Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints
Authors: Dapeng Jiang
Xiangzhe Kong
Jiaqi Han
Mingyu Li
Rui Jiao
Wenbing Huang
Stefano Ermon
Jianzhu Ma
Yang Liu
Venue: ICML 2025 poster (2025)
Keywords: Cyclic peptide design
diffusion model
geometrically constrained generation
Primary area: applications->chemistry_physics_and_earth_sciences

Abstract: Cyclic peptides, characterized by geometric constraints absent in linear peptides, offer enhanced biochemical properties, presenting new opportunities to address unmet medical needs. However, designing target-specific cyclic peptides remains underexplored due to limited training data. To bridge the gap, we propose CP-Composer, a novel generative framework that enables zero-shot cyclic peptide generation via composable geometric constraints. Our approach decomposes complex cyclization patterns into unit constraints, which are incorporated into a diffusion model through geometric conditioning on nodes and edges. During training, the model learns from unit constraints and their random combinations in linear peptides, while at inference, novel constraint combinations required for cyclization are imposed as input. Experiments show that our model, despite trained with linear peptides, is capable of generating diverse target-binding cyclic peptides, reaching success rates from 38\% to 84\% on different cyclization strategies.

Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints
Dapeng Jiang" 12* Xiangzhe Kong" 13+ Jiaqi Han
Mingyu Li' Stefano Ermon Jianzhu Ma Yang Liu
Rui Jiao
Wenbing Huang
Abstract
A
B
Cyclic peptides, characterized by geometric con- straints absent in linear peptides, offer enhanced biochemical properties, presenting new oppor- tunities to address unmet medical needs. How- ever, designing target-specific cyclic peptides re- mains underexplored due limited training data. To bridge the gap, propose CP-Compp Composer, novel generative framework that enables zero-shot cyclic peptide generation via composable geo- metric constraints. Our approach decomposes complex cyclization patterns into unit constraints, which are incorporated into diffusion model through geometric conditioning on nodes and edges. During training, the model Icarns from unit constraints and their random combinations in linear peptides, while at inference, novel con- straint combinations required for cyclization are imposed as input. Experiments show that our model, despite trained with linear peptides, is ca- pable of generating diverse target- parget-binding cyclic peptides, reaching success rates from 38% to 84% different cyclization strategies.
C
D
Figure I. Four common strategies to form cyclic peptides. (A) Stapled peptide where lysine (K) at position and an aspartic acid (D) at position i 4-3 are connected via dehydration condensation on side chains. The aspartic acid can also replaced with glutamic acid (E) position + 4. (B) Head-to to-iil peptide where the first residue and the last residue form an amide bond for connection. (C) Disulfide peptide where two cysteines (C) non-adjacent in sequence are spatially connected through a disulfur bond. (D) Bicycle peptide which triangle hetween three cysteines (C) non-adjacent in sequence.
13,5-trimethyllbeezzeee form
increasing attention (Zorzi al., 2017). These constraints stabilize the peptide conformation, enhancing biochemical properties including binding affinity, in vivo stability, and oral bioavailability (Ji et al., 2024), which are essential for identifying desired drug candidates (Zhang & Chen, 2022),
1. Introduction
Peptides occupy an intermediate position between small molecules and antibodies, offering unique advantages over conventional drug formats, such as higher specificity and enhanced cell permeability (Fosgerau & Hoffmann, 2015; Lee et al., 2019). Among them, cyclic peptides, which intro- duce geometric constraints into linear peptides, have earned
Existing literature on target-specific peptide generation pri- marily focus on linear peptides, utilizing autoregressive models (Li al., 2024a), multi-modal flow matching (Li al., 2024b; Lin al., 2024), and geometric latent dif- fusion (Kong et al., 2024). However, these methods are not directly applicable to cyclic peptide design due to the scarcity of available data (Rettie et al., 2024). Other ap- proaches either impose geometric constraints on linear pep- tides through post-filtering (Wang al., 2024b), which typi- cally results in low acceptance rates, or rely on hard-coded model design (Rettie al., 2024), which lacks general- izability across different cyclization patterns. In contrast, we hypothesize that the complex geometric constraints of cyclic peptides can be decomposed into fundamental unit constraints, resembling how complex mathematical formu- las are built from basic arithmetic operations. While existing datasets rarely contain peptides that satisfy intricate cyclic
'Equal contribution 'Institute for Al Industry Research (AIR), Tsinghua "Xingiian College, Tsinghua University Department of Computer Science and Technology, Tsinghua University "Stanford University 'Gaoling School Artificial Intelligence, Renmin University of China "Beijing Key Laboratory of Research on Large Models and Intelligent Governance 'Department of Elec- tronic Engineering, Tsinghua University. Correspondence to: Yang Liu <liuyang201 (etsinghu.ccu.co. edu.cc >, Jianzhu Ma <ma- jianzhu tsinghua.edu.cn.
Proceedings of the 4nnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints
constraints, they typically include abundant instances of sin- gle unit constraints and their random combinations, which serve the building blocks for more complicated designs. Therefore, we reason that framework could potentially be developed to learn these unit constraints from available linear peptide data, circumventing data limitations and en- abling generalization to the diverse combined constraints required for cyclie peptide design.
2024), there have been growing interests in scaling these models systems of larger scales, such antibody (Luo et al., 2022), peptide (Kong et al., 2024), and protein (Yim et al., 2023; Watson et al.. 2023; Anand & Achim, 2022) in general, or to those with complex dynamics, such as molecu- lar dynamics simulation (Han et al., 2024b). Despite fruitful achievements, how to impose diverse geometric constraints stills remain under-explored for geometric diffusion models, which aim to address in this work.
In this paper, we present Up-Composer, framework for zero-shot cyclic peptide generation, relying solely on avail- able data for linear peptides, Our work is equipped with the following contributions. 1) Decomposing cyclization strategies into fundamental geometric constraints. We identify four common chemical cyclization strategies (Fig- ure 1) and formalize cyclic peptide design as geometrically constrained generation problem. By analyzing cyclization patterns, we derive two fundamental unit constraints, type constraints and distance constraints, allowing description of diverse cyclization strategies to be specific combinations of these units. 2) Encoding constraints with geometrie condi- tioning. We incorporate unit constraints into a the denoising network of diffusion model (Kong et al., 2024) using ad- ditional vectorized embeddings of types and distances on geometric graphs, which enables flexible conditioning compositions of constraints required for eyclic peptide gen- eration. 3) Enabling zero-shot cyclic peptide design. We jointly train conditional and unconditional models on unit constraints and their random combinations found in linear peptide data. At inference, novel constraint combinations corresponding desired cyclization strategies, which are unseen during training, are imposed as input conditions. The model is guided by the difference in score estimates between conditional and unconditional models, enabling zero-shot generalization to cyclic peptides. 4) Assessing generated eyelic peptides on comprehensive metrics. Ex- periments demonstrate that our Co-Cooppser generates cyclic peptides with complex geometric constraints effee- tively, achieving high success rates from 38% to 84%, while maintaining realistic distributions on amino acid types and dihedral angles. Molecular dynamics further confirm that the generated cyclic peptides exhibit desired binding affinity while forming more stable binding conformation compared to the native linear peptide binders.
Diffusion guidance. Diffusion sampling can be flexibly controlled by progressively enforcing guidance through the reverse denoising process. Dhariwal & Nichol (2021) pro- poses musssffier-uudaane which employs an additionally trained classifier to amplify the guidance signal. Classifier- free guidance (CFG) (Ho & Salimans, 2022) is a more widely adopted alternative that replaces the classifier with the difference of the conditional and unconditional score, which has been further generalized to the contiico scenario by composing multiple scores in diffusion sam- pling (Liu et al., 2022; Huang et al., 2023). Diffusion guid- ance has also been explore for solving inverse problems on images (Song et al., 2024; Kawar et al., 2022; Song et al., 2021b), molecules (Bao et al., 2022), and PDEs (Jiang et al., 2024). Our approach instead extends CFG to compose geo- metric constraints with application to cyclic peptide design.
Peptide design. Target-specific peptide design initially re- lied on physical methods using statistical force fields and fragment libraries (Hosseinzadeh et al., 2021; Swanson et al., 2022). With the rise of equivariant neural networks (Sator- ras et al., 2021; Han et al., 2024a), geometric deep gen- erative models have emerged. PepFlow (Li et al., 2024b) and PPFlow (Lin et al., 2024) use multi-modal flow match- ing, while PepGLAD (Kong et al., 2024) applies geometric latent diffusion with a full-atom autoencoder. However, these methods struggle with cyelic peptide design due to limited data. Prior works introduce disulfide bonds via post-filtering (Wang al., 2024b) or enforce head-to-tail cyclization through hard-codedo model design (Rettie et al., 2024). In contrast, our approach decomposes cyclization into fundamental unit constraints, enabling zero-shot cyclic peptide generation with broad flexibility across diverse pat- terns.
