molecule types. This work is pioneering step toward uni- fied generative modeling of molecular binders, and may inspire future advancements in this promising direction.
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Unified Generative Modeling of 3D Molecules for De Novo Binder Design
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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
A. Principal Subgraph Algorithm
Here we borrow descriptions of the principal subgraph algorithm from Kong et al. (2022) to improve the readability of this paper. Algorithm 1 provides the pseudocode for the block-level molecular decomposition with the principal subgraph algorithm. This algorithm takes imput the atom-level molecular graph, a vocabulary of principal subgraphs, and their recorded frequencies of occurrence derived during the principal subgraph extraction process. It iteratively merges two neighboring principal subgraphs whose union has the highest recorded frequency in the vocabulary. This process continues until no unions of two neighboring subgraphs exist in the vocabulary. The function MergeS Sugrruu processes the input molecular graph G and the selected top-1 fragment F. If G contains F. the function merges the two adjacent nodes (e.g. i and ;) in G that make up F into a new node representing F = F, F, U Eig. We further modify the original algorithm to prioritize merging neighboring fragments within the same ring. implemented using the function R ngg r or. This function identifies all neighboring fragments sharing ring with the input fragment in the molecule. For any pair of neighboring fragments/ i and under consideration for merging, if one fragment has a neighbor in the same ring while the other does not, the pair is discarded to prioritize merging fragments within the same ring. In this paper, use the vocabulary of 300 principal subgraphs extracted from ChEMBL (Zdrazil et al., 2024) with kekulized representations.
Algorithm Subgraph-Level Decomposition (borrowed and adapted from Kong et al. (2022)
1: Input: A 2D graph G decomposed into atoms, the set V of learned principal subgraphs, and the counter C' of the frequencies for learned principal subgraphs.
2: Output: A new representation g' of G that consists of principal subgraphs in V.
3: g' +-
4: while True do
5: freq f- 1; + None
6: for (F..
g' do F1, F3 f- RRingPrior(F)), RingPrior(FF) {Get neighboring fragments in the same ring with fragments i and i}
7:
8:
if (F3 & IF and F3 # 8) xor (Fi & Fj and R # 0) then
9:
continue
{If of the fragment has a neighbor in a same ring while the other does not, discard this pair]
10:
end if
11:
F Merge( (Fr,
Merge neighboring fragments into new fragment)
12:
+ TOMILEES))))
{Convert graph to SMILES representation)
13:
i V and C[s] freq then
14:
freq + Css] F
15:
16:
end if
17:
end for
if freq =-1 then
19:
break
(No further merging needed}
20:
else
21:
G' + MergeSSbGGrrap
{ Update the graph representation)
22:
end if
23:
end while
B. Algorithms for Training and Sampling with the Iterative Full-Atom Variational Autoencoder
We present the pseudocodes for training and sampling with the iterative full-atom variational autoencoder in Algorithm 2 and 3, respectively. It is worth mentioning that the molecular binder and binding site are encoded independently into latent representations ensure that the encoded binding site does not include any information on the reference binder. During training, 5% residues of the binding site sampled for reconstruction, enriching the information encoded into the latent point clouds of the binding site. Ground truth for inter- block bonds is provided with 50% probability to encourage the model to learn inter-block structural constraints, and facilitate additional refinement cycle with fixed inter-block bonds during inference. The iterative decoder framework allows greater flexibility in controlling molecular geometry. For instance, clash avoidance can be incorporated by introducing repulsive force on the binding site atoms during each iteration. This framework also offers the potential for fine-graine -rained physical manipulations, such as optimizing directional and angular constraints for hydrogen bonds achieve more precise interactions, which we leave as a direction for future work.
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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
Algorithm 2 Training Algorithm of the Iterative Full-Atom Autoencoder
input geometric data of complexes
output encoder Es, decoder D
1: function Encode(Ea, 9)
2: {1i 2 Pi; o:)] +- (G)
(Encoding) {Reparameterizationn
3: [(6;, 6:) ~ ~0,
4: Z (1u + 3 o, f7 + t 00O))
5: return 2
6: end function
7: Initialize Eg. De
8: while Φ, & have not converged do
9: Sample (g) ~ S
10: Z,, By + Encode(E (Ep, G2); Encode(E,, Gy)
{Encode the molecular binder and the binding site separately {Index of the sampled 5% residues the binding site for reconstruction) (Index of the nodes that need reconstruction [Block type prediction
11: Sample I I
12:
I+ T Ul,
{ 1} D&i (2,,
14:
Sample ~~ (0, 1), X ~ ~N(E,,
{ (Sample a time value and the initial atomic coordinates at t=1]
15:
V'+ + x X
[Ground-tree truth motion vectors] [Interpolation to get atomic coordinates at t (Provide the ground truth of inter-block bonds with 50% probability) {'Taacher forcing on atoms and bonds]
16:
+ x + +1--) X
17:
B, - pf 0.5 else Bıj. p (0.
18:
((H,, ( = (1 B; Bij.
X(),,
22. Zy. Gy.t)
19:
16
9.P9 = Softmax (MLP)) + +hig)), +j
[Bond prediction {Calculate loss)
up
20:
= Eie (Cx + L + Auiaa Cais (1)) (1))/[T)
=
21:
* optimizer( (CAE: o,
22:
end while
23:
return Egr D
Algorithm Sampling Algorithm of the Iterative Full-Atom Autoencoder
input encoder Es, decoder De. binding site Gy, latent point clouds 2, and Z,, number of iterations N output molecular binder Gz
function DecodeStruct(D; ((A;, B;, B,y)}; Z., Zy, 9.)
