Pareto-Optimal Energy Alignment for Designing Nature-Like Antibodies
Authors: Yibo Wen
Chenwei Xu
Jerry Yao-Chieh Hu
Kaize Ding
Han Liu
Venue: NeurIPS 2025 poster ()
Keywords: Antibody Design
Diffusion Models
Model Alignment
Primary area: machine_learning_for_sciences

Abstract: We present a three-stage framework for training deep learning models specializing in antibody sequence-structure co-design.
We first pre-train a language model using millions of antibody sequence data.
Then, we employ the learned representations to guide the training of a diffusion model for joint optimization over both sequence and structure of antibodies. 
During the final alignment stage, we optimize the model to favor antibodies with low repulsion and high attraction to the antigen binding site, enhancing the rationality and functionality of the designs.
To mitigate conflicting energy preferences, we extend AbDPO (Antibody Direct Preference Optimization) to guide the model toward Pareto optimality under multiple energy-based alignment objectives. 
Furthermore, we adopt an iterative learning paradigm with temperature scaling, enabling the model to benefit from diverse online datasets without requiring additional data.
In practice, our proposed methods achieve high stability and efficiency in producing a better Pareto front of antibody designs compared to top samples generated by baselines and previous alignment techniques.
Through extensive experiments, we showcase the superior performance of our methods in generating nature-like antibodies with high binding affinity.

Pareto-Optimal Energy Alignment for Designing Nature-Like Antibodies
Yibo Wen
Chenwei Xu
Jerry Yao-Chieh Hu
Kaize Ding
Han Liu
Northwestern University
(yibo, cwx, www.j,uue....nn.m now.://o...tthwweerr..cc (kaize Shaize.ding,oe hang.aaamlnooooohhsstttta edu
Abstract
We present three-stage framework for training deep learning models specializing in antibody
co-design. We first pre-train a language model using millions of antibody sequence data. Then, employ the learned representations to guide the training of diffusion model for joint optimization over both sequence and structure of antibodies. During the final alignment stage, optimize the model to favor antibodies with low repulsion and high attraction to the antigen binding site, enhancing the rationality and functionality of the designs. To mitigate conflicting energy preferences, we extend AbDPO (Antibody Direct Preference Optimization) to guide the model toward Pareto optimality under multiple energy- based alignment objectives. Furthermore, we adopt an iterative learning paradigm with temperature scaling, enabling the model benefit from diverse online datasets without requiring additional data. In practice, our proposed methods achieve high stability and efficiency producing better Pareto front of antibody designs compared to top samples generated by baselines and previous alignment techniques. Through extensive experiments, we showcase the superior performance of our methods in generating nature-like antibodies with high binding affinity.
Introduction
Antibodies are large, Y-shaped proteins that play crucial role in protecting the human body against various discase-causing antigens [Scott et al., 2012]. As shown in Figure 1, an antibody consists of two identical heavy chains and two identical light chains. Antibodies possess remarkable abilitics to bind a wide range of antigens, and the tips of the Y shape exhibit the most variability [Collis et al., 2003, Chiu et al., 2019]. These critical regions, composed of specific arrangements of amino acids, are known as Complementarity Determining Regions (CDRs) since their shapes complement those of antigens. To great extent, the CDRs at the tips of light and heavy chains determine antibody's specificity to antigens [Akbar et al., 2021]. ]. Hence, the key challenge in antibody design is identifying and designing effective CDRs as part of the antibody framework that bind specific antigens.
Recently, various deep learning models achieve great success the long- standinn problem of antibody design and optimization. For example, Madani al. [2023] and Rives al. [2019] borrow idcas from language models and treat proteins as sequences to predict their structures, functions, and other important properties. These methods benefit from having access large datasets with millions of protein sequences, but often lead to subpar results in generation tasks conditioned on protein structures [Gao et al., 2023, Martinkus al., 2024]. Due the determinant role of structure in protein function, co-designing sequences with structures emerges as a more promising approach (Anishchenko et al., 2020, Harteveld et al., 2022, Jin et al., 2022a.b). Among all, diffusion-baan
Future updates be found at tattps://aree www.oogg/bb... abs///ab///// 2aabs/2412 //////2222.200 20984.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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CDRs
Ya
CDRs
V-
C'n
Can
Antigens
C1
Light chain
Cm
Cm
CDRs variable domain light chain V2
Heavy
Gio
Gin
H
A73
Antibody
CDRs on variable domain of heavy chain Vi
CDR-HB in Antigen-Antibody Complex
Figure 1:
Illustration of an antibody binding to an antigen. The antibody's 's light and heavy chains are shown with their variable (V) and constant (C) regions. The third CDR in the heavy chain (CDR-H3), colored in orange, is critical for determining the binding affinity to the antigen.
methods stand out by learning the reverse process of transforming desired protein structures from noise [Vinod, 2022, Lisanza et al., 2023, Martinkus al., 2024]. These methods achieve atomic- resolution antibody design and state-of-the-art results in various tasks, including sequence-structure co-design, ix-bbacboone CDR design, and antibody optimization [Luo et al., 2022, Zhou et al., 2024b].
Despite the prevalence of generative models, two key problems persist in effective antibody sequence- structure co-design. First, datasets containing complete 3D structures of antibodies are orders of magnitude smaller than sequence-only datasets. For example, the most common dataset for antibody design, SAbDab [Dunbar al., 2014], only contains few thousand antibody structures despite daily updates. The scarcity of high-quality antigen-antibnn antibody pairs, coupled with high variability of CDR structures [Collis et al., 2003], further constrains the performance learning-based approaches. Second, existing methods overlook energy functions during supervised training and struggle to generate antibodies with low repulsion and high binding affinity. Contrary to traditional computational methods, recent efforts [Luo et al., 2022, Jin et al., b022a.b, Kong al., 2022] shift their focus from searching for minimal energy states to optimizing metrics such as Amino Acid Recovery (AAR) and Root Mean Square Deviation (RMSD). However, these metries are prone to manipulation, often fail to differentiate between different error types, and ignore important side chain structures CDR-antigen interactions [Zhou al., 2024b]. Overreliance these metrics gives rise to irrationality in generated structures and widens the gap between in silico and in vitro antibody design.
To address these challenges, we introduce three-stage training pipeline that focuses on the rationality and functionality of the antibody. Inspired by the recent success of Large Language Models, we adopt a similar training paradigm comprising pre-training, transferring and alignment.
1. Pre-training. We first utilize pre-trained antibody language model, trained millions of amino acid sequences, to alleviate the shortage of structured antibody data. This approach enables the model to capture underlying relationships between proteins and internalize fundamental biological concepts such as structure and function [Rives et al., 2019, Chowdhury et al., 2021].
2. Transferring. We use the language model's learned representations to train a smaller model on curated antibody-antigen dataset, adapting it for antigen-specific antibody design. The diffusion-baree based model is able to recover not only sequences but also coordinates and side-chain orientations of each amino acid conditioned on the antigen-antibody framework [Luo et al., 2022].
3. Alignment. For the final stage, we conduct energy-based alignment of the diffusion model using Pareto-Optimal Energy Alignment as an extension of Direct Preference Optimization (DPO) [Wallace et al., 2023]. By reusing designs generated by the model and labeling them with biophysical energy measurements, we compel the model to favor antibodies with lower repulsion and higher affinity in a data-free fashion. Additionally, we introduce an iterative version of the alignment algorithm an online setting, allowing the model to benefit from online exploration. To balance exploration and exploitation during alignment, scaling during the sampling process. Empirical results verify that our methods surpass existing alignment methods, consistently generating antibodics with energies closer to Pareto optimality.
propose decaying temperature

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In summary, our main contributions are as follows:
We devise the first three-stage training framework for antibody sequence-structure co-design, consisting of pre-training, transferring, and alignment.
We propose an efficient multi-objective alignment algorithm with online exploration which consistently produces better Pareto front models in terms of energy without extra data.
Our approach achieves state-of-the-arr performance in generating more natural-like antibodies with better rationality and functionality.
2 Related Work
Computational Antibody Design. Deep learning methods are widely used for antibody design, with many latest works incorporating generative models [Alley et al., 2019, Saka et al., 2021, Shin et al., 2021, Akbar et al., 2022]. Jín et al. [2022a] introduce HERN, a hierarchical message-passing passing network for encoding atoms and residues. Kong et al. [2022] propose MEAN, utilizing E(3 E(3)-equivariant graph networks to better capture the geometrical correlation between different components. Additionally, Kong et al. [2023] propose dyMEAN, focusing on epitope- binding CDR-H3 design and modeling full- atom geometry. Luo et al. [2022] propose a diffuusio model that uses residue type, atom coordinates, and side-chain orientations to generate antigen-specifee CDRs. Martinkus et al. [2024] propose Ab-Diffuser, which incorporates more domain knowledge and physics- based constraints.
Diffusion-based Generative Models. Diffusion models are type of generative model with an encoder-decoder structure. It involves a Markov-chain process with diffusion steps to add noise to data (encoder) and reverse steps to reconstruct desired data from noise (decoder) [Weng, 2021, Luo, 2022, Chan, 2024]. DDPM [Ho et al., 2020] is one of the most well-known diffusion models utilizing this process. Song et al. [2020a] propose DDIM, which is an improved version of DDPM that reduces the number of steps in the generation process. Score-matching [Hyvärinen and Dayan, 2005, Vincent, 2011, Song et al., 2020b] is also a popular research area in diffusion models. The key idea of score- motee-matching the data distribution. Later, Song et al. [2021] propose a solver for faster sampling in the context of score-matching methods using stochastic differential equations.
Langevin dynamies generate samples and estimate the gradient of
Alignment Generative Models. Preference alignment during fine-tuning improves the quality and usability of generated data. Reinforcement Learning (RI.) is one popular approach to align models with human preferences, and RLHF [Ouyang al., 2022] an example of such algorithm. Rafailov et al. [2024] propose DPO Different from RL-based approaches, DPO achieves higher stability and efficiency as it does not require explicit reward modeling. Building upon DPO, recent works such as DDPO [Black et al., 2023], DPOK [Fan et al., 2024], and DiffAC [Zhou et al., 2024a] demonstrate the possibility of adapting existing alignment techniques to various generative models. SimPO [Meng et al., 2024] improves DPO by using the average log probability of a sequence as the implicit reward.
alternative approach to align with human preferences.
Preliminaries
Problem Definition. In this work, we represent each amino acid by its residue type 8; LACDEFGHIKLMNPPRSTTE
coordinate æ; E R3, and orientation O E SO(3), where i e (I...., ..,..,,,, J. Here, is the total number of amino acids in the protein complex, which may con- tain multiple chains [Luo et al., 2022]. We focus on designing CDR, a critical functioning component of the antibody, given the remaining antibody and antigen structure. Let the CDR of interest consists of m amino acids starting from index I + 1 to + m on the entire antibody- total of N amino acids. We denote the target CDR as R = {( Lj, O,) lj =1+++ 1...., ..I [ m) and the given siribody-antigee framework as F = {s x; O.) l A.l....NN.. 1,........ I...., m)). Therefore, our objective is to model the conditional distribution P(R (F).
framework with
Direct Preference Optimization. To tackle the common issues of fine-ture mee-tunng with Reinforcement Learning (RL), Rafailov et al. [2024] propose DPO as an alternative for effective model alignment. In the setting of DPO, we have an input æ and a pair of outputs (y1, 3/2) from dataset D. and a corresponding preference denoted as yo yt x where yo and y are the "winning" and "losing" samples amongst (y1, y2) respectively. According to the Bradley-Terry (BT) model [Bradley and Terry, 1952], for a pair of outputs, the human preferences governed by ground truth reward