3. Method
2. Related Work
In this section, we detail our method, CP-Composer. We first introduce basic concepts of peptide modeling and cyclic strategies in Sec. 3.1 and specify these strategies as con- straints in Sec. 3.2. We further present the guided generation framework and the encoding strategy for incorporating the constraints in See. 3.3 and Sec. 3.4, respectively. We finally describe the training and inference schemes in Sec. 3.5. The overal workflow is depicted in Fig. 2.
Geometric diffusion models. Besides their success on ap- plications like image (Rombach et al., 2021; Song et al., 2020: 2021a) and video (Ho et al., 2022) generation, diffu- sion models have become a preeminent tool in modeling the distribution of structured data in geometric domains. While early works have explored their applicability on tasks like molecule generation (Xu et al., 2022; 2023; Park & Shen,
2

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Zero-Shot Cyclic Peptide Design via Composable Geometrie Constraints
Training
Type Constraints
Node Encodings
Edge Encodings
Distance Constraints
Zero-shat Generation
One-hot Encodings
RBF Encodings
Sampled Constraints
Composed Encodings
Composed Encodings
Target Constraints
+
c
+
alla.
X3
alla
T
Laa
Classifier Free Guidance
E C.O).
92
GG..ccm c.
Linear Peplide
Cyclic Peplide
Figure 2. Overall training and inference design of CP-C Jo-Cooposer. We define two unit constraints, type constraint and distance constraint ($ 3.2), which are incorporated into the diffusion model via geometric conditioning ($ 3.4). During training, the model learns from single unit constraints and their combinations observed linear peptides. At inference, novel combinations corresponding to specific cyclization strategies are imposed with guidance signal amplified by classifier-free guidance, enabling zero-shot cyclic peptide design ($ 3.5).
3.1. Preliminaries
specific amino acid types and/or their pairwise distances. Taking the disulfide peptide as an example (Fig. IC), to link two cysteines at indices i, with a disulfur bond of length ds, a disulfide peptide constrained by"
Representing peptide as geometric graph. We represent the binding site and peptide as a fully-connected geometric graph G (V, 8) where V is the set nodes and is the set of edges. Each node is a residue, binded with node features (h,, X2) with h; E R being the one-hot encoding of the amino acid type and X, R2xx3 being the coordinate of the k; atoms.
Dissuttdde... = (f arg max (h:) arg max(2))), kc}. {1}x - x112=ds]]
(1)
where ke represents the index of cysteine (C) in the one- hot embeddings. This constraint can be decomposed into two node-level constraints on the amino acid types and one edge-level constraint on the distance. We refer to these as unit geometric constraints with further details on these constraints provided in Sec. 3.2. We demonstrate that all four cyclic strategies can be expressed as combinations of these unit geometric constraints in Appendix B.
Geometric latent diffusion model for peptide design. Our model is built on PepGLAD (Kong et al., 2024), latent geometric diffusion model, but is adaptable to other diffusion-basee frameworks. It employs a variational au- toencoder to project peptide graphs G into residue-level latents 9_ = ((z,, ) with an encoder εx, and cor- responding decoder De for the inverse, where z; E R is the E(3)-invariant latent and Σ, Rd is the B(3)-equivariant counterpart. A diffusion model is learned in the compact latent space, with the denoiser eg (g( .t) parameterized by an equivariant GNN (Kong et al., 2023). The sampling pro-
3.2. Decomposing Cyclization Strategies as Geometric Constraints
In this work, we consider two types of unit geometric con- straints, namely type constraint and distance constraint. In particular, type constraint operates on node-level by enfore- ing the node to be of certain type, while distance constraint takes place on edge-level, specifying a pair of nodes to reside certain distance.
cess initiates with latents T = {(x (T) _((T) {(T))) Tiz1 drawn from the prior and gradually denoises it using DDPM (Ho et al., 2020) sampler for a total of steps. The final latents ((0) are decoded back to the data space using decoder Dz--
Cyclic peptide and cyclization strategies. Unlike common linear peptides, which are chain-like structures, a cyclic pep- tide is formed by animo acids connected in a ring structure. As shown in Fig. 1, we primarily focus on four types of cyclic peptides in this paper: stapled, head-to-tail, disulfide and bicycle peptides. Each strategy applies constraints on
Definition 3.1 (Type constraint). A type constraint is set Cr == {(i, 4) hev, where each entry (i, 4,) represents that node should be of type 4, while Vy C V is the set of nodes to enforce the type constraint.
For simplicity, we slightly abuse the notation |X; X, 112 where the distance is measured using the nodes' C. coordinates.
3

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Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints
Definition 3.2 (Distance constraint). A distance constraint is set CD == { dij) ((kj)))),) (()) where each element ji, diz) represents that node i and should be positioned at the distance of dij, while &D S & is the set of edges to enforce the distance constraint.
By further leveraging the relation log log logg!
V d log Po [C) V t lo R ( C.
Ea (G .t) into Eq. 5, we obtain the expression in Eq. 3.
Conceptually, Eq. 2 adopts energy gerrgy-guidace that di- rectly models log pt (CIG!") by an externally trained en- engy function. Eq. 3 instead follows the convention in classifier-free guidance by rewriting V Voto (ogg!() =
Notably, our taxonomy of geometric constraints is particu- larly interesting due to its completeness, in the sense that each of the eyclic strategies C described in Sec. 3.1 can be decomposed into combinations of type constraints Cr and/or distance constraints Cp. We defer the detailed expla- nations to Appendix B.
V g (0) gft log Po R ca(g!) C,
ea (G! .t,, which gives Eq. 3 after simplification.
In recent studies, how to obtain the conditional score ég (G C,t) still remains unclear. Notably, C is com- plicated geometric constraint, which is fundamentally dif- ferent from a class label (Ho & Salimans, 2022) or a target value (Bao et al., 2022), where an embedding (e.g., one- hot for class label) can be readily adopted as the control signal to feed into the denoiser. In the following section, we will introduce our approach to encode type and distance constraint.
Problem definition. We formulate the task of cyclic peptide design as finding the candidate peptides G that satisfy con- straint C, where C is any one of the four eyclic constraints.
3.3. Inverse Design with Diffusion Guidance
To perform inverse design, a widely adopted approach is to progressively inject certain guidance term into diffusion sampling towards the design target (Bao al., 2022; Song et al., 2023), which share similar spirit classifier guid- ance (Dhariwal& & Nichol, 2021). Specifically, at each sam- pling step t, the conditional score is derived by Bayes' rule:
3.4. Encoding Constraints via Geometric Conditioning
To encode the constraints as control signals, we propose geometric conditioning that embeds the type and distance constraints into the denoiser through vectorization.
V Φ log (c (C) V o log pa (
+ V t lo (CI6L)),
Conditioning type constraints. For type constraint Cr (i,4)) where 4 10, K - 1} is the desired node type for node i, we operate node-level by augment- ing the E(3)-invariant node feature h; with an additional vector 1; E RR which serves as the control signal. This cor- responds to the encoding function (r( = {(i, ())ev that lifts I to the embedding space where
where the last term V of log (C) takes the effect as guidance, which can typically be a hand-crafted energy func- tion (Kawar et al., 2022; Song et al., 2024) or a pretrained neural network (Dhariwal& & Nichol, 2021; Bao et al., 2022).
However, empirically the approach is often demonstrated unfavorable since the guidance term in Eq. 2 is the gra- dient of neural network, which detriments sample quality due to adversarial effect (Ho & Salimans, 2022). Distinct from the approach above, we propose an alternative that, inspired by classifier- free guidance, guides the sampling by directly composing unconditional and conditional score without additional gradient terms. In detail, we have,
(One-hot(k)
i VT, ie V.V.
1: 1
(6)
0
Such design of the control signal is simple yet effective, since different type constraints will induce different signal 4, thus making the constraints distinguishable to the network. More importantly, for any type constraint, the conditional score E (g("" C, t) obtained by this means still enjoys E(3)- equivariance, since I; is E(3)-invaii.n..