2: At 1.0/N
3:
X ~ NN
(Sample initial coordinates]
4:
for in 0, 1,,,, N do
5:
8 1.--0- n At
6:
((H), Vi9 (EEL) De, B.U BBj, X()), Zy, 1)
7:
X:- + X + AtV,
{Update coordinates]
8:
H H
9: end for
10: BiJ (M + li <3.5A} if Bij = 0 else Bij (Inter-block bond prediction)
11: return {(X Byy) [
12: end function
13: {s [ + De, (Zz: Zy)
[Block type prediction on nodes from the molecular binder) (Get atom types and intra-block chemical bonds from the vocabulary l 1,) + DecodeStruct(D4, ((A,, B, 0)} 2,, 2y, 9y) (Decode coordinates and inter-block bonds}
14: A,, B; +- Tookkup(s; V)
15:
16: Go + (I[A, X,) | 1,), ( B,,)) i L,, i j})
[Re-encode the generated binder} [(X,, By) li La) DecodeStruct(Dg, ((A,, B,, Biy) Zz, Zy, Gy) (Refinement with given inter-block bonds) 19: Ge + (f(A,, X,) LL, (BB, B,y) E I,, i 1,ii111 (j})
17: 2, + Encode(E Gz)
20: return 92
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Unified Generative Modeling of 3D Molecules for De Novo Binder Design
C. Design Choices on the Iterative Full-Atom Variational AutoEncoder
C.1. Why Do We Need the Compressed Latent Space?
We incorporate a latent space primarily to facilitate the implementation of the diffusion model. our unified representation, each graph node corresponds to a block, such as residue or a chemical fragment, whose atom count varies depending on its type. As result, the block coordinates X, R=,x3 and atom types A, n are variable in size during denoising, making direct diffusion on these inputs infeasible due the fixed-dimensional nature of standard diffusion models. To overcome this, we employ an all-atom variational autoencoder (VAE) that encodes each block into fixed-length latent vectors and 2, thereby enabling diffusion to operate efficiently and consistently in this exed-dimensional continuous latent space.
C.2. Balancing KL Weights on 2; and E
Different KL weights (i.e., a and Xg in Eq.2) applied to the invariant (z,) and the equivariant (ž,) latent variables shape the latent space in distinct ways. To evaluate whether the resulting space is suitable for generative modeling, we use the diffusion loss as a proxy, with a lower loss indicating a better latent space for diffusion. Larger KL weights promote smoother, more continuous latent spaces that benefit diffusion modeling, but excessive regularization may overly compress the representations, diminishing expressivity through information loss. Therefore, these weights must strike a balance to ensure the latent space both smooth and sufficiently informative. As shown in the validation loss curves in Figure4, we choose the weight combination that yields the lowest validation loss.
zi loss/Validation
z Doss/Validation
total loss/ /ass/aaiaation
1.4
6.9
0.8
0.7
0.6
1s
0.5
0.5
0.4
0.6
0.5
22k
40k
2 = 0.4, 2g = 0.8
2 = 0.6,
22 = 0.8 2g = 0.8, 02 = 0.8 4g 0.6, 2g 1.0
Figure 4. Validation loss curves for the latent diffusion model trained on VAE latent spaces with varying KL weights, where λ and A2 indicate the KL. weights on the invariant and the equivariant latent variables, respectively, as in Eq.
C.3. Ablation Studies on Extra Noises on z
We manually introduce additional noise to the latent coordinates ž; before decoding to enhance robustness against errors introduced by the diffusion model. This strategy is particularly beneficial for small molecules, which often exhibit more complex inter-block connectivity than peptides or antibodies, where blocks are typically connected by peptide bonds. These more intricate structures more sensitive coordinate perturbations, making robustness especially important. While increasing the KL weight might seem like an alternative way to enforce smoother latent spaces, our current setting of 0.8 for ž already imposes strong regularization. Further increasing it would excessively compress the latent space and degrade the diffuusion model's performance, as discussed in Figure 4. As shown in Table 9, adding extra noise significantly improves the tolerance of the autoencoder to coordinate inaccuracies from diffusion, tremendously enhancing stability and affinity of the generated molecules.
Table Ablation studies on extra noises and increased KI. weights on latent coordinates E. vina(minimize)
model
vina(score only)
vina(dock)
w/o extra noise + d2 = 0.8
-4.62
-5.58
-7.24
w/o extra noise + X = 1.0
-4.42
-5.59
-7.09
w/ extra noise + d = 0.8
-5.72
-6.08
-7.25
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Unified Generative Modeling of 3D Molecules for De Novo Binder Design
D. Algorithms for Training and Sampling with the Latent Diffusion Model
We present the pseudo codes for training and sampling with the latent diffusion model in Algorithm and 5, respectively.
Algorithm 4 Training Algorithm of the Latent Diffusion Model input geometric data of complexes S, encoder Eg, decoder D3 output denoising network 60
1: Fix parameters & and {
2: Initialize 6g
3: while / have not converged do
4: Sample (92, ~
5:
Zzi 2y f Encode(E G2), Encode(E,, Gy) I~ U(1,T), ((6, 6i) ~ I)
(Encoding) {Sample noises)
6:
7:
2 + ( liE Ue. [ =
Va [|],, 2
+ (1 [E, E]}
{Sample intermediate states at time t}
8:
D = E, |ll., El col co(2, 2y, //]]| ||
9:
0 - optimiier((
0)
10: end while
return Eg
Algorithm 5 Sampling Algorithm of the Latent Diffusion Model
input encoder Es. decoder Dg. denoising network ea, binding site Gy, diffusion steps T,, decoding iterations N output molecular binder Gx
1: Zy + Encode(E&, G.)