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model r(z, y) such that BT preference model is
p(y > y2 x) = (r( yn) r(x, y2)),
(3.1)
where (.) is sigmoid. Then, the optimal policy गे is defined by maximizing reward:
x x)
= argmax
E E.D..yrT(l)))
[f(x,)) - log Ter
(3.2)
where (I is the inverse temperature controlling the KL regularization. By solving (3.2) analytically, Rafailov et al. [2024] give relation between the ground-truth reward and optimal policy:
(y x) (err x)
r(z, y) Blogg
+ log (z))
(3.3)
where 7(x) = Ey Terly x)) exp (r(x,))/3). This allows rewrite BT preference model (3.1) without reward model (only in Ty Tzet)::
P( > a)) o (glog
(1 x)
म.. (31z xr)
Blog
(3.4)
Tee x)) Te y/ x3)
In this way, the maximum likelihood reward objective for a parameterized policy Te becomes:
To(yu x) x)) Trer
x) (B xx) ]
To (m
(To; Tiet) (M.
E log a (Blog
33 log
(3.5)
This derived loss function bypasses the need for explicit reward modeling, enabling an RL-free approach for preference optimization. While DPO is first designed for language models, we are able to re- re-formulate it for diffusion models and arrive at a similar differentiable objective following [Wallace et al., 2023], or see Appendix A.3 for details.
Methodology
In this section, we present our energy alignment method for designing nature- like antibodies, named AlignAb. We introduce Pareto-Optimal Energy Alignment to fine-tune the model under conflicting energy preferences Section 1. Then, we present an iterative version of the algorithm and discuss how to mitigate mode collapse during sampling with temperature scaling in Section 4.2. Finally, we summarize the alignment algorithm and three-stage training framework in Section 4.3.
4.1 Pareto-Optimal Energy Alignment (POEA)
Pre-trained models often struggle to produce natural-like antibodies because they tend to ignore important physical properties during the optimization process. These physical properties manifest themselves as various energy measurements such as Lennard-Jones potentials (accounting for at- tractive and repulsive forces), Coulombic electrostatic potential, and hydrogen bonding energies (Adolf-Bryfogle et al., 2017]. We aim to close this gap by aligning the pre-trained model to favor antibodies with low repulsion and high attraction energy configurations at the binding site. While AbDPO [Zhou et al., 2024b] demonstrates the potential naïve DPO in antibody design, there are two primary distinctions in this context:
(DI) The ground -trut reward model, given by energy measurements, available.
(D2) There are multiple, often conflicting, energy-based preferences.
Therefore, we propose Pareto-Opting Energy Alignment to address (D1) by adding ground-trute reward margin, and (D2) by extending DPO to multiple preferences.
Incorporating Reward Model. Since we have access to the ground-truth reward model, it would be unwise to ignore this extra information and perform alignment with just the preference labels. We show how to extend DPO and incorporate the available reward values in the training objective. Let's consider new reward function r'(x, y) r(x,y) + f(x) by adding the ground-truth reward model r(x, y) and random reward model f(x) which depends only on the input. According to (3.3), we express r' (z..) y) in terms of its optimal policy under the KL constraint:
T (y
x)
r' v) =3log
+ 1og ((x),
(4.1)
Tree x))

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where Z(z) =
Ey Trerl z) exp (2/x,)))3) Note that (z y) and r(z, y) induce the same optimal policy by construction (see Lemma A.2 and Appendix A.2 for details):
( x)
[r(,, y) Bog
argmax x (nD.arra((pa))
E
Ter(z x)
Then, cast the random reward model f() into function of गद and r:
((x) = Blog (H (t) ( x))
+ Blog 7(x) r r(z, v).
(4.2)
Finally, we replace r(x, y) with (xx in the original preference model p(y) > y/2 x = o(((,, v1) -1)- y2), and hence DPO loss (3.5) becomes below loss over the parametrized model ιy as
E (R.3
log o 1oo
To x)) x))
log
Tee /
x
Ar
(4.3)
Tear (th
Tref
y1
x
where A, = r(z, Vw) r r(z y1) is the positive reward margin between Yo and yr. Notably, the obtained loss differs from the vanilla DPO loss (3.5) by including an additional reward margin A,- To better understand how the derived loss facilitates the alignment process, we take the gradient of the loss and interpret each term individually:
]1.
-B
E (R. (w.
(fs((,, 91) Fe (z, yw) A.)
V e log π. (B x))
Ve log ( 2))
combined sample weight
(11): likelihood yar
(1l1): likelihhodd of Br
Xad 2) the implicit reward defined by the models. Similar the DPO gradient, term (II) and (III) aim to increase the likelihood of the preferred sample you and decrease that of the dispreferred sample yI- The key difference lies in term (I), where weighting incorporates both the implicit reward margin ñ0(x, yw) - fæ y1) and the explicit ground truth reward margin A,, ensuring larger reward gaps lead to stronger weight adjustments.
where Fz 9) 8 log [x(y(z)
Multi-Ohjective Alignment. Given n ground-truth reward models r r= [r....,,,
we construct
a dataset = {(x; yr, r(z, 3:)]} that records the reward values for each input and its corresponding output. In practice, each reward value is an energy measurement associated with certain physical properties. Following Zhou et al. [2023], the goal for multi-objective preference alignment is not to learn single optimal model but rather Pareto front of models { w r, w 92} and each solution optimizes for one specific collective reward model f:
M (ly x))
T argmax E EYDD
f(x,y) - Bog
(4.4)
( x))
where w [WI, wn s.t. Σ Wi = 1 is weighting vector in the preference space Ω. To obtain preference pair (x., Yw: V1), we first select two random data points (ær, ye. r(x, y:)) and (x, (x, v2)) from and then compute their collective rewards f(x, ys) and f(r, yz). Among (yi, Mj), 1, we assign Vou y/ which satisfies f(z, Vw:) > f(z, 31).
To incorporate multiple preferences, we replace the original reward model r in (4.3) with the collective reward model f T and arrive at Pareto Pareto-Optimal Oatim---pmeeeeeeeeeee Aliigmeen (POEA) loss:
CPOEA Teet) =
log o (3 log
Te (B xx)
3 log To(y x)
Ar)]
(4.5)
(xt Ne.8hw D
Tiee (3) x)
where AP = f(x, )w) f(x, ). This simple formulation inherits the desired properties from its single-objective counterpart, ensuring that produces the optimal model म. for each specific w. In practice, we calculate the reward margin with energy measurements following Equation (D.4).
4.2 Iterative Alignment with Temperature Scaling
Iterative Online Alignment. To further exploit the available reward model, we develop an iterative version of our alignment method as an analogy to online reinforcement learning (RL). Instead of relying on large offline dataset collected prior to training as in AbDPO [Zhou et al., 2024b], our approach starts with an empty dataset and augments it with an online dataset constructed by querying the current model at the start of each iteration. This method mirrors how online RL agents gather
5

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data and learn by interacting with the environment, enabling continuous policy improvement. We present the detailed algorithm in Algorithm Ideally, we are able to repeat the process until no further improvement is observed, and we select the best model based on validation metrics.
Temperature Scaling. While CDRs exhibit substantial sequence variation across antibodies [Collis et al., 2003], parameterized neural networks often struggle to capture this diversity and suffer from mode collapse during training [Bayat, 2023]. To quantify this effect, we measure the entropy of generated sequences, defined as H - Σ log p, and compare it with that of natural CDR-H3 sequences. As shown in Table 1, a clear entropy gap emerges, indicating reduced diversity and potential model collapse, particularly evident when comparing results at different training steps.
To mitigate this issue, introduce temperature scaling during inference. This technique adjusts the logits prior to the softmax operation modulate sampling randomness (i.e., entropy). Specifically, the scaled softmax given by Softmax(z:/ (z/ = exp(a./T)
Table 1: CDR-H3 Entropy
Method
Entropy (1)
Reference
3.95
Σ, cxp(=;/Tj' where T denotes the temperature. A higher T increases diversity, while a lower T promotes determinism. Since our diffusion model uses multinomial distribution to model antibody sequences (see Appendix 1) inject small temperature factor inference time to enhance sequence diversity. Inspired by the e-greedy strategy in RL, we adopt a decaying temperature schedule to balance exploration and exploitation. We validate this approach by applying a small temperature scale (I' = 1.5) to the pre-trained diffusion model DiffAb [Luo et al., 2022]. The resulting model, DiffAb-TS, produces sequences that match the diversity of natural CDR-H3 sequences, as shown in Table 1.
MEAN
2.18
DiffAb (100k step)
3.57
DiffAb (200k step)
3.29
DiffAb-TS
3.84
Algorithm 1 Iterative Pareto Optimal Energy Alignment
1: Input: Initial dataset D. 0, KL regularization coefficient 8, total online iterations T, batch size m, reference model Tett, initial model To Tel and reward model A.
2: for t = 0, 1, ................... do
3: Sample input prompts æ; ~ X' for = I,...,m.. m.
4: Generate two responses for each prompt: y, (1) (2)
2; Tel- x.).
5: Calculate rewards f(r;; si ()) and f(x,, yi (2)) for all i E [m]. and collect them as Dr.
6: Optimize T with Do.r according to (4.5):
Te( x)) To ( x) - B Blo
1; )}
T++1 f- argmin (1.ww. Dou
log a Boog
(e x))
Tred (y1 x²)
7: end for
8:
Output: Best-performing policy ग.- selected from (To, ,i...., oT} using a validation set.
4.3 Ttree-Stage Training Framework
Inspired by the recent success of large language models, we adapt the widely used three-stage training framework the task of antibody design in combination with our devised alignment method.
Pre-training. Due to the limited availability of structured antibody data, we leverage the abundant online antibody sequences for pre-training using a BERT-base model [Devlin et al., 2019]. Following Gao et al. [2023], we employ a masked language modeling objective, where we mask all residues within CDRs and aim to recover them. This approach enables the antibody language model to learn expressive representations that capture the underlying relationships between proteins and internalize fundamental biological concepts such as structure and function.
Transferring. We use the pretrained BERT model as frozen encoder to train downstream diffusion model. Specifically, this transfers learned representations to the diffusion model for anti- body generation (see details of embedding fusion in Appendix E. Crucially. this representation enhancement addresses the challenge of antigen-specific antibody design: datasets are limited and curated by human experts. The diffusion-based model recovers sequences, coordinates, and orientations of each amino acid, conditioned on the entire antigen-antibody framework. For detailed formulation diffusion models for antibody generation, Appendix A.I.