Eo( c, (tt)) (w + (CE( (,t, - wE)( (3)
where w is the guidance weight and the guided score éo will replace eæ for score computation. In particular, the rationale of Eq. 2 and Eq. 3 are linked by the following distribution
Conditioning distance constraints. For distance constraint Cp = { d.g) ()) Ja,ne, where dy specifies the distance between node i and j, we instead design the encoding func- tion as (CD) = ((t.j. (y)Jeeee where the control signal d,j is defined at edge-level:
p. (C) (e (CC
(4)
with the corresponding conditional score
V o log P.....G (g!") (C)
ag log Pa (g! + W Φ logg((C!!!
d,j RBF(d.)
(1,5) E ED.
(7)
x (t) + w 90 log (C
(5)
(i,5) E EVED.
4

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Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints
Here RBF(.) is the radial basis kernel that lifts the distance from scalar high-dimensional vector (Schütt et al., 2018), and & denotes that the edges not in the set En will not be featurized. The control signal di is then viewed as a special type of edge feature, which will be further pro- cessed by an additional dyMEAN layer (Kong et al., 2023), whose input will be the subgraph (V, E)) with edge features {diy ((J)EED More details are deferred to Appendix C.2. Akin to the analysis for type constraints, our way of encod- ing distance constraints also preserve the =quuvvauieee of the conditional score, with proof in Appendix A.2.
Algorithm 1 Training Procedure of CP-Composer
Input: Data distribution D, mask probabilities for type and distance constraints pr. PD: encoder Eg. score network cØ. diffusion scheduler Scheduler()
I: while not converged do
2: Sample 9 ~ D, Cr Unif(Cr(S)), and Cp ~ Unif(CD(S))
{c.f. Eq. 8-9)
3: Cr + Ø with probability Pr
CD t with probability pn
(e, gl ,t) + Scheduler((g(9))
5:
6: Take gradient step on
Moreover, the encoding is also injective, as formally stated in Theorem 3.3. Such property is crucial for effective guid- ance since different constraints will be projected as different control signals, always making them distinguishable to the score network.
[(0) = || E (g( Cr, Cp, 1)
7: end while
constraint, we select the following design space:
CD = (CDlCp ((i, | X, (1l1)) dg(i,)) E (3,
Theorem 3.3 (Injective). Both fr and SD are injective. That is, S(C²) = S(C2) if and only if C² = C2, where (f,C),C*) can be (fr, () or (fD, Cb. C)) Furthermore, their product function j(Cr,Cn) = (fr(CT), fo(C)) is also injective.
(3,4, 4, (E = 6),
which spans across all possible distance constraints that specify the distance between node i and j to be their Eu- clidean distance in G, while the shortest path distance be- tween i and j. i.e., (i equals to 3. 4, or 6. We design Cg)( and (g)) such that Cr (g) x (g) covers the con- straint space of cyelic peptides, where x is the Cartesian product. This permits compositions within the space Cr x CD()) at inference time without necessarily seeing such particular combination in training data, e.g., the four compositional constraints of cyclic peptides.
Composing type and distance constraints. Our approach of encoding the type and distance constraints in node- and edge-level respectively also facilitates conveniently com- posing them together. In particular, we can easily devise co(g.") Cr, (D,,t) t) by simultancous feeding the type and distance control signals in Eq. 6 and into the score network, which corresponds to enforcing a compositional constraint (Cr; CD) This extension is critical since it enables us to enforce richer combinations of the constraints at inference time, even generalizing to those unseen during training. In this way, we are able to design cyclic peptides with training data that only consist of linear peptides due to the general- ization capability of our approach.
approach to generalize to novel
Training. We employ a single network eœ to jointly opti- mize the conditional and unconditional score during training, following the paradigm in Ho & Salimans (2022). At each training step, we first sample G from training data distri- bution D and derive the candidate constraints Cr()) and CD( We then sample a type constraint Cr and a distance constraint Cn uniformly from the candidates Cr (9) and CD respectively. To jointly optimize the conditional and unconditional score networks, we replace Cr and Cp by empty set Ø with probability pr and pD respectively, where the empty set will enforce no meaningful type and/or dis- tance control signal which degenerates to the unconditional score. Finally, we encode G into latent space by Ex, sample the noise e and diffusion step t, and compute the noised latent _(ب) The noise prediction loss (Ho et al., 2020) is adopted to train the score network. We present the detailed training procedure in Alg. 1.
3.5. Training and Inference
With the geometric conditioning technique to derive the conditional score, we are now ready to introduce the training and inference framework.
Design space for constraints. For linear peptide G sam- pled from training set with features {hh; X.) we con- sider the following design space for type constraint:
Cr( = (Cr|Cr= = {(i, arg max((a)))ee, S 4),
Inference. At inference time, we will select one of the four cyclic constraints at one time, Each constraint is represented by (C), Cb) where Cj and Cp are the target type and distance constraint, respectively. We start from the initial latent gLT) sampled from the prior and perform standard
which include all of the type constraints that control the type of the node to be the same as that of node in g and the number of constraints to be fewer or equal to 4. For distance
5

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Zero-Shot Cyclic Peptide Design via Composable Geometrie Constraints
Table I. Success rates and KL divergence for generated samples from different cyclization strategies.
Stapled peptide
Head- to to-tail peptide
Suec.
AA-KL
B-KL
S-KL
Succ.
KA-KL
B-KL
S-KL
PepGLAAD (Kong et al., 2024)
22.80%
0.1035
1.1401
0.0126
30.23%
0.1052
1.1347
0.0125
w/ EG (Bao al., 2022)
25.41%
0.0744
1.1821
0.0127
61.63%
0.0798
1.0891
0.0128
CP-Com PP-Coopseer w 0.0
25.71%
0.0932
1.1179
0.0126
37.21 %
0.1021
1.0787
0.0118
CP- PP-Composer w 1.0
30.00%
0.1017
1.1235
0,0161
55.81%
0.1008
1.0604
0.0124
CP- Composer w 2.0
21.42%
0.1067
1.0996
0.0147
65.11%
0.1055
1.1005
0.0126
+CADS (Sadat et al., 2024)
27.14%
0.0807
1.0975
0.0119
45.54%
0.0798
1.0589
0.0132
CP-C EP-Cooposer v = 5.0
38.57 %
0,1812
1.1515
0,0180
74.42% %
0.1320
1.0523
0.0122
CP- UP-Composer 10.0
32.86%
0.3532
1.1726
0.0232
68.60%
0.1784
1.0301
0.0175
Disulfide peptide
Bicycle peptide
Succ.
AA-KL
B-KI.
S-KL
Suec.
AA-KI.
B-KL
S-KT.
PepGLAD (Kong et al., 2024)
0
0.0808
1.1324
0.0124
0.0838
1.1823
0.0238
w/ EG (Bao et al., 2022)
0
0.0711
1.0891
0.0103
0
0.0729
1.0968
0.0228
EP-Composer w = 0.0
7.50%
0.1016
1.1062
0.0151
0
0.1225
1.1980
0.0252
CP-Composer v = 1.0
21.25%
0.1477
1.0939
0.0151
11.53%
0.1638
1.1490
0.0395
CP-C UP-Composer 2.0
41.25%
0.2873
1.0994
0.0379
30.76%
0.2147
1.1195
0.0735
+CADS (Sadat al., 2024)
3.75%
0.0939
1.0788
0.0162
3.85%
0.0901
1.0624
0.0684
Composer ws 5.0
82.50
0.5139
1.0397
0.1913
84.62%
0.3385
1.0759
0.3351
CP-Composer w = 10.0
62.50%
1.6965
4.0312
1.1046
38.46%
1.2677
8.1935
0.3374
Algorithm 2 Inference Procedure of CP-Composer
dataset (Kong et al., 2024; Tsaban et al., 2022) for test- ing. PepBench contains 4,157 protein-peptide complexes for training and 114 complexes for validation, with a target protein longer than 30 residues and a peptide binder between 4 25 residues. ProtFrag encompasses 70,498 synthetic samples resembling protein-peptide complexes, which are extracted from local contexts in protein monomers. LNR consists of 93 peptiie complexes curated by domain experts, with peptide lengths ranging from 4 to 25 residues.
Target type and distance constraint (Cz, Cb), dif- fusion sampler Sampl 1 e er(-), guidance weight w, step T, score network 60, decoder D3
Input:
1: Initialize latents G!T) from prior
2: for t= T,T T 1,... , do
Compute score é (w 1) C7. t) wen(g 0, (Eq. 10}
4: g Sampler(0 E,t) (E,)
(Denoising step)
We evaluate zero-shot cyclic peptide generation in Sec. 4.1, demonstrate the flexibility of composable geometric con- straints with high-order multi-cycle constraints in Sec. 4.2, and assess the stability and binding affinity of the generated cyclic peptides through molecular dynamics in Sec. 4.3.