[Eccde the binding site into the latent space] (Sample initial states for diffusion]
2: {(2, ) (0,
3: for in T, 1..... d do
4:
z [ 1,}
[Latent Denoising Loop for nodes in the molecular binder]
5:
प [|]
6:
|,, E I)
7: d. + va iit
vI-a co (2), 2y. + 3,e;
(Update the latent point cloud of the molecular binder)
8: [2!-1 2 t u:
9: end for
10: Zg ((2)/ 1 [
11: G. t Decode De, gy: Zn, Zy N)
[Iterative decoding in Algorithm 3}
12: return G.r
E. Discussion on Equivaauiare
We briefly outline how ((3)-equivariane) is preserved throughout our framework, building upon established theoretical foundations.
For the diffusion component, GeoDiff (Xu et al., 2022) demonstrates that Equiviarieee is maintained via an equivariant denoising kernel (Proposition 1), which in our paper instantiated using an equivariant transformer (Jiao et al., 2024). This transformer operates on scalar features, preserving equivariance through inner products and unbiased linear transformations applied to velocity vectors, in accordance with the scalar-based design principles Villar al. (2021).
For the variational autoencoder, the encoder outputs latent variables using the same equivariant transformer, ensuring E(3)-equivariance by design as the latents are the direct output of the transformer. The decoder adopts a short flow matching approach, with a similar theoretical foundation as GeoDiff on equivariant flow matching (Song et al., 2023) (Theorem 4.1). Since the vector field is predicted by an Eqquiiarat network, the decoding process consistently maintains Euuueaaurae across all stages.
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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
F. Implementation Details
F.. Baselines
Peptide For RFDiffusion, as the training codes for custom datasets are not open-source, we directly utilize the official pretrained weights for binder design and the provided inference framework. The number of cycles for inverse folding and Rosetta relaxation is set to one. For PepGLAD and PepFlow, we the official implementations and retrain the models the same datasets as single-domain model, with the default hyperparametens specified in their repositories.
For all baseline methods, including MEAN, dyMEAN, DiffAb, GeoAB-R, and GeoAB-D, employ their official implementations to retrain the models the same datasets as our single-domain model, using the default hyperpa- rameters provided in their repositories.
Antibody
Small Molecule
The bascline results are borrowed from CBGBench (Lin et al., 2024d), where the models are retrained on the same datasets and splits as our single-domain model.
F.2. UniMoMo
We provide the hyperparameters for training our single-domain and multi-domain models in Table 10.
Table 10. Hyperparameters of UniMoMo with single-domain multi-domain data.
Value
Name
Description
UniMoMo (single)
UniMoMo (all)
Variational AutoEncoder
epoch
250
250
Number of epochs to train.
warmup
2000
2000
Number of warmup steps for the LKL. with linear schedule.
le-4
le-4
Learning rate.
embed.size
512
512
Dimension of the atom and block type embeddings.
dden size
512
512
Dimension of hidden states.
latent_size
8
8
Dimension of latent states.
edge_size
64
64
Dimension of edge type embeddings. Number of RBF kernels for embedding the spatial distances. Cutoff distance for RBF kernels.
n.rbf
64
64
cutoff
10.0
10.0
n-layers
6
Number of layers in the encoder and the decoder. Number of heads for multi-head attention.
head
8
8
0.4 (small molecule)
X1
0.6
The weight of KL divergence on the sequence.
0.6 (others)
Xa
0.8
0.8
The weight of KL divergence on the structure.
Adia
0.5
0.5
The weight of local distance loss.
mask_ratio
0.05
0.05
The ratio of residues on the binding site for reconstruction.
10
Number of iterations for reconstruction.
Latent Diffusion Model
hi nideen.size
512
512
Dimension of hidden states.
100
100
Number of total steps for diffusion.
n.rbf
64
64
Number of RBF kernels for embedding the spatial distances.
cutoff
3.0
3.0
Cutoff distance for RBF kernels in the normalized latent space. Number of layers in the denoising network.
n_layers
6
6
head
8
8
Number of heads for multi-head attention.
G. Physical Corrections Generation
To enhance the physical plausibility of generated structures, different constraints could be incorporated into the proposed framework. Here we illustrate two common strategies to correct the clashes and the local geometries.
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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
G.1. Clashes Avoidance
Clashes frequently occur in structures generated by deep learning models. In UniMoMo, we decouple coarse global arrangement and fine-grn tineggriied local geometry using latent diffusion and a full-atom variational autoencoder, which allows us to explicitly handle steric clashes during decoding by adding repulsive forces to the predicted vector field (Eq.5) during iterative reconstruction. At each step, we compute pairwise distances between generated atoms and those in the contexts (i.e. the binding site), and apply a force when their van der Waals radii overlap beyond a threshold á (Ramachandran et al., 2011) 1), which we use 0.3A in this paper. Specifically, r, and r, are the radii of atoms i and j. and oy and d" are their coordinates at time step t, the magnitude of the repulsive force is defined as:
fag = rs Tst - | 23 II, 0,
| x else,
<rtttr
(17)
Then for each iteration during decoding, the clashes can be repaired by further updating the atomic coordinates as fij. where j iterates over all atoms in the fixed context.
G.2. Bond Validity
Existing literature often relies on OpenBabel (O' (O'Boyle et al., 2011) to assign chemical bonds based on pairwise atomic distances. In contrast, our unified framework determines bonding through block-defined intra-block bonds and model- predicted inter-block bonds. While this model-driven approach allows greater flexibility, such as accommodating non- standard amino acids for future extension, it may introduce issues like invalid valencies and inconsistencies between predicted 2D topology and 3D geometry (e-g., excessively long bond lengths or distorted bond angles). To address valency violations, rank predicted bonds by their output probability and add them sequentially. Any bond that exceeds valency constraints is discarded. For 2D-3D consistency, we compute empirical distributions of bond lengths and angles, with bond lengths discretized from I, to 1.7À (in 0.005Á bins), and angles from 0" to 180 (in 2 bins). If over 10% of the bonds in generated molecule fall into zero- zero-probale pero-probability regions of these distributions, the molecule is considered 2D-3D inconsistent and discarded.