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Alignment. Lastly, we align the trained diffusion model via Pareto Meeimmal-Eeegy-AAAe (POEA) from (3.2), an extended version of multi-objective DPO-diffusion for antibody design. Importantly, the Pareto weight w allows us to incorporate designers" preferences, enabling balanced control over multiple objectives (physical, chemical, and biological properties) by domain experts. In summary, we propose POEA (3.2) to address issues of conflicting energy preferences and potential mode collapse during the aligmment stage. We take advantage of ground-truth reward models (see detailed reward calculations in Appendix D) by incorporating reward margin in the loss function and utilizing online exploration datasets.
5 Experimental Studies
We evaluate our proposed framework, AlignAb, on the task of designing antigen-binding CDR- H3 regions. In Section 5.1, outline the experimental setup for the three training stages. We then introduce the evaluation metrics and discuss the main results in Section 5.2, followed by comprehensive ablation studies in Section 5.3.
5.1 Experiment Setup
Energy Definitions. We introduce four key energy measurements where we use the first two to evaluate the rationality and functionality of antibodies and use the rest to generate preferences during alignment. To determine the rationality and functionality of different CDR designs, we identify two key energy measurements: CDR Evoral and CDR-Ag AG.
(1) CDR Evstl represents the combined energy of all amino acids within CDR, calculated using the default score function in Rosetta [Chaudhury et al., 2010]. This energy is strong indicator of structural rationality, as higher Fmuull suggests large clashes between residues.
(2) CDR-Ag AG represents the binding energy between the CDR and the antigen, determined using the protein interface analyzer in Rosetta [Chaudhury et al., 2010]. This measurement reflects the difference in total energy when the antibody is separated from the antigen. Lower AG corresponds to higher binding affinity, serving strong indicator of structural functionality.
To generate energy-based preferences during model alignment, we use two fine-grained energy measurements: CDR-Ag Ecep and CDR-Ag Ean-
(3) CDR-Ag Ean captures the attraction forces between the designed CDR and the antigen.
(4) CDR-Ag Eap captures the repulsion forces between the designed CDR and the antigen.
As suggested by Zhou et al. [2024b], we further decompose Eat and Lxep at the amino acid level to provide more explicit and intuitive gradients. We include detailed calculation formulas for the energy measurements and their corresponding reward functions in Appendix D. We exclude CDR Evcal and CDR-Ag AG measurements when determining the preference pairs because our experiments demonstrate that CDR-Ag Emt and CDR-Ag Ag Exep are sufficient for effective model alignment. This simplification reduces the computational cost associated with tuning multiple weights for different reward models, resulting in a more efficient and stable alignment process.
Datasets. For pre-training, we utilize the antibody sequence data from the Observed Antibody Space database [Olsen et al., 2022]. Following Gao et al. [2023], we adopt the same preprocessing steps including sequence filtering and clustering. Since we focus on CDR-H3 design, we select 50 million heavy chain sequences to pre-train the model.
To transfer the knowledge, use the antibody-antigen data with structural information from SAbDab database [Dunbar et al., 2014]. Following Kong et al. [2022], we first remove complexes with a resolution worse than 4A and renumber the sequences under the Chothia scheme [Chothia and Lesk, 1987]. Then, we identify and collect structures with valid heavy chains and protein antigens. We also discard duplicate data with the same CDR-H3 and CDR-L3. We use MMseqs2 [Steinegger and Söding. 2017] to cluster the remaining complexes with threshold of 40% sequence similarity based on the CDR-H3 sequence of each complex. During training, we split the clusters into a training set of 2,340 clusters and a validation set of 233 clusters. For testing, we borrow the RAbD benchmark [Adolf- [Adolf-Bryfogle et al., 2017] and select 42 legal complexes not used training.
For alignment, we avoid using additional datasets and only draw samples from the trained diffusion model. During each iteration, we first generate 1, 1,280 unique CDR-H3 designs and collect them as the online dataset. Then, we reconstruct the full CDR structure including side chains at the atomic level
7

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Table 2: Summary of CDR Exotal. CDR-Ag AG, CDR-Ag Ean, and CDR Eiep (kcal/mol) of reference antibodies, ranked top-1 antibodies and total antibodies designed by our model and other baselines (MEAN, HERN, dyMEAN, ABGNN, DiffAb, AbX). We compute the generation gap as the mean absolute error relative to the reference. Lower values are better in all measurements. Our results show that our generated antibodies are closer to references compared to all baseline methods.
CDR Exad Avg.
CDR-Ag AG
CDR-Ag Em Avg.
CDR-Ag Enp Avg.
Gap
Method
Top
Top
Avg.
TTop
Top
Top
Avg.
Reference
-19.33
-16.00
-18.34
18.05
MEAN
46.27
186.05
-19.94
-5.13
-5.16
7.77
29.21
31.16
14
HERN
7.345.11
10.599.92
640.50
2.795.15
-6.64
-1.98
1.67
36.88
1453.75
2416.97
dyMEAN
5,074.11
12,311.15
4,452.26
10,881.2 ..22
-12.62
-5.06
139.42
1,762.55
2422.10
6183.425
ABGNN
1315.34
3022.88
-11.52
16.08
-1.63
-0.48
22.15
8.84
354.38
778.54
DiffAh
-1.50
158.90
-6.18
260.30
-12.30
-15.71
18.63
603.58
19.74
263.44
AbX
13.56
25,33
94.76
170.34
-13.68
-15.12
21.38
38.20
37.75
63.43
AligmAb
-6.37
30.45
-8.81
25.16
-14.89
-14.81
15.52
56.22
17.91
39.00
using PyRosetta [Chaudhury al., 2010], and record the predefined energies for each CDR residue level. We repeat this iterative process 3 times for each antibody-antigen complex in the test set.
Baselines. We compare AlignAb with 5 recent ofth-offtheeart antibody sequence co-design baselines. MEAN [Kong et al., 2022] generates sequences and structures using a progressive full-shot approach. HERN [Jin et al., 2022a] generates sequences autoregressively and refines structures iteratively. dyMEAN [Kong et al., 2023] generates designs with full-atom modeling. ABGNN [Gao et al., 2023] introduces a pre-trained antibody language model combined with graph neural networks for one-shot sequence-struetie
generation. DiffAb [Luo et al., 2022] utilizes diffusion models to model type, position and orientation of each amino acid. AbX [Zhu et al., 2024] integrates evolutionary priors. physical interaction modeling, and geometric constraints into a score-based diffusion framework for sequence-structure co-design. All methods except for MEAN generating multiple antibodies for a specific antigen. To ensure a fair comparison, we implement a random version of MEAN by adding small amount of random noise to the input structure.
capable of
5.2 Antigen-binding CDR-H3 Design
Evaluation Metrics. To better measure the gap between designs generated by different models and natural antibodies, we use CDR Evaal and CDR-Ag AG as defined above, rather than commonly used metrics such as AAR and RMSD, Additionally, we include CDR-Ag E. and CDR-Ag Exp used during model alignment. Zhou et al. [2024b] argue that these physics- measurements are indispensable in designing nature-like antibodies and act as better indicators of the rationality and functionality of antibodies. Based on energy measurements, we compute energy gap as the mean absolute error relative to natural antibodies. We sample 1, 1,280 antibodies using each method and perform structure refinement with the relax protocol in Rosetta [Chaudhury et al., 2010]. To select the best sample from each test case, we aggregate rankings of CDR Funal and CDR-Ag AG.
Results. We report the main results in Table 2. We also include metrics for RMSD and AAR in Table 4 and additional binding and developability metrics in Table 5. We present visualization examples in Figure 4. Overall, AlignAb outperforms baseline methods and narrows the gap between generated and natural antibodies. Furthermore, AlignAb demonstrates the smallest difference between top samples and average samples, suggesting a higher consistency in the generated antibody quality.
While baseline methods possess lower values for certain energy measurements, the generated anti- bodies are often far from ideal. For instance, MEAN, despite achieving a low CDR-Ag AG, exhibits significantly higher CDR Fmsua, indicating less favorable overall interactions and potential structural clashes. HERN, dyMEAN and ABGNN show poor performance across most metrics, with high CDR Exoal values, suggesting strong repulsion due close aatigen-antibood proximities. Comparatively, DiffAb demonstrates a more balanced approach. It benefits from the theoretically guaranteed diversity of diffusion models and produces higher variance in the quality of the designed CDRs. This provides DiffAb higher probability of generating high-quality top-1 1 designs compared to other baselines. AbX further improves over DiffAb by incorporating evolutionary, physical, and geometric constraints, producing antibodies with more realistic structures and better binding energies. However, AlignAb surpasses all baselines, including AbX, showcasing smallest energy gap relative to natural antibodies. Through its energy alignment, AlignAb reduces average CDR Frstal CDR-Ag AG and CDR-Ag Frep by large margin, while maintaining reasonable CDR-Ag Fatt values. This indicates antibodies generated by AlignAb have fewer clashes and exhibit strong binding affinity to target antigens.
8

---

Table 3: Ablation studies for the proposed AlignAb framework. Lower values are better in all measurements. Results show that each component contributes to improved antibody quality, with the full method (Iterative POEA) achieving the lowest energy gap and strongest overall performance.
Method
CDR Evotat 4
CDR-Ag 4
CDR-Ag Eatt
CDR-Ag Exep
Gap +
Reference
-11.03
16.75
-22455
15.77
w/o Alignment
128.10 10
235.82
-14.31
479.00
205.82
w/o Pre-training
50.23
76.89
-13,84
118.29
56.33
DPO
113.59
183.19
-19.98
352.15
158.74
POEA
48.53
74.85
-13.41
103.54
51,59
Iterative POEA
34.13
55.71
-14.60
59.06
32.39
We anticipate further performance improvements beyond current results with several simple modifi- cations. Due to limited computational resources, we assign the same weight to the reward models across all test data (see Appendix E.2). By tuning the reward weightings, we are able to optimize the energy trade-offs between multiple conflicting objectives for each -anteendy complex, potentially resulting in an improved Pareto front of optimized models. Additionally, increasing the sample size and number of iterations for alignment will likely enhance the overall performance and reliability of the generated antibodies. These preliminary results underscore the potential of AlignAb in generating nature-like antibodies. We include the full evaluation results in Table 6.
5.3 Ablation Studies
Our approach combines a three-stage training pipeline (pre-training, supervised fine-tuning, and preference alignment), a Pareto-Optimal Energy Alignment objective, and an iterative online ex- ploration strategy with temperature scaling. To quantify the contribution of each component, we evaluate variants of AlignAb on the first 10 antigens in the test set by generating 32 candidates for each antigen and report the average energy metrics. We present quantitative results in Table 3 and qualitative examples for a specific antigen with PDB ID Snuz in Figure 2.
Three-Stage Training. We assess the contribution of each stage using the metrics described in Section 5.2. We observe that the variant without alignment stage performs poorly across all energy metrics as indicated by Table highlighting that preference aligmment essential for steering the generator toward energetically favorable designs. The variant without pre-training stage, which disregards knowledge learned from large-scale antibody pre- pre-training, also degrades performance relative to the full method. This confirms that pre-training provides a strong inductive bias that yields more realistic and stable initial proposals before alignment. Taken together, these results indicate that pre- pee-training, supervised fine-tuning, and preference alignment are mutually reinforcing and are all essential components of a robust pipeline for high-quality antibody design.
Pareto- OptitalOptimal Energy Alignment. We evaluate the impact of the proposed POEA algorithm through controlled ablations. As shown in Table 3. the DPO baseline, which follows the original DPO formulation, performs significantly worse than our proposed method. This validates that our multi- objective POEA function substantially more effective at balancing competing energy terms than a naive DPO approach. We also compare our full, iterative method to a single-iteration variant. The iterative method consistently achieves the highest performance across all metrics. This demonstrates that our iterative online exploration paradigm, where the model refines its policy over multiple turns, critical for converging to the most optimal designs. This aligns with our analysis Figure 2, which shows that the full framework with online exploration and temperature scaling produces superior Pareto front compared to offline alignment or alignment without temperature scaling.
Balancing Conflicting Objectives. One of the central challenges in antibody design is resolving conflicting biophysical objectives, such as maximizing binding affinity (low Eat) and minimizing steric clashes (low Ersp). Figure 2 visualizes this trade-off by plotting the Pareto front of these two energy values. Our full method, AlignAb, consistently occupies the lower-left region of the plot, maintaining smaller gap to the reference antibody (yellow) compared to baseline methods like DiffAb and other alignment variants. This position indicates that AlignAb achieves superior balance and lower overall energy. The figure also illustrates the typical failure modes that arise from unbalanced objectives. When attractive energy Emn weighted too strongly in Figure (C), the model overemphasizes bulky aromatic residues such as Tyrosine and Tryptophan, causing steric clashes and elevated Frep- Conversely, wverhhhig the repulsive term Frep in Figure (D) biases the model toward small residues like Serine and Glycine, which results in weak binding affinities.