5: end for Return: )
diffusion sampling with the guided score:
E( C7 CD. t) =(w + () C7, tb
4.1. Zero-Shot Cyclic Peptide Generation
wwe ( 0,0,),
(10)
Metrics. We evaluate the generated peptides based on two key aspects: eyclic constraint satisfaction and generation quality. For each target protein in the test set, we generate five candidate peptides and compute the following metrics. Success Rate (Suec.) measures the proportion of target proteins for which at least one of the five generated peptides satisfies the geometric constraints of the specified cycliza- tion strategy. Amino Acid Divergence (AA-KL) calculates the Kullback-Leibler (KI.) divergence between the amino acid composition of reference peptides and all of the gen- erated samples. For cyclization patterns that impose amino acid constraints at specific positions, we exclude these con- strained amino acid types when computing the distributions, as successful designs inherently deviate from the reference distribution these amino acid types. Backbone Dihe-
where a modified classifier-free guidance is employed to further amplify the guidance signal. The sample is acquired by decoding (0) back to the data space using the decoder De. The inference procedure depicted in Alg. 2.
4. Experiments
Task. We evaluate CP-Composer target-specific cyclic peptide design, aiming to co-design the sequence and the binding structure of cyclic peptides given the binding site on the target protein.
Dataset. We utilize PepBench and ProtFrag datasets (Kong al., 2024) for training and validation, with the LNR
6

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Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints
able geometric constraints. In Table 3, we further compare CP-Composer with DiffPepBuilder (Wang et al., 2024a). Although DiffPepbuilder is method specifically designed for disulfide peptide generation, CP-Composer shows bet- ter success rates than DiffPephuilder. These results show the effectiveness of CP-Composer. We visualize examples of generated peptides for each cyclization strategy Fig. 3, with more cases in Appendix E. Furthermore, the weight parameter effectively balances success rates and gen- eration quality, with increasing control strength yielding higher constraint satisfaction yet slightly higher KI. diver- gence, indicating a trade-off between constraint satisfaction and distributional fidelity. This flexibility allows users to customize the method based on specific application needs, prioritizing either higher success rates or closer resemblance to natural peptide distributions.
Stapled Peptide
Head-To- Told-To--he Tail Peptide
Disulfide Peptide
Bicycle Peptide
Figure Four types of generated eyclic peptides, with the red boxes highlighting the position for cyclization.
4.2. Flexibility in High-Order Combinations
dral Angle Divergence (B-KL) and Side-Chain Dihedral Angle Divergence (S-KL) indicate the KL divergence be- tween the distribution of the dihedral angles in reference peptides and the generated samples, assessing rationality in the generated backbonn and side chains, respectively.
Baselines. First, we compare our CP-Composer with the backbone model PepGLAD (Kong et al., 2024) without ad- ditional guidance validate the effectiveness of our frame- work with composable geometric constraints. We further im- plement baseline with the prevailing Energy-based Guid- ance (EG) (Dhariwal & Nichol, 2021; Bao et al., 2022) applied to node embeddings and pairwise distances to as- sess the advantages of our approach, with implementation details in Appendix C. To compare UP-Composer with other cyclic peptide generation method, we implement DiftPep- Builder (Wang et al., 2024a), model specifically designed for disulfide peptides. Furthermore, we also incorperate our method with advanced sampler Condition Annealed Dif- fusion Sampler(CADS) (Sadat et al., 2024) to analysis the performance of our method combining with other sampler.
Stapled Stapled
SSSS Head-to-Tall
-S-S-
-S-S- SSSS -S-S-
Figure 4. Generated peptides conforming to high-order combina- tions of cyclizations, with the red boxes highlighting the positions for cyclization.
Setup. To demonstrate the flexibility of our framework in handling composable geometric constraints, we investigate more complex and customized scenarios that involve mul- tiple cyclizations within a single peptide. Specifically, we explore the following high-order combinations: 2t has two stapled pairs in one peptide. -S-S- + H-T includes one disulfide bond and one head-to-tail in one peptide: 2*. S-S- contains two disulfide bonds one peptide; SS-S-S- involves three disulfide bonds in one peptide; The flexibility of CP- CP-Composer enables seamless implementation of these complex constraints: simply combining the individual unit constraints for each cyclization strategy allows the model to accommodate them simultancously.
Results. As shown in Table 1, CP-Composer significantly improves constraint satisfaction rates across all cyclization strategies compared to unguided basclines, while maintain- ing fidelity to reference distributions in amino acid com- position and structural dihedral angles. The energy-guided baseline proves effective in simple cases requiring control over a single pairwise distance (i.e., head-to-tail cycliza- tion), but struggles with more complex scenarios involving combinations of distance constraints and type constraints. This limitation is evident from its lower success rates stapled peptides and complete failure in handling more in- tricate cyclization patterns including disulfide and bicycle peptides. In contrast, ue-poop consistently achieves high success rates across these challenging cases, demon- strating the strength of our framework design with compos-
Results. As shown in Table 2, despite the increasing com- plexity of the constraints, CP-Composer achieves reasonable
7

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Zero-Shot Cyclic Peptide Design via Composable Geometrie Constraints
Unnor peptine
Cyclc peptise
RMSD (A) 3
0
20
40
60
80
100
Time [ns]
Linear peptóc Cyclic peptice
RMSD (A)
20
60
100
Figure 5. RMSD trajectories from 100 molecular dynamics simulations for two target proteins, each bound to either native linear peptide binder or eyclic peptide generated by our model. The target proteins and their corresponding linear peptide binders are derived from PDB 3RC4 (top) and PDB 4J86 (bottom), respectively.
success rates across all high-order cyclization scenarios. The control strength parameter w remains effective, with higher values leading to enhanced success rates. The only excep- tion is 2 2*apppled, likely due to the inherent difficulty of the Staple strategy, which already exhibits the lowest success rate in Table 1. This indicates that our framework effectively learns to generate peptides that conform to the joint distribu- tion of multiple constraints. Fig. 4 visualizes peptides with these high-order cyclization patterns, highlighting the flex- ibility of Po-mossser in designing structurally feasible peptides tailored for customized requirements.
4.3. Evaluations by Molecular Dynamics
Setup. We perform molecular dynamics (MD) simulations using the Amber22 package Halomon--Ferree et al., 2013) to compare the stability and binding affinity of linear pep- tides from the test set with cyclic peptides generated by model. We use the ffI force field for proteins and pep- tides (Maier et al., 2015) with all systems solvated in water, and 150 n. nM Na /C+ counterions are added to neutralize charges and simulate the normal saline environment (Jor- gensen al., 1983; Li al., 2024c). The SHAKE algorithm is applied constrain covalent bonds involving hydrogen atoms (Ryckaert et al., 1977). while non-bonded interac- tions are truncated at 10.0 Á, with long-range electrostatics treated using the PME method. To estimate peptide binding energies, we further employ MM/PBSA calculations (Gen- heden & Ryde, 2015). Notably, while MD simulations provide high accuracy evaluating conformational stability and binding affinity, they are very computationally expen- sive. Therefore, randomly select two target proteins from the test set and generate tail and disulfide bond cyclization strategies for evaluation. More details on the setup of MD are in Appendix C.3.
Table 2. Success rates for high-order combinations of multiple cyclizations within the same peptide.
Stapled
-S-S+HH-T
2*-S-S-
3+
w 1.0
2.5%
0
2.0
7.5%
10.0%
26.0%
17.2%
2.5
7.5%
20.0%
34.0%
34.5%
w 3.0
7.5%
26.0%
62.0%
65.5%
cyclic peptide using head-to-
Table 3, Success rates comparison between DiftPepBuilder and our method
Results. As shown in Fig. 5, the root mean square deviation (RMSD) trajectories of the two linear peptides from the test exhibit significant fluctuations, indicating vibrate binding conformations. In contrast, the RMSD trajectories of the cyclic peptides generated by our model are quite flat, producing consistently lower RMSD compared to the linear peptides, suggesting that the introduced geometric constraints effectively enhance conformational stability. Ta- ble presents the average RMSD values with standard devi- ations, along with the binding affinity (AG) estimated via
Succ.