H. Ablations on the Number of Iterations
We conduct ablation study the iterative decoding module, which primarily impacts the physical validity of local geometries, including bond lengths, bond angles, and dihedral angles. As shown in Table 11, reducing the number of iterations significantly degrades the precision of atom-level geometries, resulting in substantial divergence from natural distributions. Notably, when N = 1, the decoding process becomes non-iterative, leading to a tremendous drop in performance compared to its iterative counterparts.
Table 11. Ablations on the effect of the number of iterations in the decoder.
N
Peptide JSDab
Antibody JSDbb
Small Molecule
JSD
JSD
JSD
JSDBA
0.393
0.358
0.376
0.374
0.4216
0.5328
0.281
0.232
0.277
0.260
0.3625
0.4976
0.273
0.203
0.270
0.242
0.3470
0.4724
10
0.205
0.180
0.224
0.221
0.3223
0.3848
Implementation of Amino Acid Recovery (AAR)
We found that various implementations of AAR exist in the current literature, which we illustrate as follows. DiffAb (Luo et al., 2022) calculates AAR using a global pairwise alignment two sequences with the BLOSUM62 matrix (Henikoff & Henikoff, 1992) and the Needleman- Wunsch algorithm (Needleman & Wunsch, 1970), as implemented in Biopy- thon (Cock al., 2009). then computes the ratio of matched amino acids between the generated and reference sequences.
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Unified Generative Modeling of 3D Molecules for De Novo Binder Design
MEAN (Kong al., 2023a) uses simpler approach, directly matching amino acids from the start of both sequences without alignment. PepGLAD (Kong al., 2024b) assumes that sequence alignment for peptides should not necessarily start the beginning; for instance, the AAR of ARGFE to RGFED would be 80% rather than 0%. Therefore, it implements a sliding window approach, taking the maximum match ratio as the result. PepFlow (Li et al., 2024b) utilizes Sequen.ceattche cher from the di fflib package in python, which employs the Ratclif/OOhrshellp algorithm. This method recursively identifies the longest common substring (LCS) on either side of the previous LCS. For example, comparing DIET and TIDE results in an AAR of 50% by first identifying I as the initial LCS, followed by E as secondary LCS on the right side of the previous LCS. This often leads to much higher AAR values than other methods.
Given the biological relevance of the BLOSUM62 matrix (Henikoff & Henikoff, 1992) and the Needleman- Wunsshh algorithm (Needleman & Wunsch, 1970), we adopt the implementation of DiffAb to calculate AAR in our study.
J. Descriptions of Metrics in CBGBench
The evaluation of CBGBench (Lin et al., 2024d) involves the following four aspects: substructure, chemical property, geometry, and interaction.
Substructure The comparison focuses on atom types, ring types, and functional groups, assessing how closely the generated distributions align with the reference. Two types of metrics are involved: Jensen-Shannon divergence (ISD), and mean absolute error (MAE). JSD(L) calculates the divergence between the overall probablistic distributions on the specific substructures of the generated and the reference molecules. MAE(J) calculates the difference between the molecule-level occurring frequencies of substructures (e.g. carbon atoms occur 16 times in one molecule on average) of the generated and reference molecules. Atom types considered include C, N, O, F, P, s, C1, while ring types range from 3 to 8 atoms. Functional groups are evaluated based on 25 categories identified using the EFG algorithm (Salmina et al., 2015).
Chemical Property The evaluation of chemical properties builds on prior work, incorporating several key metrics. These include QED(T), which provides a quantitative estimation of drug- (Bickerton et al., 2012); SA(t), the synthetic accessibility score (Ertl & Schuffenhauer, 2009) normalized to [0, 1). with higher scores indicating better synthesizability; and (-)P(-), the octanol-water partition coefficient, with optimal values typically ranging between -0.4 and 5.6 for drug candidates (Ghose et al., 1999). Additionally, the LPSK(1) metric measures the proportion of generated drug molecules that satisfy Lipinski's 's rule of five (Lipinski, 2004), guideline for assessing drug-like properties.
Geometry This panel assesses the authenticity of generated molecules by analyzing local geometries, including bond lengths, bond angles, and atomic clashes. (L) quantifies the -hannonn divergence between the bond length distributions of generated and reference molecules. Similarly, JSDBA (L) evaluates the divergence for bond angles, which are discretized every two degrees between 0º to 180" Clashes between generated molecules and target proteins are identified based on van der Waals radius overlaps of 2 0.4A (Ramachandran et al.. 2011). Ratio (4) measures the average proportion of clashing atoms, while Ratio (L) reflects the average proportion of molecules with at least one clashing atom.
Interaction The evaluation of interactions encompasses two primary aspects: Vina scores and interaction distributions. For the Vina score analysis, three modes of oDock Vina (Trott & Olson, 2010) are utilized: Score, which directly calculates the energy for the generated binding conformation; Min, which optimizes the docking pose of the generated molccule while keeping its internal geometry fixed; and Dock, which simultaneously optimizes both the docking pose and internal geometry. For each mode, E(() represents the average Vina energy, while IMP (% (t) calculates the percentage of generated molecules with better Vina energy than the reference molecules. Two metrics are further introduced reduce the bias of Vina energy on the size of molecules: mean percent binding gap (MPBG) and ligand binding efficiency (LBE). MPBG(1) measures relative improvement of generated molecules over reference molecules in terms of Vina energy for each binding pocket, defined MPBG- = Σ, Eri.a= E,.dd LBB((T) evaluates the average energy contribution per atom, N-E..s
calculated as LBE- = -E/Na Interaction distribution metrics assess the similarity between generated and reference molecules across seven interaction types identified by PLIP (Salentin et al., 2015). JSDoA (() and MAEos (L) evaluate overall distributions of interaction types, while JSDpr(L) and MAErr(() focus on per-pocket distributions.