---

246
DifAAb
237
AlignAb (offline)
AlignAb (wlo TS)
CDR Antign Repalsion Eay (keal/mpl)
AlignAb
Refergree
Pareto Efficient
(A) RNTLIGDYEDY
(C) YYYYYGYYFDY
-24
-16
-12
(B) RRNRYGGYFDY
CDR-Antigen Aftraction Ex (keal/mol)
(D) DSGSGGYGFDY
Figure 2: Frontiers of CDR-Ag Eat and CDR-Ag Exep alignment and typical samples produced by different reward weightings POEA. (A) is the reference CDR-H3 (colored in orange) from PDB ID) Snuz. (B) is the best CDR-H3 design generated by AlignAb with low overall energy and high similarity with the reference structure. (C) is the typical type of design when Fat reward dominates, and often consists of large side chains and contains structural collisions. (D) is the typical type of design when Eee reward dominates, and often lack of side chains with weak binding with the antigen.
In contrast, our multi multi-objecttiv POEA formulation able to identify Pareto-optimal solutions in Figure 2 (B) that achieve both strong attraction and low repulsion. This allows our method to produce stable, high-affinity antibody designs that closely resemble the reference structure Figure 2 (A), This demonstrates that AlignAb effectively balances conflicting objectives through Pareto-guided optimization, leading to nature-like antibodies with well-formed binding interfaces.
6 Conclusion
In this work, we adapt the successful paradigm of training Large Language Models to the task of antibody scquence-structtue co-design. Our three-stage training pipeline addresses the key challenges posed by limited structural antibody-antie -mttigen data and the common oversight of energy considerations during optimization. During alignment, we optimize the model to favor antibodics with low repulsion and high attraction to the antigen binding site, enhancing the rationality and functionality of the designs. To mitigate conflicting energy preferences, we extend AbDPO in combination with iterative online exploration and temperature scaling to achieve Pareto optimality under multiple alignment objectives. Our proposed methods demonstrate high stability and efficiency, producing a superior Pareto front of antibody designs compared top samples generated by baselines and previous alignment techniques. Future work includes further investigating the performance of the framework using larger fine-tuning datasets and extending our method to other structures such small molecules.
Acknowledgments
The authors would like to thank Abhishek Pandey and Weimin Wu for valuable conversations and Jiayi Wang for coordinating computational resources. The authors would like to thank the anonymous reviewers and program chairs for constructive comments.
Han Liu is partially supported by NIH R01LM1372201. NSF AST-2422845 Simons Foundation MPS- AI-00010513, AbbVie, Dolby and Chan Zuckerberg Biohub Chicago Spoke Award. This research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology. The content is solely the responsibility of the authors and does not necessarily represent the official views of the funding agencies.
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13

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Appendix
A Supplementary Backgrounds
15
A.I Diffusion Processes for Antibody Generation
15
A.2 Optimal Policy of Equivalent Reward Functions
15
A.3 DPO for Diffusion Model Alignment
16
B Additional Numerical Experiments
16
B.1
Additional Evaluation Metrics
16
B.2 Additional Binding and Developability Metries
"...............................
17
B.3
Additional Ablation Examples
17
B.4
Detailed Evaluation Results
17
C Additional Visualization
19
Energy Calculation and Reward Models
20
Implementation Details
21
E.1
Model Details
21
E.2 Training Details
F Broader Impact
21
14

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A Supplementary Backgrounds
A.1 Diffusion Processes for Antibody Generation
diffusion probabilistic model consists of two processes: the forward diffusion process and the reverse generative process. Let T denote the terminal time, and [T] denote the diffusion time step. Let R' {(s}. 2.j Oj) j 1+ 1,............ ......... ... Il m) denote sequence of latent variables sampled during the diffusion process, where (s). x.j. Of) is the intermediate state for amino acid j at diffusion step L. Intuitively, the forward diffusion process injects noises to the original data RD, while the reverse generative process learns to recover ground truth by removing noise from RJ, To model both the sequence and structure of antibodies, Luo et al. [2022] defines three separate diffusion processes for qRR RR) as follows:
4s3 b9) ((1(s)) a' 1(0)) + (1 (1-a")
a²) 20
1
1).
(a0) 2 N((a)) V (1 (1- a²)r),
q( (00 0.) IGso03)
(0) ScaleRot Va', 0,,), a²)
where a² = -1= 3r and { is the predetermined noise schedule. Here, C denotes the categorical distribution defined on 20 types of amino acids; /N denotes the Gaussian distribution on R3; IGso() denotes the isotropic Gaussian distribution SO(3). We use 1 to represent one-hot encoding function and ScaleRot to represent rotation angle scaling under a fixed axis.
To recover RD from R. given specified aatibody-antigen framework F, Luo et al. [2022] defines the reverse generation process p(R R- , at each time step as follows:
p(5} R R = C(5) 1-1
=
fo, (R', Fi)l),
p( 11 = = ((2j-11
fer F)L),, 111.
p(0) 1-1 (R( = Ig (0
where all three fe are parameterized by SE(3)-cquivarian neural networks and f(-[i denotes the output for amino acid j. Therefore, the training objective consists of three parts:
H+
c. = ERENP
DKL (a(s) 15) p(s)-) (
(A.1)
m
j=t+1
C.
ERINP m
|ag for F)b]?
(A.2)
/=++1
6.
BRINP
[10))) Soo (R', F)li) 7 ||
(A.3)
m
Finally, the overall loss function is L = Unifoomie (1... T) Cb + C.2 + C)) After training the model, we can use the reverse generation process to design CDRs given the auibody-antigen framework.
A.2 Optimal Policy of Equivalent Reward Functions
We cite the following definition and lemmas from DPO [Rafailov et al., 2024]:
Definition A.1. We say that two reward functions r(x, y) and r'(z, y) are equivalent iff r(z,8) y) (zz v) f(x) for some function f.
Lemma A.1. Under the Plackett-Luce, and in particular the Gradley-Terry preference framework, two reward functions from the same class induce the same preference distribution.
15

---

Lemma A.2. Two reward functions from the same equivalence class induce the same optimal policy under the constrained RL problem.
A.3 DPO for Diffusion Model Alignment
Here we review DPO for diffusion model alignment [Wallace et al., 2023]. By alignment, we mean to align the diffusion models with users' preferences.
Let D = ((x, Nwr w)} be dataset consisting input/prompt and pair of output from preference model Pref with preference > yt. Our goal is to learn a diffusion model pe (3) x) aligning with such preference associated with Pref. Let I denote the diffusion terminal time, and denote the diffusion time step. Let y be the intermediate latent variables and Rly, y²:)) be the commutative reward of the whole markov chain such that
r(x,8") (palu""T1e,p) [R(y. ).
Aligning Po to Pref needs
max EuwD pot upe ~ (r y y0 DKL [po (x)
(y xx] }
Mirroring DPO (3.2), we arrive EimO-simlliiie DPO objective for diffusion model [Wallace et al., 2023, Appendix S.2]:
LDPO-Diftuson (Po,
po(x xzy0) Pret(ato
Po p0 xx/) xrt Prrt(a 1-1 xz))
log
[8Tlog
ST log
(2x LnD, t-21(0,7) 87 (-
1...,t-po(t (4)
where Ul denotes uniform distribution, is KL regularization temperature. We remark this objective has simpler form for empirical usage, see [Wallace et al., 2023, Eqn. 14].
B Additional Numerical Experiments
This section provides supplementary results to support the main findings. Appendix B.1 reports additional metrics (AAR and RMSD) comparing method baselines. Appendix B.2 reports additional binding and developability metrics to illustrate the effect of alignment stage. Appendix B.3 presents ablation examples illustrating CDR-antigen interaction trade-offs. Appendix B.4 includes detailed evaluation results across benchmarks.
B.1
Additional Evaluation Metrics
Table 4: Summary of AAR and RMSD metrics by our method and other baselines. We follow the default sampling settings from all baselines and use ranked top-1 samples generated by our method. AlignAb* indicates the AlignAb framework without the alignment stage.
Metrics
HERN
MEAN
dyMEAN
ABGNN
DiffAb
AlignAb*
AlignAb
AAR 1
33.17
33.47
40.95
38.3
36.42
37.65
35.34
RMSD +
9.86
1.82
7.24
2.02
2.48
2.25
1.51
16

---

B.2
Additional Binding and Developability Metrics
Table 5: Summary of Boltz-2 IPTM for binding correlation and TAP scores for developability. We report averages over 16 candidates for each of the first 10 test antigens. AlignAb* indicates the AlignAb framework without the alignment stage. Higher Boltz-2 IPTM and lower deviation from reference TAP scores desirable.
Method
Boltz-2 IPTM
PSH
PPC
PNC
SFyCSP
Reference
0.728
118.554
0.096
0.522 0.402 + 0.280
-0.471 0.070 + 1.384
AlignAb*
0.669 + 0.118
119.720
7.397
0.085 + 0.068
AlignAb
0.698 + 0.104
120.510 + 6.069
0.073 1 0.049
0.363 + 0.065
-0.116 + 1.072
B.3
Additional Ablation Examples
DilAbb
DifAbb
Aligt&2 (ofline)
Aligobb (ofllee)
Aligsdh
AligzA3
Aliachb
CDD Repitton (leltto))
Referree
CDR-Aatipes Ressiiss Eup (Aaabtaa)
Purcio Eificient
Paztoo Effician
-12
CORAAsiiessAltiiiin Ooalisal
1008/Ariggmm..om (kealluxd)
(a) liqd
(b) 2ypv
127
DelAb
DifAAb
192
AligzAz (offline)
AligsAh ofllnn
AligrAb
Aliynsh
AligAbb
AlinAhh
CDR Ant.gnm Begitton (Bokinee)
Refermne
Ael--ditiees Eup (lcalteo))
Parzto lificiess
Parato Dfficim:
300
060
CDR-Antipr Aftacion (salinal)
(c) 3hi6
(d) 4ydk
Figure 3: Frontiers of CDR-Ag Fan and CDR-Ag Frep alignment produced by different reward weightings POEA with four PDB examples.
B.4 Detailed Evaluation Results
17