Disulfide Peptide 2*-S-S-
CP-Composer
41.25%
62.00%
DillPepBuilder (Wang et al., 2024a)
23.07%
32.78%
In Table 3, we compare CP- CP-Composer with DiffPepBuilder. The results show that our method outperform the cycplic peptide generation model under high-order cyclization see- nario: two disulfide bonds in one peptide. This indicates the flexibility of our framework.
8

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Zero-Shot Cyclic Peptide Design via Composable Geometrie Constraints
able strategies. Our framework offers principled approach to eyclic peptide design, with potential extensions to broader biomolecular applications involving geometric constraints.
Table RMSD trajectories from molecular dynamics after 50 ns (average values and standard deviations), along with binding affini- (AG) estimated by running simulations with MM/PBSA.
Peptide
RMSD (À) AG-MM/PBSA (kcal/mol)
Acknowledgements
PDB: 3RC4
Lincar (test set)
2.57=0.51
-9.73
This work jointly supported by the National Key R&D Program of China (No.2022ZD010500) the National Natural Science Foundation of China (No. 61925601,
Cyclic (ours)
1.44-1:0.33
-10,66
PDB: 4J86
Linear (test set)
3.37++0.73
-15.17 17
Cyclic (ours)
1.56:1:0.40
-20.41
No. 62376276, No. 62276152), Beijing Nova Program (2023048427)), China's Village Science and Technology City Key Technology funding, Beijing Natural Science Foundation (No. QY24249) and Wuxi Research Institute of Applied Technologies.
MM/PBSA simulations. The results indicate that eyclie pep- tides achieve significantly stronger binding affinities than their linear counterparts, thanks to their enhanced stability in the binding conformations.
Impact Statement
4.4. Generalization beyond Available Data
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
In Fig. 6, visualize the structural embeddings of peptides generated under different cyclization strategies, along with linear peptides from the test set, using ESM22650M(LLn) Lin et al., 2023) and T-SNE (Van der Maaten & Hinton, 2008). The results reveal distinct clusters corresponding to different cyclization strategies, all of which are clearly separated from the linear peptides. This indicates that CP-Composer gener- alizes well beyond the available data, effectively exploring unseen regions of cyclic peptides.
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Zero-Shot Cyclic Peptide Design via Composable Geometrie Constraints
A. Proofs
A.1. Proof of Theorem 3.3
For clarity, we restate Theorem 3.3 below.
Proposition 3.3 (Injective). Both fr and fo are injective. That is, f(C!) f((3) if and only if C¹ = C², where
(J,C), C²) can be (ST, CT, C+) or (JD, DD P). Furthermore, their product,functio ((C,,Dn) = (I((C),, also injective.
To prove Theorem 3.3, we first prove the following lemma.
Lemma A.2. gf R RK is injective, then f(x) ((k.g(k:)))evv is also injective, where % {(i, ki)
Proof. f(x²) = f(x²) = (li.g(k)))ev, =
= De = Vx2 -Vx = g g(k)), Vi
Vx - Vz: Vg= Vx, k = k Vi E Vx = ((i, )iEE = {(i, ki)JiEVis = X x², where the third
deduction step leverages the injectivity of function g.
Now we are ready to prove Theorem 3.3.
Proof. We first prove the injectivity of fr. We choose g to be the one-hot encoding function One-hot(,). IR + RKK It is straightforward that this function is injective. By leveraging Lemma A.2, the proof is completed.
+ R Such map is injective, since [lő(d)) o(d2)]l =< d1.de d1 > + < d2, d2 > -2 < d1, d2 >= + 1 2 exp(->>144 d2ll?), which implies o(di) = ((22) > d1 d2, hence injectivity. By leveraging Lemma A.2, the proof is completed.
For the injectivity of fp. similarly we instantiate g as the RBF feature map ((-)
Since both fr and [n are injective, fD(C)) = C C7, C₁ = C - (,) (C7, C3). Therefore the product function f(Cr, Cp) =
(Jr(C)), (n(()) = [+((+) (oCC),
(M(CCT),n((Cnp) also injective, which concludes the proof.
A.2. Equivariance
Proposition A.3 (Equivariance). The conditional score co CC,) is E())-equivariant, where C is Cr or Cp-
The proof is straightforward since our encodings of Cr and Cp are both E(3)-invariant, therefore the -quuvvaaraee of the score is preserved, following the proof in Kong et al. (2023).
B. Decompositions of Cyclic Strategies
As illustrated Fig. 1, cyclic peptides are looped by four strategies, each which can be decomposed into unit geometric constraints defined in See. 3.2 as follows. Specifically, the pair (1,4) indicates type constraint that node is required be type 4; and the triplet (i, j, dlj) means distance constraint that the pairwise distance between node i, should be dij-
Stapled peptide. Given lysine (K) located at index i, a stapled peptide can be formed via a covalent linkage between the lysine and either an aspartic acid (D) at + with constraints as
DSapled-DD (1(i, K), (i+ 3, D)}, ((,1+3,dxx)))
(11)
or glutamic acid (E) i 4, with constraints as
Csuplod-EE (((i, K). (i 4,E)), ((1, +, 4,dxs))).
(12)
where dKD, dxg are the lengths of covalent linkages between the K-D and K-B pairs, respectively.
II practice we truncate the infiniteddimensional feature space by setting limit on the number of bases, similar to Schiit et al. (2018).
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Zero-Shot Cyclic Peptide Design via Composable Geometrie Constraints
Head-to-tail peptide. Given peptide composed of N amino acids indexed by 0, 1, ,N an additional amide bond is linked between the head and tail amino acid as
Ceen--tottil
(f), -.1dd))).
(13)
where dp is the length of the amide bond.
Disulfide peptide. Connecting two cineeins (C) at i,j with a disulfur bond, a disulfide peptide is constrained
by
DDssallide, (((.,(
(14)
where dg is the length of the disulfur bond.
Bicycle peptide
To link the three cysteines (C) i, i, k. bicycle peptide constrained by
CBicyde,,s5. = (1. C) (4; C)}, ((,,j, dr,
(15)
where dr is the side length of the equilateral triangle formed by the centered 1, 1,35-trimeethylbeezzeee.
C. Implementation Details
C.1. Energy-based classifier guidance
With the definition of the geometric constraints, now introduce their corresponding energy function, scalar function that evaluates the satisfaction of the constraint given the input geometric graph.
Definition C.1 (Energy function of constraint). An energy function of constraint C is differentiable function gc(+) X' R20 such that ge (G) = 0 if X' satisfies the constraint C and gr(9) A 0 otherwise.
Intuitively, the energy function serves as an indicator of constraint satisfaction, following the conventional way of handling equality constraints (Bertsekas, 2014).
One naive way to tackle inverse problem is to directly optimize the energy function (Yang et al., 2020; Goldenthal et al., 2007) of the constraint with respect to the initial latents _LT), since its minima correspond to the data points & that satisfy the constraint. However, the large number of sampling steps T required by diffusion models makes the optimization computationally prohibitive, the gradient needs be backpropagated through the denoiser T times. Moreover, the energy function is not guaranteed to be convex, which further troubles the optimization.
Energy-based classifier guidance has been introduced to inject constraint as guidance of diffusion sampling in soft and iterative manner. In our setting, we can pair up P: (C)gz) and the energy function through Boltzmann distribution, Le., Pe (C = exp(=9e:DP(( where is the normalizing constant. this way, we have,
Vg, log pr (9= CC) = Vs log (( - w
(16)
where w E R is added to control the guidance strength. Performing such sampling procedure is equivalent to sampling from the posterior (Ye et al., 2024):
P(GICC) = pc)))ex)(-_
(17)
which concentrates the density more on the regions with lower energy function value, biasing the sampling towards data points better satisfying the constraint C (Cr, CD).
In our implementation, we adopt the guidance function in Kong et al. (2024) the energy function sc- In particular, the choice of w significantly influences the generation quality. A larger w typically enhances control strength but degrades generation quality when becoming excessively large. To strike a balance between controllability and quality, we conduct a sweep across various w values and ultimately employ w e {10, 30, 50} for mnergy-based classifier guidance. The best performance across different w values reported for all conditions.
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Zero-Shot Cyclic Peptide Design via Composable Geometrie Constraints
C.2. Distance Constraints as Edge-Level Control
To inject the edge-level control into the model, we apply the adapter mechanism by adding an additional dyMEAN block (Kong al., 2023) to each layer, and changing the message passing process into
X x;")) (dy)).neeo [(h (1+0.5) X (((+0.5) Nev AME( (
(1)
(18)
((h (41) x ((+)) Jiev = AME( ((+0.5) x (((100.)) )re.