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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
K. Case Study
Figure and we provide additional designs of peptides, antibodies, and small molecules on four targets: SARS receptor binding domain, cluster of differentiation 38, Influenza H5 HA head domain, and HIV envelope glycoprotein gpl60.
A
B
SARS Receptor Binding Domain (RBD)
cluster difforentiation 38
(CD38)
Peptide
Antibody
Small Molecule
Peptide
Antibody AG 59.15
Small Molecule
24.30
3G 49.81
-6.59
-23.53
035
2004
5.04
0/3
Rosetta ScOre
Rosetta Score
Score
RocarTE Scare
Rosetta Score
Score
Figure 5. Designed peptides, antibodics, and small molecules, as well as their in silico binding affinity distributions, for the same binding site (A) SARS receptor binding domain (PDB ID: 2GHW) and (B) cluster of differentiation 38 (PDB ID: 4CMH).
A
B
Influenza H5 HA domain
HIV envelope
glycoprotein gp160
Peptide
Antibody 3G
Small Molecule
Peptide
Antibody
Small Molecule
24.64
Vina Score 6.98
26.51
Vine Score 7.60
025
Daevely
5.04
5.00
-25 20
15-10-13 -3
-26
-30
-41-3-2-4
E45
21----1--111
Figure 6. Designed peptides, antibodies, and small molecules, well their in silico binding affinity distributions, for the same binding site on (A) Influenza HS HA head domain (PDB ID: 4XNQ) and (B) HIV envelope glycoprotein gp160 (PDB ID: 4YDK).
L. Self-Adaptive Molecular Sizes
We investigate how the choices of number of blocks influence generations on the same binding site. Using the GPCR case from 4.4, we evaluate different block configurations averaged over 100 generations. For peptides, we vary the number of
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Unified Generative Modeling of 3D Molecules for De Nove Binder Design
blocks into three categories: small (4-10 blocks), medium (11-17 blocks), and large (18-24 blocks). For small molecules, the original algorithm follows the standard protocol of sampling the number of blocks based the spatial size of the binding site (Guan et al., 2023a). We modify this by shifting the distribution =5 blocks to assign less more number of blocks. As shown in Table 12, peptide results align with expectations, where larger binders generally yield lower binding energies by forming more interactions. Remarkably, for small molecules, the model exhibits a self-adaptive behavior. When fewer blocks are used, it generates larger fragments with more atoms to fill the pocket; conversely, with more blocks, it opts for smaller fragments to avoid steric clashes, indicating context-aware flexibility in generation.
Table Comparisons energies and number of atoms in each block for peptides and small molecules under different settings of designated number of blocks.
Peptide
Small Molecule
#Blocks
Rosetta dG
#Blocks
Vina Score (dock)
Avg. #Atoms per Block
small (4-10)
-8.09
small (n-5)
-6.72
5.10
medium (11-17)
-16.93
medium (n)
-7.42
4.06
big (18-24)
-22.39
big (n+5)
-7.44
3.35
22


Reviews:
[{"review_id": "N1OMrXQmo9", "reviewer": "Reviewer_tPcN", "summary": "This paper addresses the task of generating de novo binder molecules to target proteins. Importantly, the paper introduces a single unified framework and model, *UniMoMo*, that can generate peptide binders, antibody binders, and small molecule binders. To this end, the paper proposes a variational autoencoder that encodes different types of molecules building block-wise in a unified latent space. Atomistic details are encoded in latent space and reconstructed with an interative decoder. A diffusion model is trained afterwards in latent space for generation, while conditioning on protein target information. Crucially, the paper demonstrates meaningful improvements by training a model jointly on all molecule types, indicating a certain type of knowledge transfer. The authors extensively validate their model and show strong performance, outperforming baselines in many experiments.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your appreciation and insightful feedback, which is very helpful in improving our paper!\n> W & Q2: If my understanding is correct, the method only works if the binding site on the target protein is known. What if we do not know the binding site?\n\nYes, your understanding is correct. Our method requires prior knowledge of the binding site, in line with the convention established in previous studies [a], since most public benchmarks are built upon this setting. This is also biologically reasonable. For example, to study a protein-protein interaction, a binder is often designed at the interface to inhibit the PPI. If truely no biological knowledge is available, pocket detection tools like MaSIF [b] should be able to identify potential sites for pocket-based design models.\n\n[a] Pocket2mol: Efficient molecular sampling based on 3d protein pockets. ICML 2022\n\n[b] Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning. Nature Methods\n> C: Equation (13) is missing the square root over $1-\\bar{\\alpha}^t$.\n\nThanks for catching this! We apologize for the typo and will correct it in the revision\n> Q1: How exactly is the invariance of the latents guaranteed, as well as the equivariance of the coordinates?\n\nFor the diffusion part, GeoDiff [c] proves that the diffusion process maintain equivariance via an equivariant denoising kernel (Proposition 1), which in our work is the equivariant transformer[d]. The transformer is scalar-based[e], which maintain the equivariance with inner product and unbiased linear transformation on the velocities.\n\nFor the VAE part, the encoding equivariance is determined by the network used, which is also an equivariant transformer. The decoder employs a short flow matching, with a similar theoretical foundation as GeoDiff on equivariant flow matching [f] (Theorem 4.1).\n\nThanks for pointing this out! We will add a detailed discussion in the revision for clarity.\n\n[c] GeoDiff: A Geometric Diffusion Model for Molecular Conformation Generation. ICLR 2022.\n\n[d] An Equivariant Pretrained Transformer for Unified 3D Molecular Representation Learning. preprint.\n\n[e] Scalars are universal: Equivariant machine learning, structured like classical physics. NeurIPS 2021.\n\n[f] Equivariant Flow Matching with Hybrid Probability Transport for 3D Molecule Generation. NeurIPS 2023.\n> Q3: Why not use the original building block coordinates $\\vec{X}_i$, together with the other latents $z_i$ to encode all the additional information? Related, an ablation study over the KL weights $\\lambda_1$ and $\\lambda_2$ in equation (2) would be interesting.\n\nThanks for the valuable question. The block coordinates $\\vec{X}_i\\in\\mathbb{R}^{n_i\\times 3}$ vary in length due to different number of atoms per block (e.g. residue), which makes direct diffusion challenging, as it typically operates in a fixed-length space. A similar issue arises for $H_i$. Thus, we use an all-atom VAE to compress these irregular matrices into fixed-length latent vectors $z_i$ and $\\vec{z}_i$, making diffusion feasible.