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-0.31
-2140
102.42
19.10
57.92
-19.06
10:25
0.62
160.29
20.64
4304
.5521
-0.39
8:76
1941
-21.09
35.0
-2196
42.01
-21.00
6.12
44.0)
-2947
-90.9
-11M
.77.3
-2.88
1782
-5.84
555.0
-1.16
1.53
16.12
15.38
4.00
15
3043
19.38
26.79
30.00
15.31
5.40
11
24 24.00
9.00
59.00
14 14.25
5.00
6.76
17.8
19
36.30
30.92
19:40
14:30
40.59
25 25.06
10:44
11.39
11:01
16.28
18.72
11
14.06
10
12.65
reforence
Table Detailed evaluation results for various metrics for 42 antigens. The data source is the same as that Table
16.00
-8
3.66
8.01
12.68
14441
-2
-2.60
-3..2
9.11
22 49
110
15.44
23.11
46331
5.00
11.76
-55
-13
-34.2
-27.0
-00.6
32
-2.
-6666
13.48
25 64
-77
-2.99
24
-21
-26
-4431
9..00
18:24
7.06
6.66
4.68
23.08
12.27
1665
28.71
11.28
14.51
2015
2011
3.70
1194
13.63
10.34
-4416
-1.13
-16.0
-50
17.75
-3.90
-
-2.05
-5.0
42.87
-1588
-2634
-1585
-24
5000
-1007
-15122
-992
15.09
-9.38
7.83
6.51
3.71
15.26
23.05
-747
9.59
15.00
-21 10
-10.27
-9002
100
99.4
-14.3
-1.16
-66.9
-9.1
4.05
-21
-14.08
-500
-55
-25 22..2
3.000
-16 16.48
4.55
-2115
-5.24
1.47
0.00
0.00
0
4.8
251
115
9:75
0.0
255
475
6.91
0.00
238
0.00
000
0.00
0.58
000
2.25
000
010
000
3.39
000
0.0
857.2
ABENN
1.29
0.00
0.00
1.05
4.36
2.54
2.90
0.00
40.91
0.00
11558
-825
4.25
2238
0.00
0.74
0.00
0.00
0.00
0.03
0.46
000
0.00
0.06
40.0
0.00
0.00
4107
2279
0400
1-46
3.02
0.00
-000
000
5.76
-0.42
Tonal
1.251.38
1054.35
943.27
951.3
656.84
104468
1.24.76
1216.00
562.2
1,57996
1.025.24
1.182788
1024.00
1.597.12
12
89987
1,7080
1.757
1553.42
1937.00
1.23445
2077322
1977.32
1885
931.27
1477004
1.409 84
1313.3
1509
26
1,167.00
15.65
-959
4.83
2834
29.56
80080
23.6
1004
3025
1416
01.8
-24
146
51.30
-642
25.42
400
1500
1955
1333
423
541
5266
-226
17.55
17.40
16608
-2000
12995
-007
12222
-802
-1004
33.39
1.12
0.41
0.15
4.01
300
8.8
11.47
3-4
6.7
2804
240
856
3.31
915
838
0.58
7.30
406
365
755
6,67
755
25.20
488
5.82
4.10
20.99
200
28.63
4.6
16.20
28.27
8.9
199
1214
6.54
5.0
9.55
MEAN
Nonepp
0.00
0.01
4.52
1.43
.9.59
0.15
0.84
8.56
4.82
4.90
1.68
-7.09
821
4222
4.52
4.9
-504
4.17
1.5
14.27
-290
4.16
11441
13300
33
-1.53
0.00
-1
-17 36
0.0
-12 28
233
-1.57
18.48
Total
51.17
1.24
9.07
16.30
42277
60.34
-207
2342
52.28
16.99
21
35.90
71.23
222
52.28
11.39
14:8
50.7
27.28
11573
52.4
16830
32.22
164.9
45
10735
257
107
102
10.0
7582
7693
d6
0.73
20 80
101.33
21.13
36.2
8.22
13.05
318
13.98
17.00
23
20.55
20
12.36
33
10.50
12
18.32
22.15
14.90
22
17008
70.11
-1.78
12
20.26
46
42.05
27.
-1.05
21.09
41
27 57
1.96
35 10
18,02
9.95
4.22
7.65
1361
26.50
1767
27.50
22.29
1331
1939
11
1059
10.50
17.17
1135
220
692
844
1799
2226
1147
1846
1168
2009
5260
19.33
2101
800
1739
16.57
16
649
17
2422
9.0
2722
AlgerAb Nousgp
24.32
11.42
1.42
.7.00
7.10
-7.39
1296
2363
1982
9.65
2206
3.45
1877
4.2%
800
1.38
-70
17.30
15008
10.40
2624
1034
22118
237
-1444
20.55
-0.54
1557
555
23448
19.4
1063
1574
5.88
0.37
3.11
5.88
186
-7.0
29
22
10.32
11.44
18
2.68
1.74
-555
57 26
4.50
-9.2
1.02
3.59
-44
391
18.
14.30
19923
3.00
14.73
4.70
58.0
10
100.5
333
115 48
39
-00
3.71
6.52
104.22
5.85
23.88
-10.47
25.18
2.58
1..00
22.36
40.41
54.84
42.20
2410
39.42
-601
15.29
11991
-2.
199.99
2362
35.54
20.24
49.58
5.04
46000
54.56
40.37
1961
1600
4100
32.30
27.33
1.118
9.33
5.25
17.79
99
18.56
23.45
48 50
21.21
10.07
11.42
18.77
18.35
22.82
3.77
10.14
26.09
17.45
17.42
40
9.40
24.19
8.05
45
16.30
19.0
19 98
10.80
36.29
26
88
23
12
23 10
DatAAh
13:00
5.78
2.98
10
4.10
12.98
11.40
12.04
21.28
9862
-509
1981
5.00
17.99
-212
5.71
46.74
-285
-988
-00.5
-1.111
-.099
-7-97
-1743
-2.09
-.3
33.
13.34
11.97
18-47
-4.59
-885
15.90
200
9.85
4600
Tota
3:38
2.15
1.35
5.00
9.64
-0.97
4.79
-300
-1022
10.27
835
.862
2.28
507
431
-261
-741
-3277
0.76
0.57
551
6.86
-982
-807
-855
1.59
9930
243
0.88
-3311
-2.00
-391
13.70
0.73
0.38
PDB
168
162
1kd
Incb
tosp
10.3
282x
Zomr
2208
200y
1634
40v
4,69
4gdm
408
4hv
4:01
4y6k
5hx7
San2
50%
5113
5ky
Smar
18

---

C
Additional Visualization
Reference
MEAN
HERN
(A) RNTLIGDYFDY
(B) RGYYYYYYFDY
(C) DYDYGYYLDV
dyMEAN
DifTAb
AlignAb
(D) ENHRGSGYSDH
(E) GYGGSDYAYDY
(F) RRNRYGGYFDY
Figure 4: Visualization of reference antibody for antigen (PDB ID 5nuz) and different antibodies designed by our method and other baselines. The designed CDR-HI structures are colored in orange and the designed CDR-H3 sequences recorded accordingly.
19

---

D Energy Calculation and Reward Models
In Section 5, we introduce the calculation of two ammctionality-assciaatee energies, CDR-Ag Fan and CDR-Ag Frep- Following Zhou [2024b], we denote the residue with the index in the antibody- antigen complex as A,. We then represent the side chain of the residue as A and backbone of the residue as A respectively.
We define the interaction energies between a pair of amino acids as EP, with the default weights defined by REF15 LAdolf-Bryfogle et al., 2017]. EP consists of six different energy types: EP htond- EP au. Eep EP... sol. EP elec. and EPI- Following the settings from Section 3, we define the indices of residues within the CDR-H3 range from + to ( + m, and the indices of residues within the antigen range from g + to g + n. Thus, for the CDR residue with the index j. the CDR-Ag Ean and CDR-Ag Peep are defined as:
CDR-Ag Ag E
Σ
Σ (bbund elc,))),
; ) + (P," AA"))
(D.I)
img
CDR-Ag Ene
Σ
(Pp A. + (A5, ),,, +2 (P +2 EP A
(D.2)
From Equations (D.1) and (D.2), conclude that the interaction energy between the CDR and the antigen is determined by both side-chain and backbone interactions. The CDR-Ag Fan considers interactions primarily from side-chain atoms in the CDR-H3 region. In contrast, CDR-Ag Eiep assigns higher costs to repulsions from backbone atoms in the CDR-H3 region. This reason for the different that side-chain atoms contribute most of the interaction energy between CDR-H3 and the antigen, as shown in Figure 1. Therefore, CDR-Ag Eau exhibits benefit in interactions, while CDR-Ag Exe represents repulsive costs.
To guide the model alignment process, we utilize the above two energy definitions to compute the final rewards follows:
1+m
++m
Fan (z. =)= =- Σ
CDR-Ag 1=++1
(iep( y)=
Σ +=+1
CDR-Ag top
(D.3)
where lower energy corresponds to higher reward. Therefore, we compute the final collective reward with predetermined weights as f(x, y) = WanTan (n,, y) "repprrpp(2; y). We observe the repulsion reward is often several orders of magnitude bigger than the attraction reward. Therefore, we utilize the following reward margin in our actual experiments:
A log(f(z, vw) f(x,
(D.4)
20