(19)
where &D S El is the of constrained edges, and AME is the Adaptive Multi- Multi-Channel Equivariant layer proposed in Kong et al. (2023). Readers are referred to the original paper for further details.
C.3. Molecular Dynamies
We perform molecular dynamics (MD) simulations to assess the stability and binding affinity of linear peptides from the test set and eyclic peptides generated by our model. Simulations implementation of particle-mesh Ewald (PME) MD and executed on GeForce RTX 4090 GPUs (Salomon-Ferrer et al., 2013). For system preparation, the ffI4SB force field is applied to proteins and peptides (Maier et al., 2015). All systems are solvated to a 10 Á truncated octahedron transferable intermolecular potential three-point (TIP3P) water box and 150 nM "at counterions are added to neutralize charges and simulate the normal saline environment (Jorgensen et al., 1983; Li et al., 2024c). Prior to equilibration, two rounds of energy minimization are performed: the first relaxes solvent molecules and Na /CI counterions while keeping all other atoms fixed, and the second relaxes all atoms without constraints. The systems are then gradually heated from 0 K to 310 K over 500 ps under harmonic restraints of 10 kcal mol Á on proteins and peptides. Subsequently, equilibration is carried out at 300 K and I bar under NPT conditions, with harmonic restraints on protein and ligand atoms progressively reduced from 5.0 to 3.0, 1.0, 0.5, and finally 0.1 kcal mol A spanning a total of 2.5 ns. Production simulations are performed with temperature (300 K) and pressure (1 bar) using the Langevin thermostat and Berendsen barostat, respectively. The SHAKE algorithm is applied to constrain covalent bonds involving hydrogen atoms (Ryckaert et al., 1977), while non- bon-bonded interactions are truncated at 10.0 Å, with long-range electrostatics treated using the PME method. To estimate peptide binding energies, we further employ MM/PBSA calculations (Genheden & Ryde, 2015). While MD simulations provide high accuracy evaluating conformational stability and binding affinity, they are computationally expensive. Therefore, we randomly select two target proteins from the test set and generate one cyclic peptide using head-to-tar and disulfide bond cyclization strategies for evaluation.
conducted using the Amber22 package with the CUDA
C.4. Hyperparamter details
We train CP-Composer on 24G memory RTX 3090 GPU with AdamW optimizer. For the autoencoder, we train for up to 100 epochs and save the top 10 models based validation performance. We ensure that the total number of edges (scaling with the square of the number of nodes) does not exceed 60,000. The initial learning rate is set to 10-1 and is reduced by factor of 0.8 if the validation loss does not improve for 5 consecutive epochs. Regarding the diffusion model, we train for no more than 1000 epochs. The learning rate is 10-4 and decay by 0.6 and early stop the training process if the validation loss does not decrease for 10 epochs. During the training process, we set the guidance strength as 1 for sampling at the validation stage. The structure details of the autoencoder and the diffusion model are the same as Kong al. (2024). For the RBF kernel, we use 32 feature channels.
D. Further Analysis
D.1. Necessity of RBFs
We evaluate the influence of the RBFs to the quality of the generation of peptide under most difficult setting: Bicycle peptide (26 samples in test set). In Table 5, Based on the validation and parameter sensitivity study, we can conclude the necessity of RBF design to support the distance control. Further, an saturation beyond 16 channels observed, indicating that finite RBFs is enough for empirical performance.
D.2. Generation efficiency
In Table 6, we show the runtime comparison between our method and the DiflPepBuilder when they both use a 24GB RTX3090 GPU.
15

---

Zero-Shot Cyclic Peptide Design via Composable Geometrie Constraints
Table 5. Success among different number of RBFs
Succ.(w=2)
Bicycle peptide
RBFs=0
26.92%
RBFs=16
30.76%
RBFs=32
30.76%
Table Runtime of our method and BifiPer
CP-Composer
DiffPepBuilder
second per peptide
1.42s
29.94s
Stapled peptide
Hcad-to-Tai peptide
Disulfide peptide
Bicycle peptide
Figure 7. Four types of generated cyclic peptides, with the red boxes highlighting the position for cyclization.
E. A Additional Visualizations
In Fig. 7, we show more cases the stapled, ta-tal, disulfur and bicycle peptide.
F. Code Availability
The codes for our CP-Composer is provided at the link ctwp://ph..ocoom///////o/o//// http://cco0222cccccoooeeeeaaaaa Composer_final.
16


Reviews:
[{"review_id": "FdGjJjFQAn", "reviewer": "Reviewer_1riF", "summary": "The paper proposes CP-Composer, a novel diffusion-based generative framework for zero-shot cyclic peptide design. The authors motivate their approach by highlighting the data scarcity problem in cyclic peptide design, where obtaining experimental data for diverse cyclization patterns is challenging. The key innovation presented in the paper is the decomposition of complex cyclisation constraints into simpler, composable \"unit constraints\" representing type and distance relationships. This decomposition allows the model to be trained on more readily available linear peptide data, learning these unit constraints and their combinations, and then generalizing to unseen, complex cyclic constraints at inference time. The method is evaluated on several cyclisation strategies (stapled, head-to-tail, disulfide, and bicycle peptides), demonstrating improved success rates in generating valid cyclic structures compared to existing baselines. The authors also present results from molecular dynamics simulations, providing evidence for the stability and binding affinity of the generated peptides. The primary application is the design of novel cyclic peptides, which have potential as therapeutic drug candidates. Overall, the paper presents a well-written and technically sound approach, contributing to the fields of peptide design and constrained generative modelling.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your suggestions!\n\n> Q1:Comparing against any existing methods specifically designed for cyclic peptide generation is important for contextualizing the performance gains.\n\nWe include CADS, an advanced diffusion conditional sampler, and DiffPepBuilder, a model specifically designed for disulfide peptides, as below:\n\n|Succ.|Staple|Head-Tail|Disulfide|Bicycle|\n|-|-:|-:|-:|-:|\n|Ours|21.42%|65.11%|41.25%|30.76%\n|CADS|27.14%|45.54%|3.75%|3.85%| \n|DiffPepBuilder|-|-|23.07%|-|\n\nFor CADS sampler, we set the w=2 and use the initial noise scale as 0.25. CADS is acceptable under simple constraints but struggles with more complex constraints like disulfide and bicyclic peptides. Notably, our zero-shot approach outperforms DiffPepBuilder, which is specifically designed for disulfide peptides.\n\n> Q2: The connection between the ideal conditional score (Eq.2) and the implemented guided score (Eq.3) should be strengthened.\n\nIn fact, the rationale of Eq.2 and Eq.3 are linked by the following distribution\n$$ \\tilde{p}\\_t(\\mathcal{G}\\_\\mathbf{z}^{(t)}|\\mathbb{C}) \\propto p\\_t(\\mathcal{G}\\_\\mathbf{z}^{(t)})  p\\_t(\\mathbb{C}|\\mathcal{G}\\_\\mathbf{z}^{(t)})^w, $$\nwith the corresponding conditional score\n$$\\nabla\\_{\\mathcal{G}\\_\\mathbf{z}^{(t)}}\\log \\tilde{p}\\_t(\\mathcal{G}\\_\\mathbf{z}^{(t)}|\\mathbb{C}) =\\nabla\\_{\\mathcal{G}\\_\\mathbf{z}^{(t)}}\\log p\\_t(\\mathcal{G}\\_\\mathbf{z}^{(t)})  +w\\nabla\\_{\\mathcal{G}\\_\\mathbf{z}^{(t)}}\\log p\\_t(\\mathbb{C}|\\mathcal{G}\\_\\mathbf{z}^{(t)})\\approx\\epsilon\\_\\theta(\\mathcal{G}\\_\\mathbf{z}^{(t)},t) + w\\nabla\\_{\\mathcal{G}\\_\\mathbf{z}^{(t)}}\\log p\\_t(\\mathbb{C}|\\mathcal{G}\\_\\mathbf{z}^{(t)})  .$$\n\nIn particular, Eq.2 directly models  $\\log p\\_t(\\mathbb{C}|\\mathcal{G}\\_\\mathbf{z}^{(t)})$ by an externally trained energy function. Eq.3 instead follows classifier-free guidance by rewriting $\\nabla\\_{\\mathcal{G}\\_\\mathbf{z}^{(t)}}\\log p\\_t(\\mathbb{C}|\\mathcal{G}\\_\\mathbf{z}^{(t)})=\\nabla\\_{\\mathcal{G}\\_\\mathbf{z}^{(t)}}\\log p\\_t(\\mathcal{G}\\_\\mathbf{z}^{(t)}|\\mathbb{C})-\\nabla\\_{\\mathcal{G}\\_\\mathbf{z}^{(t)}}\\log p\\_t(\\mathcal{G}\\_\\mathbf{z}^{(t)})\\approx\\epsilon\\_\\theta(\\mathcal{G}\\_\\mathbf{z}^{(t)},\\mathbb{C},t)-\\epsilon\\_\\theta(\\mathcal{G}\\_\\mathbf{z}^{(t)},t),$ which gives Eq.3 after simplification.\n\n> Q3：A more thorough analysis of failure cases would be insightful to understand the method's limitations.\n\nAs for failure cases, they commonly occur when excessively large controling strength w degrade molecular quality. We analyzed peptide structures generated with w=6 (https://anonymous.4open.science/r/Rebuttal-68EF/readme.md) and found that they often exhibited strained backbones and unrealistic conformations. This highlights the trade-off between guidance strength and structural integrity, suggesting that an adequate selection strategy for w could further improve robustness.\n\n> Q4: The relative advantage of CP-Composer is difficult to assess and the section would benefit from a more extensive comparisons with advanced baselines, which should also generalise to this more challenging setting.\n\nFirst, our model allows arbitrary high-order combinations, as shown in the paper. Second, the comparison with DiffPepBuilder below indicate that, despite being a general zero-shot model, our approach outperforms the baseline specifically designed for disulfide peptides.