\n\nRegarding $\\lambda_1$ and $\\lambda_2$, this is a really insightful question. A higher $\\lambda$ smooths the latent space, improving continuity for later generative modeling but also increasing compression, which may limit expressivity. Thus, the weight can neither be too low nor be too high, as shown in the [validation loss curves](https://anonymous.4open.science/r/UniMoMo-CEA0/assets/l1l2.png). Ultimately, we select the combination with the lowest validation loss.\n> Q4: The authors manually add extra noise to $\\vec{z}_i$ before feeding it to the decoder, to enforce robustness. A more principled way would be to increase the KL weight.\n\nThanks for the suggestion. The extra noises primarily benefits small molecules, which have more intricate inter-block connections than peptides and antibodies connected by peptide bonds, thus require higher robustness to coordinate errors introduced by diffusion. Given that the weight of KL loss is already high (0.8), further increasing it would overly constrain the latent space (as in Q3 above and the table below). \n|model|vina(score only)|vina(minimize)|vina(dock)| \n|-|-|-|-| \n|w/o extra noise|-4.62|-5.58|-7.24|\n|w/o extra noise+KL 1.0|-4.42|-5.59|-7.09|\n|w/ extra noise|-5.72|-6.08|-7.25|\n> Q5: Are \"motion vectors\" the vector field in the flow matching framework?\n\nYes, we will replace them with \"vector fields\" in the revision to avoid ambiguity.\n> Q6：How exactly is the model told to either generate a peptide, a small molecule, or an antibody for the different applications?\n\nThanks for the insightful question! We apologize for not making this clear in the paper. We assign a binary prompt to each block, with 1 indicating amino acid (AA) and 0 without restriction. For peptide and antibody benchmarks, all blocks are assigned 1 to ensure AA generation. For small molecules, we use 0 to allow arbitrary fragment generation. We will clarify this in the revision.", "claims_and_evidence": "Yes, the paper supports all its claim by extensive experiments.", "methods_and_evaluation_criteria": "Yes, all proposed methods and evaluation criteria make sense to me and are appropriate for the tackled problem. Overall, the method and design of UniMoMo is well motivated, although some of its details seem ad-hoc and could be explained better. See my questions below.", "theoretical_claims": "The paper does not rely on complex proofs, novel mathematical frameworks, or theoretical claims. Rather, the paper proposes a novel unified molecule generation system.", "experimental_designs_or_analyses": "All experimental designs and analyses seems appropriate to me, as well as sound and valid.", "relation_to_broader_scientific_literature": "The paper is appropriately positioned with respect to the broader literature. Most importantly, the paper discusses many previous related works tackling structure-based drug design.\n\nWhile there already exist related frameworks, including latent diffusion models, for similar molecular modeling tasks, the particular framework proposed by the authors seems novel. The way the variational autoencoder is designed in this paper and the unified decomposition of different types of molecules into graphs of coarse building blocks seem new to me.", "essential_references_not_discussed": "I am not aware of any essential but missing references.", "other_strengths_and_weaknesses": "**Strengths:**\n- The paper runs very extensive evaluation experiments for all the different molecule types that UniMoMo can generate. I appreciate the detailed evaluations and the strong results.\n- The experiment on the GPCR is very interesting, showing that the model leverages aspects it has learnt from different molecule modalities when generating its small molecule binder.\n- The finding that jointly learning a model over different molecule types improves performance in all applications is very interesting and significant, I believe. To the best of my knowledge, this has not been done or shown before in this fashion in a binder generation setting.\n- While the overall framework and model is somewhat complex, the paper makes a good job explaining the approach and the supplementary material includes a lot of details. The paper is mostly clear and easy to read.\n- The tackled applications, antibody design, small molecule drug design, and peptide design for target proteins are impactful with direct real world applications, which further underscores the relevance of the method.\n- UniMoMo builds on established and existing concepts (molecule autoencoders, latent diffusion, etc.), but its detailed architecture, joint building block-wise representation and latent encoding and decoding scheme are novel, to the best of my knowledge.\n\n**Weaknesses:**\n- Some method details are not well motivated or explained, see questions below.\n- If my understanding is correct, the method only works if the binding site on the target protein is known and given.\n\nWhile I have several questions about the method and believe that some details could be explained and motivated better, I think UniMoMo is overall a strong model and this is an interesting paper. Hence, I am recommending acceptance.", "other_comments_or_suggestions": "I believe equation (13) is missing the square root over $\\sqrt{1-\\bar{\\alpha}^t}$, keeping in mind that in equation (12), we have the variance, and when doing reparametrized sampling we need the standard deviation.", "questions_for_authors": "1. In line 096 in the introduction, the authors point out that the method uses E(3)-*invariant* latent states and E(3)-*equivariant* coordinates. This *invariance* and *equivariance* is later in the method section not further discussed. But how exactly is the invariance of the latents guaranteed, as well as the equivariance of the coordinates? I would suggest the authors to discuss this in more detail.\n2. My understanding is that UniMoMo tackles the situation where the location of the binding site on the target molecule is known and given. Can the authors clarify? What if we do not know the binding site? Can we still use and apply UniMoMo?\n3. The authors construct its latent space through encoding both into \"abstract\" latents $z_i$ and coordinate-valued latents $\\vec{z}_i$. Why exactly is this separation needed? Also, why use coordinate-valued latents $\\vec{z}_i$ at all, and why not instead directly use the original building block coordinates, $\\vec{X}_i$, together with the other latents $z_i$ to encode all the additional information? I think this could be explained and motivated better, and it also could be interesting to run an ablation study for this modeling choice.\n    - Related, an ablation study over the KL weights $\\lambda_1$ and $\\lambda_2$ in equation (2) would be interesting.