---

E
Implementation Details
E.1
Model Details
AlignAb consists of two parts: a pre-trained BERT model from AbGNN [Gao et al., 2023], and pre-trained diffusion model from DiffAb [Luo et al., 2022]. For the pre-trained BERT model, our model uses a 12-layer Transformer model with a BERT base configuration, We set the embedding size to 768 and the number of heads to 12. For the pre-trained diffusion model, our model takes the perturbed CDR-H and its surrounding context as input. For example, 128 nearest residues of antigen or the antibody framework around the residues of CDR-H3. The input consists of both single and pairwise residue embeddings. The number of features with single residue embedding is 128. consists of the encoded information of its amino acid types. torsional angles, and 3D coordinates of all heavy atoms. The number of features with pairwise residue embedding is 64. consists of the encoded information of the Euclidean distances and dihedral angles between the two residues. To combine the feature embeddings with the hidden representations learned from the pre-trained BERT model, extract the embedding for each residue from the final layer of the BERT model and concatenate with the single and pairwise residue embeddings. We then utilize multi-layer perception (MLP) neural networks to process the concatenated embeddings. The MLP has 6 layers. In each layer, the hidden state 128. The output of this neural network is the predicted categorical distribution of amino acid types, C. coordinates, so(3) vector for the rotation matrix.
The diffusion models aim to generate amino acid types, C. coordinates, and orientations. Hence, for training the diffusion models, we take the output of MLP as input for diffusion models. We set the number diffusion (forward) stets to be 100. For the noise schedules, we apply the same setting of DDPM [Ho et al., 2020], utilizing / schedule with 0.01. The noises are gradually added to amino acid types, Ca coordinates, and orientations.
E.2 Training Details
Transferring, We train the diffusion model part of AlignAb following the same procedure as Luo et al. [2022]. The optimization goal is minimize the rotation, position, and sequence loss. We apply the same weight to each loss during training. We utilize the Adam [Kingma and Ba, 2014] optimizer with init_ lea_ninnnnnnateeaaaa and siip-gradeent_ooe satttt-oomm1000 100. We also utilize a learning rate scheduler, with factor=O. 8, min_ 1ann_1r5e-6,, 6, and patience=10. We perform evaluation for every 1000 training steps and train the model on one NVIDIA GeForce GTX A100 GPU, and it can converge within 36 hours and 200k
betas= (0.9,0. (999), patch_size-tl
steps.
Alignment. After obtaining the diffusion model, we further align it with energy-based preferences provided by domain experts. We utilize the Adam [Kingma and Ba, Le__earning_rate=2e-.. 2014] optimizer with We set the KL regularization term 3 = 100.0. In each batch, we weagrrdienttnormmttee
betas=(0.3 (0.9 0.000,,0.9990
batch_size=$
select 8 pairs of baergy-based preference data with labeled rewards. We do not use learning rate scheduling during alignment stage. For rewards, we set the Wan and Wrep with a fixed ratio 1:3. In each alignment iteration, fine-tune the diffusion model for 4k steps. We repeat this process times for each antigen in the test set.
F Broader Impact
This research advances the intersection of machine learning and therapeutic antibody design by providing a generalizable framework for sequence-structure co-design. The proposed method not only enhances the rationality and efficiency of antibody generation but also offers scalable approach applicable to broader biomolecular engineering tasks. By enabling more accurate and interpretable Al-driven design pipelines, this work can accelerate the discovery of life-saving therapeutics and benefit researchers and practitioners developing biologics for global health and social good.
21