\n\n|2*-S-S-|CP-Composer|DiffPepBuilder|\n|-|-:|-:|\n|Succ.|62.0%| 30.48%|\n\n> Q5: The authors use t-SNE plots to visualise the generation of non-linear peptides. This could be strengthened by adding quantitative sequence analysis and a comparison of training and generated peptide sequences.\n\nSorry for the confusion. Our current cluster analysis in Figure 6 is already based on the embedding generated from ESM2 model, which outputs embeddings based on the sequence information.\n\n> Q6: Could you elaborate on the specific challenges posed by Disulfide and Bicycle peptides for the baselines? \n\nDisulfide and Bicycle peptides need requires more strict constraints than Stapled peptide and Head-to-tail peptide. Dislfide peptide need one distance constraint unit and two type constraint unit. Bicycle peptides need three distance constraint units and three type constraint units. While the Head-to-tail peptide only needs one distance constraint unit and the Stapled peptide needs one distance constraint and two type constrinis easier to reach as both K-D and K-E are accepted.\n\n> Q7: Have you investigated any techniques to further improve the success rates, particularly for the higher order combinations?\n\nAs an initial attempt at zero-shot cyclic peptide generation, our focus is to demonstrate the feasibility and generalizability of our framework, which already shows promising results. However, in more complex constraint combinations, conflicts may arise, potentially driving the generated peptides in divergent directions. Addressing these conflicts to further improve success rates is an important challenge that we leave for future research.", "claims_and_evidence": "The central claim of the paper is that CP-Composer enables effective zero-shot cyclic peptide design via composable unit constraints. However, to more convincingly demonstrate the advantages of the proposed approach and solidify its claims, the authors should expand the baseline comparison and provide a more rigorous theoretical justification for the guidance mechanism. Specifically, the comparison should be extended to include more advanced guidance techniques, such as the unified guidance framework presented in [1], which could readily incorporate the proposed unit constraints, a simply classifier-free guidance together with the CADS sampler [2]. Additionally, comparing against any existing, even if limited, methods specifically designed for cyclic peptide generation is important for contextualizing the performance gains. Moreover, the connection between the ideal conditional score (Eq.2) and the implemented guided score (Eq.3) should be strengthened. A more formal derivation, potentially drawing inspiration from the diffusion posterior sampling approach of [3] or the generalized h-transform [4] (who essentially end up with the same terms as Eq.3 for controlled generation), would provide a more solid theoretical foundation for the chosen guidance strategy. Addressing these points would enhance the paper's claims.\n\n\n&nbsp;\n\n[1] Ayadi, S., Hetzel, L., Sommer, J., Theis, F., & Günnemann, S. (2024). Unified Guidance for Geometry-Conditioned Molecular Generation. Advances in Neural Information Processing Systems, 37, 138891-138924.\n\n[2] Sadat, S., Buhmann, J., Bradely, D., Hilliges, O., and Weber, R. M. Cads: Unleashing the diversity of diffusion models through condition-annealed sampling. arXiv preprint arXiv:2310.17347, 2023.\n\n[3] Chung, H., Kim, J., Mccann, M. T., Klasky, M. L., & Ye, J. C. (2022). Diffusion posterior sampling for general noisy inverse problems. arXiv preprint arXiv:2209.14687.\n\n[4] Denker, A., Vargas, F., Padhy, S., Didi, K., Mathis, S., Barbano, R., ... & Lio, P. (2024). DEFT: Efficient Fine-tuning of Diffusion Models by Learning the Generalised $ h $-transform. Advances in Neural Information Processing Systems, 37, 19636-19682.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are generally appropriate for the problem of zero-shot cyclic peptide design, utilising relevant metrics. However, the experimental design could be strengthened to better support the claims and contextualise CP-Composer's performance.\n\n- Section 4.1 (Zero-Shot Cyclic Peptide Generation): This section is meant to demonstrate the core capability of generating different cyclic peptide types in a zero-shot setting. However, the limited baselines (no existing cyclic peptide methods, basic energy guidance) weaken the comparison. Moreover, a more thorough analysis of failure cases would be insightful to understand the method's limitations.\n- Section 4.2 (Flexibility in High-Order Combinations): Here, the authors show the framework's ability to handle complex, combined constraints, supporting the claim of generalisability. However, the relative advantage of CP-Composer is difficult to assess and the section would benefit from a more extensive comparisons with advanced baselines, which should also generalise to this more challenging setting.\n- Section 4.3 (Evaluations by Molecular Dynamics): This section strengthens claims of practical utility with MD simulations, but the presented scope (two targets, two cyclization strategies) restricts general conclusions. More simulations, potentially build on faster approximate methods, would be great.\n- Section 4.4 (Generalisation beyond Available Data): Here, the authors use t-SNE plots to visualise the generation of non-linear peptides. This could be strengthened by adding quantitative sequence analysis and a comparison of training and generated peptide sequences.", "theoretical_claims": "I did not check the proofs in detail, focusing instead on the overall conceptual\nsoundness and experimental validation.", "experimental_designs_or_analyses": "I reviewed the experimental designs, as detailed above. The primary concerns are the limited choice of baselines, which hinders a comprehensive evaluation of performance, and the need for a more rigorous theoretical justification connecting the proposed guidance mechanism to established works in the field.", "relation_to_broader_scientific_literature": "The paper cites relevant works in the areas of diffusion models, geometric deep learning, and peptide design. However, the discussion of related work and the theoretical grounding could be strengthened. The discussion of diffusion guidance could be significantly improved by referencing and incorporating more advanced techniques, such as the unified guidance framework in [1] or the condition-annealed sampling approach in [2]. Furthermore, a more rigorous theoretical justification connecting the proposed guidance to established work like DPS [2] and DEFT [3] is needed. This would better position the work within the existing literature and address the limitations in the baseline comparisons.", "essential_references_not_discussed": "No essential works appear to be missing.", "other_strengths_and_weaknesses": "**Originality**: The setting of zero-shot cyclic peptide design via composable unit constraints, enabling training on readily available linear peptide data, is a novel contribution. However, the derivation of the guidance mechanism lacks novelty and could benefit from a more rigorous theoretical grounding, as discussed in previous sections. This makes the decomposition of complex cyclisation constraints into simpler, composable units (type and distance) the primary source of originality.\n\n**Significance**: The work addresses a significant challenge in drug discovery, and if the claims were fully supported by a more comprehensive experimental evaluation, the work would be relevant for the peptide design community.\n\n**Clarity**: The paper is well-written and structured logically, with core concepts and the proposed method clearly explained. The figures are informative, enhancing overall clarity.", "other_comments_or_suggestions": "No.", "questions_for_authors": "1) Could you elaborate on the specific challenges posed by Disulfide and Bicycle peptides for the baselines? Here, CP-Composer achieves the best success rates (even better than Stapled and HT) while the baselines fail. \n2) Have you investigated any techniques to further improve the success rates, particularly for the higher order combinations?\n\n&nbsp; \n\n____ \nI am willing to increase my score if the authors address the raised concerns.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Sasf85xOhR", "reviewer": "Reviewer_ctzr", "summary": "Cyclic peptides exhibit superior biochemical properties and can be used to address emerging medical needs. However, due to the limited availability of training data, research on cyclic peptide design remains scarce. This paper introduces a novel generative model that employs a composable constraint approach, enabling the generation of cyclic peptides during inference, even without cyclic peptide training data. Specifically, the proposed method decomposes complex cyclization patterns into unit constraints, which are incorporated into a diffusion model through geometric conditioning on nodes and edges. During training, the model learns unit constraints and their various combinations from linear peptides. At inference, specific cyclization constraint combinations are imposed as input. Experimental results demonstrate that, despite being trained solely on linear peptides, the model can generate diverse target-binding cyclic peptides, achieving a significant improvement in success rate.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for the insightful comments which help improve the quality of our paper!