\n4. The authors manually add extra noise to $\\vec{z}_i$ before feeding it to the decoder, to enforce robustness. This seems very ad-hoc and in principle the sampling of the posterior distribution should already lead to noise injection making the decoder robust. A more principled way would be to increase the KL weight, such that the posterior encoding distributions themselves become wider and smoother, as opposed to manually adding noise. I would suggest the authors to better justify their choice here and also show in an ablation study that this is necessary.\n5. The authors speak of *\"motion vectors\"*. If my understanding is correct, this is the vector field that encodes the flow in the flow matching framework. If that is the case, I would suggest the authors to update their wording here, as I have never heard the expression motion vectors for this quantity before.\n6. An important detail I am missing: The authors build one joint model for all molecule types, and then apply it to the different applications in the experiments. How exactly is the model told to either generate a peptide, a small molecule, or an antibody for the different applications? Is there some conditioning given to the model to control this? Or does the model generate different molecule types entirely randomly? But that would be confusing, because the model is applied to the specific applications. I think I am missing something here and I would suggest the authors to be clearer about that.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Ic1KkK42EH", "reviewer": "Reviewer_gwNY", "summary": "In this paper, the authors propose a new generative model for 3D molecule design conditioned on a protein target. \nThe proposed model, UniMoMo, unifies generation of different ligand modalities (small molecules, peptides and parts of antibodies) into a single model. This is done by considering each molecule, independent of their modalities, as a graph of blocks (amino acids for peptides/antibodies or molecular substructures for molecules).\nThe proposed approach is a latent generative model with three parts: (i) a autoencdoer that encodes blocks into a latent space then decode the back to block types, (ii) a latent diffusion model operating on the learned latent space, and (iii) an iterative generation approach to recode full-atom geometries from the blocks.\nThe authors show good results on three benchmarks (for three different molecular modalities). More interestingly, they show that training a model on all modalities is usually better than training each modality independently.\n\n\n## Update after rebuttal\nI thank the authors for their rebuttal. I will keep my score with the requirement that the authors update the manuscript to make the points fellow reviewers and I pointed out, specially when it comes to better details and explanations.\nCongratulations!", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your appreciation and the constructive comments!\n\n> Q1: The paper only evaluates on in-silico metrics, which are known to be far from perfect. The proposed method do achieve good results on these metrics (compared to baselines benchmarked).\n\nThanks for the comments! While we are currently conducting wet-lab validations, the experimental timeline is extensive. Therefore, we plan to include these results in a future extension of this work.\n\n> Q2: During sampling time, how many \"blocks\" nodes are chosen before starting the (reverse) diffusion process? How does this choice affects experimental results (on all modalities)?\n\nFor peptides and antibodies, we follow the literature [a,b] and set the number of blocks equal to that of the reference sequence, as many metrics, including AAR and RMSD, assume generated sequences having the same lengths as the native binders.\n\nFor small molecules, the number of blocks is sampled from the statistical distribution based on the spatial size of the pocket [c]. We evaluated different settings on the GPCR case in Section 4.4, averaging results over 100 designs, where $n$ denotes the originally sampled number of blocks for small molecules:\n\n| peptide lengths | Rosetta dG |\n|-|-|\n| small(4-10)     | -8.09   |\n| medium(11-17)  | -16.93  |\n| big(18-24)    | -22.39  |\n\n| molecule fragments | Vina score (dock) | Avg.atom per block |\n| -------- | --------| -- |\n| small (n-5)  | -6.72   | 5.10 | \n| medium (n)   | -7.42  | 4.06 |\n| big (n+5)   | -7.44  | 3.35 |\n\nCommonly, larger binders lead to lower energies, since they can form more interactions. Interestingly, for small molecules, the model adapts to the number of blocks. With fewer blocks, it generates larger fragments with more atoms to fill the pocket; otherwise, with more blocks, it generates smaller fragments, avoiding overcrowding the pocket.\n\nThanks for the insightful question again! We will include the discussion in the revision!\n\n[a] Full-Atom Peptide Design based on Multi-modal Flow Matching. ICML 2024.\n\n[b] Conditional Antibody Design as 3D Equivariant Graph Translation. ICLR 2023.\n\n[c] CBGBench: Fill in the Blank of Protein-Molecule Complex Binding Graph. ICLR 2025.\n\n> Q3: I feel some information is missing on how the bonds are computed. Could the authors elaborate more on how the bonds between bonds and between blocks are computed? It seems that the latter depends on a NN prediction. How accurate is it?\n\nSorry for the confusion. For intra-block bonds, they are predetermined once the block type is assigned. For inter-block chemical bonds, we employ an MLP for prediction, using the hidden states of atom pairs as input (Eq. 6). Bond prediction is restricted to spatially neighboring atoms, excluding those that are too far apart. The predictions are dynamically changing during the flow matching process in the decoder (Figure 1B, bottom right). Ultimately, the reconstruction accuracy of the chemical bonds are around 97%, which we think is accurate enough.\n\n> Q4: How are the sequences of AAs (on both peptides and antibodies) extracted from the full atom point cloud?\n\nSorry for the confusion. In our block-level decomposition, each natural amino acid forms a block. Therefore, we can directly get the amino acid type of each block. We think this is also one merit of our block-based unified representation, without requirements to further derive an algorithm to extract the AAs.\n\n> Q5: What parts of the CDR are modelled on the Antibody experiments? More experimental details on this section is needed.\n\nSorry for the confusion. We follow the convention [d, e] and evaluate on CDR-H3, as it exhibits much higher irregularities than other CDRs and plays a crucial role in binding and interactions [f]. We appreciate the suggestion and will clarify this in the revision.\n \n[d] End-to-End Full-Atom Antibody Design. ICML 2023.\n\n[e] GeoAB: Towards Realistic Antibody Design and Reliable Affinity Maturation. ICML 2024.