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Reviews:
[{"review_id": "N4hEjP5VO6", "reviewer": "Reviewer_4zX5", "summary": "Authors present a protein sequence-structure co-design method. The main inovation is that the method consists of 3 stage pipeline: pre-training a pLM, transfering this pLM to a sequence-structure co-design method and further fine-tuning (alignment) that encourages physical plausibility by applying multi-objective DPO on generated structure energies. The method is evaluated on the standard CDR H3 task, where authors show improvement in generated structure energetics as well as RMSD to ground truth as well as competitive amino acid recovery to baselines.", "questions": "Please see the limitations above. I would love if you could address my concerns regarding metrics and ablations.\n\nAlso a couple of related references that are missing currently, that also adapt antibody sequence-structure co-design to improve energy https://arxiv.org/pdf/2406.05832v1 https://openreview.net/pdf?id=4ktJJBvvUd", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "The paper is well written and clear. The main ideas of 1) incorporating extra sequence data via pretraining and 2) improving physicality via alignment are very sensible and I can see how they would improve things. The experimental evidence provided largely corroborates that.\n\nThe insight authors provide about increasing the model entropy is quite interesting. As historically in the literature people were decreasing sampling temperature to get the most confident designs, instead of increasing it, to increase entropy, as done here.\n\nWhile this multi-objective DPO here is used for the first time in antibody energy optimization as far as I'm aware, AbDPO did both use DPO for energy optimization, as well as also split energy in two terms (repulsive and non-repulsive) https://proceedings.neurips.cc/paper_files/paper/2024/file/daef77101ba5711084a57442c8cf2709-Paper-Conference.pdf.\n\nSimilarly, while pre-training on general antibody sequences is a great idea, similar angles of using auxiliary sequence information are not new. For example AbX also utilized a pre-trained language model (ESM in their case): https://openreview.net/pdf?id=1YsQI04KaN \nAs a sidenote I think it makes sense to add AbX to the baselines, as it's not a very new work and it was shown to outperform most of the baselines currently in the paper.\n\nThat being said, re-mixing and improving known components is totally valid, if this gives us an overall better model.\n\nTo be entirely convinced I do find the experimental evaluation a bit lacking. First I'd like to see experimental confirmation (so an ablation) that shows the benefit of the multi objective DPO introduced. Is it really better than the DPO formulation use in AbDPO (or AbDPO++). While those are included as baselines, they did not use the pretrained pLM. It would also be good to see if a model using a single objective DPO, say on delta G, compares. Similarly, how well does the model do on energies (Table 2) without the alignment step?\n\nSecondly on the evaluation front, it is a bit unfortunate that the main result table (Table 2) relies only on energy metrics, the same energy metrics that are directly optimized in the alignment phase. So it's no surprise that the model does better on them. It would be great to have additional scores here. For example Boltz-2 IPTM score can correlate with binding, or some inverse folding-based scores, that don't directly rely on rosetta energy. As rosetta energy is known to be imperfect proxy for binding. The amino acid recovery and RMSD provided in Table 3 do help here a bit, but they are not in the main text and something binding-related could be a better fit.\n\nAlso, energy minimization can often make proteins more hydrophobic, which makes them less specific, and thus less useful binders. So it would be good to see if the proposed approach negatively impacts antibody developability vs model before alignment, for example using the commonly used TAP scores (https://opig.stats.ox.ac.uk/webapps/sabdab-sabpred/sabpred/tap).", "was_revised": true, "final_justification": "In the rebuttal authors addressed all the main concerns I have raised, thus I recommend acceptance.", "rebuttal": "> **W1.** While this multi-objective DPO here is used for the first time in antibody energy optimization as far as I'm aware, AbDPO did both use DPO for energy optimization, as well as also split energy in two terms (repulsive and non-repulsive). \n\n**Response:** \n\nThank you for this precise feedback. You are correct that AbDPO also addresses conflicting energies by separating them into multiple terms. However, our approach differs fundamentally in how it incorporates multi-objective optimization into the DPO framework:\n\n* **AbDPO** addresses conflicting energies at the **gradient level**. It combines energies into a single weighted loss, and then applies a post-hoc gradient surgery step to manage conflicts.   \n* **Our method** addresses this at the **objective-function level**. We extend the DPO loss itself to be inherently multi-objective, which naturally seeks a Pareto-optimal solution without needing extra gradient manipulation.\n\nThis distinction makes our framework a more direct and principled integration of multi-objective optimization with the DPO framework. Furthermore, we empirically validate this design through new ablation studies below, which demonstrate clear performance gains over AbDPO.\n\nWe will clarify this distinction more explicitly in the final version. Thank you again for the helpful comparison.\n\n> **W2.** Similarly, while pre-training on general antibody sequences is a great idea, similar angles of using auxiliary sequence information are not new. For example AbX also utilized a pre-trained language model (ESM in their case). As a sidenote I think it makes sense to add AbX to the baselines, as it's not a very new work and it was shown to outperform most of the baselines currently in the paper.\n\n**Response:** \n\nThank you for this valuable suggestion and we agree that AbX is an important baseline. Following your suggestion, we have now included AbX in our benchmark under the same experimental setup as all other baselines. \n\nAlthough AbX performs competitively, our results show that AlignAb’s energy-based preference alignment consistently outperforms all baselines, producing antibodies that are closest to natural ones.\n\n| Method | CDR $E\\_{total}$ (Top, Avg.) ↓ | CDR-Ag ΔG (Top, Avg.) ↓ | CDR-Ag $E\\_{att}$ (Top, Avg.) ↓ | CDR-Ag $E\\_{rep}$ (Top, Avg.) ↓ | Gap (Top, Avg.) ↓ |\n| :---: | :---: | :---: | :---: | :---: | :---: |\n| Reference | \\-19.33 | \\-16.00 | \\-18.34 | 18.05 | \\- |\n| AbX | 13.56, 25.33 | 94.76, 170.34 | \\-13.68, \\-15.12 | 21.38, 38.20 | 37.75, 63.43 |\n| **AlignAb** | **\\-6.37, 30.45** | **\\-8.81, 25.16** | **\\-14.89, \\-14.81** | **15.52, 56.22** | **17.91, 39.00** |\n\nWe will update the paper to clarify the distinctions between our method and prior approaches such as AbX and include this full comparative analysis in the main text. Thank you again for encouraging a more comprehensive evaluation.\n\n> **W3.** To be entirely convinced I do find the experimental evaluation a bit lacking. First I'd like to see experimental confirmation (so an ablation) that shows the benefit of the multi objective DPO introduced. Is it really better than the DPO formulation use in AbDPO (or AbDPO++). While those are included as baselines, they did not use the pretrained pLM. It would also be good to see if a model using a single objective DPO, say on delta G, compares. Similarly, how well does the model do on energies (Table 2\\) without the alignment step?\n\n**Response:** \n\nThank you for this valuable suggestion. To clearly evaluate the contribution of each component in our method, we have conducted additional ablation studies you requested.\n\nWe evaluated five key model variants to test the impact of pre-training, alignment, our proposed multi-objective approach, and iterative alignment. For each variant, we generated 32 candidates for the first 10 samples from the test set and report the average energy metrics across all candidates:\n\n* **w/o Alignment:** The model after supervised fine-tuning but before any preference alignment. This measures the performance of the base generative model.\n\n* **w/o Pre-training:** Our proposed method but without using the pre-trained language model, and using only one alignment iteration. This isolates the benefit of using large-scale antibody sequence data.\n\n* **DPO:** A DPO-based alignment implementation using gradient surgery, following AbDPO for only one alignment iteration. This directly compares our method to a simpler DPO formulation.\n\n* **POEA:** Our proposed Pareto-Optimal Energy Alignment (POEA) performed for only one alignment iteration. This isolates the core benefit of our multi-objective function.\n\n* **Full Method (Iterative POEA):** Our complete, multi-turn POEA over three alignment iterations, as described in the paper.\n\n| Method | Avg. CDR $E\\_{total}$ ↓ | Avg. CDR-Ag ΔG ↓ | Avg. CDR-Ag $E\\_{att}$ ↓ | Avg. CDR-Ag $E\\_{rep}$ ↓ | Avg. Gap ↓ |\n| :---: | :---: | :---: | :---: | :---: | :---: |\n| Reference | \\-11.03 | 16.75 | \\-12.45 | 15.77 | \\- |\n| w/o Alignment | 128.10 | 235.82 | \\-14.31 | 479.00 | 205.82 |\n| w/o Pre-training | 50.23 | 76.89 | \\-13.84 | 118.29 | 56.33 |\n| DPO | 113.59 | 183.19 | \\-19.98 | 352.15 | 158.74 |\n| POEA | 48.53 | 74.85 | \\-13.41 | 103.54 | 51.59 |\n| **Full Method (Iterative POEA)** | **34.13** | **55.71** | **\\-14.60** | **59.06** | **32.39** |\n\nFrom the above ablation results, we conclude the following key takeaways:\n\n1. **Alignment is essential:** The model without any alignment performs poorly, highlighting the importance of alignment to produce energetically favorable designs.  \n2. **Pre-training helps:** The slight performance drop without the PLM confirms that pre-training provides a useful inductive bias, leading to more realistic initial designs before alignment.  \n3. **POEA outperforms naive DPO:** Our POEA method (both single-iteration and full) is substantially better than the naive DPO approach as used in AbDPO, validating our core contribution of using a direct, multi-objective preference function.  \n4. **Iterative refinement improves results:** The full, multi-turn Iterative POEA achieves the best performance across all metrics, demonstrating the benefit of our iterative learning paradigm.\n\nWe will include this ablation table and analysis in the final version to clarify the contribution of each component.\n\n> **W4.** Secondly on the evaluation front, it is a bit unfortunate that the main result table (Table 2\\) relies only on energy metrics, the same energy metrics that are directly optimized in the alignment phase. So it's no surprise that the model does better on them. It would be great to have additional scores here. For example Boltz-2 IPTM score can correlate with binding, or some inverse folding-based scores, that don't directly rely on rosetta energy. As rosetta energy is known to be imperfect proxy for binding. The amino acid recovery and RMSD provided in Table 3 do help here a bit, but they are not in the main text and something binding-related could be a better fit. Also, energy minimization can often make proteins more hydrophobic, which makes them less specific, and thus less useful binders. So it would be good to see if the proposed approach negatively impacts antibody developability vs model before alignment, for example using the commonly used TAP scores.\n\n**Response:** \n\nThank you for these excellent suggestions and we completely agree that evaluating our method with additional orthogonal metrics is crucial. We have now performed the requested analysis using Boltz-2 IPTM and TAP developability metrics. For each case, we generated 16 candidates for the first 10 samples from the test set and report the average metrics across all candidates:\n\n| Method | Boltz-2 IPTM ↑ | PSH | PPC | PNC | SFvCSP |\n| :---: | :---: | :---: | :---: | :---: | :---: |\n| Reference | 0.728 | 118.554 | 0.096 | 0.522 | \\-0.471 |\n| w/o Alignment | 0.669 ± 0.118 | 119.720 ± 7.397 | 0.085 ± 0.068 | 0.402 ± 0.280 | 0.070 ± 1.384 |\n| **w/ Alignment** | **0.698 ± 0.104** | **120.510 ± 6.069** | **0.073 ± 0.049** | **0.363 ± 0.065** | **\\-0.116 ± 1.072** |\n\n* **Improved Binding metrics**: Our alignment improves binding metrics it wasn't directly trained on. As shown, the Boltz-2 IPTM score increases and moves closer to the reference. More importantly, while we only used attraction/repulsion for alignment, the overall binding energy (ΔG) also improved significantly as shown in Table 2, showing our method generalizes well to binding-relevant metrics.\n\n* **Developability:** Our alignment does not negatively impact developability. The TAP scores (PSH, PPC, PNC and SFvCSP) show no significant adverse changes, addressing the concern about increasing hydrophobicity.\n\n* **Flexible framework:** Our method's key strength lies in its flexibility, as it is agnostic to the scoring function used. In practice, we could directly incorporate metrics like TAP scores or even wet-lab data into the alignment objective itself. This adaptability makes it a powerful tool for future multi-objective antibody design.\n\nWe have added this new analysis to the paper to provide a more robust validation of our method. Thank you again for helping us strengthen our work.\n\n>**Q1:** Please see the limitations above. I would love if you could address my concerns regarding metrics and ablations. Also a couple of related references that are missing currently, that also adapt antibody sequence-structure co-design to improve energy.\n\n**Response:** \n\nThank you for summarizing your main points. We've addressed your primary concerns in our previous responses by running new ablation studies and adding orthogonal metrics to strengthen the evaluation.\n\nWe also appreciate you pointing out the missing references. We've reviewed them and will add them to the Related Work section in the revised version."}, {"review_id": "FvsKd6exdV", "reviewer": "Reviewer_7Jdg", "summary": "The paper considers the problem of Complementarity Determining Regions design for antibodies that bind to specific antigens. This is a fundamental problem in the field of automated computational antibody design yet it is extremely difficult to solve in practice. The main contribution of the paper is a three stage pipeline consisting of pre-training, transferring and aligning to specific rationality and functionality requirements for the antibody. The framework leverages at each stage known large language model architectures such as BERT models and encoder-decoder difusion models, respectively. For the alignment stage, a new Pareto-Optimal Energy Alignment algorithm is developed that extends the well known Direct Preference Optimization method. The experimental evaluation is carried out on standard benchmarks for antibody co-design. The results demonstrate clearly that the proposed approach outperforms in many cases existing baselines.", "questions": "- The first stage leverages BERT models. Are the larger Transformer based models suitable for it?", "limitations": "The limitations are addressed in the main paper.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n---------\n\nComputational antibody co-design is a core challenge in computational biology with significant real-world implications. Therefore, there is a clear need for the development of more efficient and practical solution methods. The paper make a clear contribution in this space.\n\nThe paper is fairly well written and organised. Therefore, the content is relatively easy to follow. The quality of the presentation is overall quite good.\n\nThe empirical evaluation is sound and the results are presented in a clear manner which makes it relatively easy for the reader to appreciate the benefits of the proposed method.\n\n\nWeaknesses\n----------\n\nI did not find any major weaknesses in this paper. In my opinion paper presents a non-trivial contribution in the area of computational antibody co-design. Perhaps, a more detailed presentation of the main differences between the proposed method and the existing baselines that also leverage language models should be included in the main paper.", "was_revised": true, "final_justification": "The authors rebuttal addressed my concerns. Therefore, I maintain my positive recommendation for the paper.", "rebuttal": "> **W1.** Perhaps, a more detailed presentation of the main differences between the proposed method and the existing baselines that also leverage language models should be included in the main paper.\n\n**Response:**\n\nThank you for the positive feedback. We agree that a more detailed comparison with other language-model-based baselines would improve the paper's clarity. In the revised manuscript, we'll expand our discussion to highlight these key distinctions:\n\n* **Differentiation in Objective:** While many LM-based baselines primarily aim to improve geometric and sequence recovery metrics (AAR/RMSD), our work introduces a final alignment stage specifically designed to **optimize for physical energies** and binding affinity proxies.  \n* **Novelty in Method:** Our core contribution is the **Pareto-Optimal Energy Alignment (POEA)** framework. This alignment stage, which directly optimizes the generative model's outputs using DPO, is a distinct feature not present in other baselines that may use a PLM simply for feature extraction.  \n* **Holistic Framework:** We will emphasize our integrated **three-stage pipeline**, which leverages the PLM not just for initial representations but as a foundational component for a downstream generative model that is then refined through our novel alignment process.\n\nWe'll incorporate these points into the Related Work and Methods sections to better contextualize our approach. Thank you again for your constructive feedback\\!\n\n \n\n> **Q1.** The first stage leverages BERT models. Are the larger Transformer based models suitable for it?\n\n**Response:**\n\nYes, our framework is modular, so more powerful language models would likely boost performance by providing higher-quality representations. Exploring the impact of larger PLMs is an excellent direction for future research. Thanks for the great question\\!"}, {"review_id": "xrQGIrDTJY", "reviewer": "Reviewer_Dd85", "summary": "This paper introduces AlignAb, an extension of AbDPO that outputs a co-design of the sequence and structure of the complementarity-determining region (CDR) 3 region of the heavy chain of an antibody that binds to a known antigen epitope. AlignAb is a new model that incorporates energy calculations of repulsion and binding coefficients at each amino acid in order to Pareto-optimize the AbDPO diffusion model.", "questions": "The authors introduced the concept of using temperature as a measure of CDR-H3 diversity and adjusted the value of T to 1.5, which is close to the natural CDR-H3 sequence. Which dataset is referenced in Table 1?", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe authors pointed out issues with amino acid recovery (AAR) and root mean square deviation (RMSD), both of which were used as evaluation indices in similar studies. They proposed using calculated energy values for attraction and repulsion forces between the CDR and antigen, employing Pareto optimization with AbDPO to generate more natural sequences. Compared to previous studies in similar domains, it is expected that more stability can be predicted.\n\nWeaknesses:\nWhat information is needed for the model's input data?　Do you need information on antigens or antibodies?　Is the sequence sufficient, or is the three-dimensional structure also needed?　Specific descriptions would be helpful. It seems that AbAlign does not accept unknown antigen-antibody complexes.\nThe same is true of the previous studies mentioned in the paper, in which AlignAb only predicts the sequence of the CDR-H3 region for a specific epitope of a specific antigen. In real-world, antigen-antibody responses are defined by the combination of all CDR regions of the heavy and light chains.\nAdditionally, this study found that predicting antibodies that outperform real-world reference antibodies is still challenging, although it performs better than previous studies in some respects. Further development is needed for drug discovery.\nIt might be better to discuss these issues in the limitations section.\n\nMinor point: \nLine 561: \"iff\" appears to be a typo for \"if.\"", "was_revised": true, "final_justification": "The authors have adequately answered the reviewers' questions in the rebuttal step. My rating was maintained.", "rebuttal": "> **W1.** What information is needed for the model's input data? Do you need information on antigens or antibodies? Is the sequence sufficient, or is the three-dimensional structure also needed? Specific descriptions would be helpful.\n\n**Response:**\n\nThank you for the question. To be perfectly clear, our model requires the local structural and sequence information from the antibody-antigen complex that surrounds the CDR-H3 binding site.\n\nSpecifically, the inputs are:\n\n* **Antigen Epitope:** The 3D structure and sequence of the antigen surface that interacts with the antibody.  \n* **Antibody Framework:** The 3D structure and sequence of the antibody's framework regions and non-H3 CDRs.\n\nEssentially, we provide the complete binding pocket as context, and the model's task is to co-design the sequence and 3D structure for the missing CDR-H3 loop to optimally fit within it. We will add a dedicated subsection to the Methods section to make these input requirements explicit.\n\n> **W2.** It seems that AbAlign does not accept unknown antigen-antibody complexes. The same is true of the previous studies mentioned in the paper, in which AlignAb only predicts the sequence of the CDR-H3 region for a specific epitope of a specific antigen. In real-world, antigen-antibody responses are defined by the combination of all CDR regions of the heavy and light chains. Additionally, this study found that predicting antibodies that outperform real-world reference antibodies is still challenging, although it performs better than previous studies in some respects. Further development is needed for drug discovery. It might be better to discuss these issues in the limitations section.\n\n**Response:**\n\nThank you for these insightful points about our work's scope and limitations. You are absolutely correct on these points.\n\nWe intentionally focused on CDR-H3 as it's the most diverse and challenging region, making it a rigorous benchmark for our alignment algorithm. Strong performance here suggests our method will generalize well to the less variable CDRs.\n\nYou are correct that practical drug discovery requires designing all six CDRs and tackling unknown targets, both of which are important future directions. Following your suggestion, we will add a detailed discussion to the Limitations section of the paper to explicitly address these points and to provide a clearer picture of the current scope.\n\n\n> **Minor point.** Line 561: \"iff\" appears to be a typo for \"if.\"\n\n**Response:**\n\nThank you for catching that, we will correct the typo in the final version.\n\n> **Q1.** The authors introduced the concept of using temperature as a measure of CDR-H3 diversity and adjusted the value of T to 1.5, which is close to the natural CDR-H3 sequence. Which dataset is referenced in Table 1?\n\n**Response:**\n\nThank you for the question. The entropy values reported in Table 1 were calculated on our test set from the RAbD benchmark. We will clarify this in the table caption for the final version."}, {"review_id": "af3sPNGfht", "reviewer": "Reviewer_MyRN", "summary": "This paper introduces a three-stage model for antibody sequence-structure co-design, AlignAb. First, an antibody language model is pretrained on sequence data, then a downstream diffusion model is trained to generate antibody structures. Finally, the diffusion model is fine-tuned using energy preferences. The authors extend Direct Preference Optimization to handle multiple, conflicting energy objectives. AlignAb generates antibodies with better energy scores on a standard benchmark.", "questions": "What is the impact of each training phase on performance ? in particular, sequence pretrainining ?", "limitations": "The authors could better explain the limitations of using Rosetta energies as a porxy for binding affinity", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\n* The paper is well-written with a clear motivation and model.\n* The paper proposes a new three-stage framework for antibody design that can help with the limited antibody structure data with pretraining and handles multiple energy objectives for Pareto optimality with DPO for finetuning. Arguably, each step in this framework have been proposed independently in different models (e.g., DiffAb, AbDPO). the novely comes from the combination of all these steps (which is not a strong novelty).\n* The framework shows superior performance in generating antibodies with favorable energy scores, compared to some standard baselines. \n\nWeaknesses\n* The proposed model relies on Rosetta energy for alignment, which is known to have a weak correlation with binding affinity. \n* It would be fairer to compare AlignAb with models that optimize for energy e.g. AbDPO, which this model extends. This comparison is important yet missing in the evaluation. In terms of comparison, it would be worth putting the AAR and RMSD metrics in the main paper; as opposed to the appendix; there the performance is somewhat matching the baselines (with a better RMSD).\n* The paper lacks a discussion on the training and inference efficiency of the model. \n* Finally, the contribution of pretraining to performance is not clearly evaluated; as it represents an additional complexity in the model, it would seem natural to evaluate its impact.", "was_revised": true, "final_justification": "the authors have provided a good rebutall, showing some additional ablation on the different components of the proposed model which all seem to improve the energy related metrics. Moreover, the authors included iPTM as an additional score which improved despite not being modelled as a reward. The additional ablations are useful but are still focused on energy related scores would benefit from reporting additionally this iPTM score or alternatively the AAR / RMSD on them. the perspectives of included other rewards is an interesting future direction.", "rebuttal": "> **W1.** The proposed model relies on Rosetta energy for alignment, which is known to have a weak correlation with binding affinity.\n\n**Response:** \n\nThank you for raising this important point. We agree that while widely used as a benchmark, Rosetta energy is an imperfect proxy for true binding affinity.\n\nOur primary goal was to demonstrate that our alignment algorithm could effectively optimize a complex, multi-term objective. However, to ensure our improvements are meaningful beyond this specific forcefield, we also evaluated our designs using an orthogonal metric, the Boltz-2 IPTM score.\n\n| Method | Boltz-2 IPTM ↑ |\n| :---: | :---: |\n| Reference | 0.728 |\n| w/o Alignment | 0.669 ± 0.118 |\n| **w/ Alignment** | **0.698 ± 0.104** |\n\nAs shown, the Boltz-2 IPTM score improves and moves closer to the reference. Crucially, our alignment framework is agnostic to the reward function. It can be readily extended to incorporate more realistic binding affinity predictors, including other computational tools or wet-lab derived data, as they become available. This flexibility is a key advantage of our approach.\n\n> **W2.** It would be fairer to compare AlignAb with models that optimize for energy e.g. AbDPO, which this model extends. This comparison is important yet missing in the evaluation. In terms of comparison, it would be worth putting the AAR and RMSD metrics in the main paper; as opposed to the appendix; there the performance is somewhat matching the baselines (with a better RMSD).\n\n**Response:** \n\nThank you for this excellent feedback. We have addressed both of your points by conducting a new ablation study and revising the main text to improve the fairness and clarity of the evaluation.\n\nTo directly assess the benefit of our proposed multi-objective alignment method (POEA), we conducted a controlled comparison with a naive DPO alignment with gradient surgery as used in AbDPO. Both methods were trained using the same preference dataset (1,280 samples), and we evaluated the energy metrics on 32 generated candidates for each of the first 10 test cases.\n\n| Method | Avg. CDR $E\\_{total}$ ↓ | Avg. CDR-Ag ΔG ↓ | Avg. CDR-Ag $E\\_{att}$ ↓ | Avg. CDR-Ag $E\\_{rep}$ ↓ | Avg. Gap ↓ |\n| :---: | :---: | :---: | :---: | :---: | :---: |\n| Reference | \\-11.03 | 16.75 | \\-12.45 | 15.77 | \\- |\n| DPO | 113.59 | 183.19 | \\-19.98 | 352.15 | 158.74 |\n| **POEA** | **48.53** | **74.85** | **\\-13.41** | **103.54** | **51.59** |\n\nThese results show that our POEA framework significantly outperforms the naive DPO approach across all key energy metrics, consistently generating more natural-like antibodies.\n\nWe also agree with your suggestion about the AAR and RMSD metrics. We will move this table from the appendix to the main paper to provide a more complete evaluation. Thanks for helping us present a fairer and more comprehensive analysis of our method.\n\n> **W3.** The paper lacks a discussion on the training and inference efficiency of the model.\n\n**Response:** \n\nThank you for pointing this out. We will add a discussion on the model's efficiency to the appendix.\n\nTo be specific, one full iteration of our alignment process takes approximately **2 hours** on a single NVIDIA A100 GPU. This consists of:\n\n* **Inference:** **0.5 hours** to generate a preference dataset of 1,280 samples.  \n* **Training:** **1.5 hours** for the alignment model to train for 4,000 steps on that dataset.\n\nWe appreciate you prompting us to include these important practical details.\n\n> **W4/Q1.** Finally, the contribution of pretraining to performance is not clearly evaluated; as it represents an additional complexity in the model, it would seem natural to evaluate its impact. What is the impact of each training phase on performance ? in particular, sequence pretrainining?\n\n**Response:** \n\nThank you for this valuable suggestion. To clearly isolate the contribution of each component in our method, we have conducted the detailed ablation studies you requested.\n\nWe evaluated three key model variants to isolate the contribution of each stage. The ablation results are reported as average energies of the 32 generated candidates for each of the first 10 samples from the test dataset.\n\n* **w/o Alignment:** The model after supervised fine-tuning but before any preference alignment. This measures the performance of the base generative model.\n\n* **w/o Pre-training:** Our full method but without using the pre-trained language model. This tests the benefit of leveraging large-scale antibody sequence data.\n\n* **POEA:** Our proposed Pareto-Optimal Energy Alignment (POEA) performed for only one round. This isolates the core benefit of our multi-objective function.\n\n* **Full Method (Iterative POEA):** Our complete, multi-turn POEA over three alignment iterations, as described in the paper.\n\n| Method | Avg. CDR $E\\_{total}$ ↓ | Avg. CDR-Ag ΔG ↓ | Avg. CDR-Ag $E\\_{att}$ ↓ | Avg. CDR-Ag $E\\_{rep}$ ↓ | Avg. Gap ↓ |\n| :---: | :---: | :---: | :---: | :---: | :---: |\n| Reference | \\-11.03 | 16.75 | \\-12.45 | 15.77 | \\- |\n| w/o Alignment | 128.10 | 235.82 | \\-14.31 | 479.00 | 205.82 |\n| w/o Pre-training | 50.23 | 76.89 | \\-13.84 | 118.29 | 56.33 |\n| POEA | 48.53 | 74.85 | \\-13.41 | 103.54 | 51.59 |\n| **Full Method (Iterative POEA)** | **34.13** | **55.71** | **\\-14.60** | **59.06** | **32.39** |\n\nFrom the above ablation results, we conclude the following key takeaways:\n\n1. **Impact of Alignment:** The baseline model without any alignment performs poorly, highlighting the critical need for an alignment stage to produce energetically favorable designs.  \n2. **Impact of Pre-training:** The slight performance drop without the PLM confirms that pre-training provides a useful inductive bias, leading to more realistic initial designs before alignment.  \n3. **Impact of Iterative Alignment:** The full, multi-turn Iterative POEA achieves the best performance across all metrics, demonstrating the benefit of our iterative learning paradigm.\n\nWe will include this ablation table and analysis in the revised paper to clarify the contribution of each component.\n\n> **L1.** The authors could better explain the limitations of using Rosetta energies as a porxy for binding affinity\n\n**Response:** \n\nThank you for this important suggestion. We agree that a clearer discussion of these limitations is needed.\n\nIn the revised version, we will expand our Limitations section to explicitly state that Rosetta energy is a simplified proxy with an imperfect correlation to true binding affinity. We will clarify that its primary role in this work is to serve as a standardized benchmark for evaluating and comparing computational alignment algorithms, rather than as a perfect predictor of wet-lab outcomes. We appreciate you helping us to better frame our evaluation."}]

Author rebuttal:

Meta-review: (a) Scientific Claims and Findings: The paper presents a three-stage framework for antibody sequence-structure co-design, leveraging pretraining, transferring, and alignment stages to generate antibodies with improved energy scores and binding affinity. The method introduces a novel Pareto-Optimal Energy Alignment (POEA) algorithm to handle conflicting energy objectives during the alignment stage. The results demonstrate superior performance over existing baselines in terms of energy metrics and binding affinity.

(b) Strengths: The paper is well-written and presents a novel approach to antibody design by integrating pretraining, transferring, and alignment stages. The introduction of the POEA algorithm is a significant contribution, as it effectively handles multiple conflicting energy objectives. The framework shows improved performance in generating antibodies with favorable energy scores and binding affinity.

(c) Weaknesses: The reliance on Rosetta energy as a proxy for binding affinity is a limitation, as it is known to have a weak correlation with true binding affinity. The paper could benefit from more comprehensive comparisons with existing models that optimize for energy, such as AbDPO. Additionally, the paper could include more detailed discussions on the training and inference efficiency of the model.

(d) Reasons for Decision: The paper presents a novel and effective approach to antibody design, with clear improvements over existing methods. The authors have addressed the reviewers' concerns through additional experiments and clarifications, demonstrating the robustness and applicability of their method. 

(e) Rebuttal Period: The reviewers raised several points regarding the novelty, evaluation metrics, and limitations of the model. The authors addressed these concerns by conducting additional ablation studies, including new metrics such as Boltz-2 IPTM, and clarifying the input data requirements. These responses were deemed satisfactory by the reviewers, leading to maintained positive recommendations.
Decision: Accept (poster)