\n\n[f] Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Structures. NeurIPS 2022.\n\n> Q6: During sampling time, given a target pocket, how does the model decide when it generates blocks that belond to small molecules, or peptides or antibodies?\n\nThanks for the insightful question! We apologize for not making this clear in the paper. We use a binary prompt for each block, with 1 indicating the generation of amino acid (AA), and 0 indicating either AAs or molecular fragments. During benchmarking for peptides and antibodies, all blocks are assigned a prompt of 1 to ensure AA generation. For small molecules, we set the prompt to 0, allowing flexible generation of molecular fragments. We will add a detailed explanation in the revision to clarify this point.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes. The authors propose a model that is modality-agnostic and show results on three different molecular modalities.", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "- The paper only evaluates on in-silico metrics, which are known to be far from perfect. The proposed method do achieve good results on these metrics (compared to baselines benchmarked).\n- I think a lot of experimental details are missing, specially when it comes to the antibody and peptides experiments. For example, which parts of the CDR is modelled? The loops? The frames? Everything? How many AAs are considered on this setting?\n- During sampling time, how many \"block\" nodes are chosen before starting the (reverse) diffusion process? How does this choice affects experimental results (on all modalities)?\n- During sampling time, given a tartget pocket, how does the model decide when it generates blocks that belond to small molecules, or peptides or antibodies?", "relation_to_broader_scientific_literature": "The paper is well-placed in the context of structure-conditioned 3D molecule generation. They provide a method that model all-atoms and can be applied on different data molecule modalities.", "essential_references_not_discussed": "Not that I am aware of.", "other_strengths_and_weaknesses": "Strengths:\n- This is one of the first approaches that proposes a unified model for structure-based molecule design that can be applied to different molecular modalities. Moreover, the authors show that training on all modalities is better than training on a single modality.\n\nWeakness:\n- The proposed approach contains many different sub-components, making it hard to reproduce/build upon, and probably reducing its effectiveness and expressivity.", "other_comments_or_suggestions": "More details on pepdtides and antibodies experimental section is neeeded.", "questions_for_authors": "- See above for more questions.\n- During sampling time, how many \"blocks\" nodes are chosen before starting the (reverse) diffusion process? How does this choice affects experimental results (on all modalities)?\n- I feel some information is missing on how the bonds are computed. Could the authors elaborate more on how the bonds between bonds and between blocks are computed? It seems that the latter depends on a NN prediction. How accurate is it?\n- How are the sequences of AAs (on both peptides and antibodies) extracted from the full atom point cloud?\n- What parts of the CDR are modelled on the Antibody experiments? More experimental details on this section is needed.\n- During sampling time, given a target pocket, how does the model decide when it generates blocks that belond to small molecules, or peptides or antibodies?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "O4DU5StxPX", "reviewer": "Reviewer_gQC8", "summary": "This paper introduces a unified framework, called UniMoMo, for general target-specific binder generation. The target is a protein, and the binders could be peptides, antibodies, or small molecules. UniMoMo aims to train a single generative model to tackle general binder generation problem, while being able to leverage datasets across different domains. The performance on various binder generation benchmarks has been demonstrated.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your appreciation and the positive comments!\n\n> Q1: How did you balance data from different all three domains during training?\n\nThanks for the question! In the current implementation, we have not extensively explored domain-specific data balancing strategies. For our joint training approach, we utilized representative datasets from each domain: CrossDocked (\\~100k samples) for small molecules, PepBench (\\~80k samples) for peptides, and SAbDab (\\~10k samples) for antibodies. As an initial effort toward unified molecular modeling, we employed simple random sampling across these datasets during training, which has demonstrated promising results. Moving forward, particularly as we scale the framework to incorporate larger and more diverse datasets, we recognize the importance of investigating more sophisticated data balancing approaches to further enhance model performance.", "claims_and_evidence": "The main claim is that by using a unified generative model, we can tackle different binder design task at once. Also, the dataset from different binder domains can help each other. This has been verified by the great experimental performance across several widely used benchmarks.", "methods_and_evaluation_criteria": "The main contributions of this unified framework are the unified representation of graph of blocks and the geometric latent diffusion model. The overall UniMoMo framework is sound. In terms of evaluation, the authors conducted experiments on widely used benchmarks for target-conditioned peptide generation, antibody generation, and small molecule generation. The performance is strong across benchmarks compared to existing methods that are specifically designed for each domain. Also, it shows that leveraging datasets across domain with the UniMoMo framework is helpful for boosting performance.", "theoretical_claims": "N/A. No major theoretical claims.", "experimental_designs_or_analyses": "All the experimental designs are closely following the community standard, and they are solid to me.", "relation_to_broader_scientific_literature": "The proposed UniMoMo is unique as it unifies binder design for different binder types. Moreover, it shows training on the combined datasets from all domains can help improve performance for each domain, which is exciting.", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "None", "other_comments_or_suggestions": "None", "questions_for_authors": "How did you balance data from different all three domains during training?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper received reasonably positive reviews. The reviewers are not very enthusiastic, mainly due to the marginal improvement in certain cases, but have expressed consistent support. Thus an accept is recommended.
Decision: Accept (poster)