\n\n> Q1: The type and distance constraints may not be independent but rather intertwined, which the authors have not discussed.\n\nSorry for the confusion. We ensure that the constraints are jointly feasible by considering their dependencies both in the data and the model. First, the constraint combinations are sampled from the joint distribution derived from real-world data, based on the dataset during training and based on chemical knowledge during inference. Second, our model inherently accounts for these dependencies, as the constraints are input together and fused within the hidden layers to output the conditional denoising score.\n\n> Q2: I believe the authors should compare their approach with basic diffusion models and some recent conditional generative models.\n\nThanks for the suggestion. We further include two more baseline methods, CADS, an advanced diffusion conditional sampler, and DiffPepBuilder, a model specifically designed for disulfide peptides, as below:\n\n|  Succ.     | Staple | Head-Tail | Disulfide | Bicycle |\n|-------|-----------:|-----------:|-----------:|-----------:|\n|ours|21.42%|65.11%|41.25%|30.76%\n| CADS | 27.14%     | 45.54%     | 3.75%      | 3.85%      | \n| DiffPepBuilder| -     | -     | 23.07%      | -      |\n\nFor CADS sampler, we set the w=2 and use the sampler with initial noise scale as 0.25. The results indicate that CADS is acceptable under simple constraints but struggles with more complex constraints like disulfide and bicyclic peptides. Notably, despite being a general zero-shot model, our approach outperforms DiffPepBuilder, which is specifically designed for disulfide peptides.\n\n\n> Q3: For the generated molecules, the authors only evaluate whether the cyclic peptide is successfully generated but do not assess the validity of the generated molecules. In addition to the success rate, they should also consider whether there are any unreasonable atomic types or coordinates in the generated structures, which could be measured using an appropriate metric. For the AA-KL and B-KL metrics, it does not clearly explain how the distribution divergence is computed.\n\nSorry for the confusion. We assess the validity of generated peptides by evaluating their residue composition and structural features to ensure they resemble natural peptides. Specifically, we use KL divergence on residue types and dihedral angles. AA-KL measures the KL divergence between amino acid distributions in generated peptides and reference peptides, excluding the controlled amino acid types. B-KL quantifies the KL divergence between dihedral angle distributions of generated and reference peptides, ensuring realistic backbone conformations. Additionally, we assess the structural stability of generated peptides using Rosetta energy scores. Our results show that 85.54% of cyclic peptides satisfying constraints achieve negative Rosetta scores, indicating their physical plausibility. This suggests that the model generates valid and stable cyclic peptides.\n\n\n> Q4: In Table 2, the success rate of “2*Stapled” does not change with variations in w. While the paper acknowledges this phenomenon, it does not discuss the possible reasons behind it. What could be causing this? Did the authors check whether the unsuccessful cases at w = 2, 2.5, and 3 were the same set of samples?\n\nWe appreciate the insightful question! Upon examining the failure cases for w=2,2.5, and 3, we found that they are nearly identical. This suggests that, beyond a certain threshold, these cases have already collapsed into failure modes. As a result, further increasing the constraint strength does not impact the success rate.\n\n\n> Q5: However, in real-world scenarios, is the combination of these conditions truly linear? (Is adding condition A and condition B really equivalent to A + B?) What do you think about this? Are there any methods to explore this further?\n\nThank you for your thoughtful question. We think there are some combinations not directly addictive. For example, a bicycle peptide may struggle to also satisfy the stapled peptide constraints, which we have observed in zero success rates for such cases. In most application scenarios, meaningful combinations are ensured by expertise in structural chemistry and biology. Additionally, low success rates for certain combinations can help identify infeasible or unrealistic configurations.", "claims_and_evidence": "Yes, the proposed claims are clear and well-supported by corresponding evidence.", "methods_and_evaluation_criteria": "Yes, the proposed method in this paper makes sense for peptide design problems, particularly for cyclic peptide generation.\n\nRegarding the method details, the paper proposes using a composable constraint approach to enforce cyclic peptide constraints. Specifically, it combines **type constraints** and ** distance constraints** as the generation constraints for cyclic peptides. This approach is quite novel and makes sense. However, these constraints may not be entirely **independent** but rather **intertwined**, which the authors have not discussed.", "theoretical_claims": "Yes, I have checked the experimental design and results of the paper and identified the following issues.", "experimental_designs_or_analyses": "Yes, I have checked the experimental design and results of the paper and identified the following issues.\n\n### Design of the experiments\n\n1. The paper only compares CP-Composer with **PepGLAD** and the **EG method**, without including other diffusion- or flow-based methods. I believe the authors should compare their approach with **basic diffusion models** and some **recent conditional generative models**, rather than only comparing it to a single backbone model.\n2. For the generated molecules, the authors only evaluate whether the cyclic peptide is successfully generated but do not assess the validity of the generated molecules. In addition to the success rate, they should also consider whether there are any unreasonable atomic types or coordinates in the generated structures, which could be measured using an appropriate metric.\n\n### Results\n\nIn Table 2, the success rate of **“2\\*Stapled”** does not change with variations in **w**. While the paper acknowledges this phenomenon, it does not discuss the possible reasons behind it. What could be causing this? Did the authors check whether the unsuccessful cases at **w = 2, 2.5, and 3** were the same set of samples?\n\n### Writing \n\nThe paper does not provide the deetailed explanation for the metrics. For the **AA-KL** and **B-KL** metrics, it does not clearly explain how the distribution divergence is computed.", "relation_to_broader_scientific_literature": "The proposed composable constraint approach for generating cyclic peptides with limited data is novel and can also provide insights for generation tasks in other data-scarce domains.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "### Pros\n\n* The article proposes a compositional conditional generative model that can generate target peptides in a zero-shot manner by combining multiple constraints.\n* The article provides a proof of the method’s validity.\n\n### Cons\n\n* The experimental section is not sufficiently comprehensive; more baselines need to be compared. \n* Additionally, some experimental phenomena require more detailed discussion (see the experimental section for details).\n* There are some grammatical issues and typos, and the writing needs improvement.", "other_comments_or_suggestions": "The writing can be improved. I notice several typos:\n\n* C.4. Hyperparamter details: Hyperparameter\n* The overal workflow is depicted in Fig. 2. --> overall\n* The sampled is acquired (near eq. 8): --> sample\n\nI’ve noticed these errors, and there may be others as well. The author should carefully proofread the text to ensure accuracy.", "questions_for_authors": "I think this method is simple and novel, and the compositionality of the conditions has been proven to be injective. However, in real-world scenarios, is the combination of these conditions truly linear? (Is adding condition A and condition B really equivalent to A + B?) What do you think about this? Are there any methods to explore this further?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "u6uP1vYGKq", "reviewer": "Reviewer_EnLZ", "summary": "This paper presents CP-Composer, a zero-shot cyclic peptide design framework using composable geometric constraints. The key innovation lies in decomposing complex cyclization strategies into type constraints and distance constraints, integrated into a geometric graph diffusion model via conditional encoding. Experiments demonstrate superior success rates across four cyclization tasks compared to baselines, while molecular dynamics (MD) simulations confirm enhanced conformational stability and binding affinity over linear peptides. The framework supports flexible cyclic peptide designs without requiring training data, offering a promising tool for customizable drug discovery.\n\n## update after rebuttal\n\nThanks for your response, I will keep my positive score.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> Q1: Limited MD Validation: Only two test cases are simulated. A larger sample size and error analysis (e.g., standard deviations across replicates) would improve confidence.\n\nSorry for the limitation, due to the time and resource limitation, we adopted the rhotheta score as an auxiliary metric to validate our generated peptides. Specifically, we first relax the peptide using a dedicated force field to establish a stable cyclic conformation; thereafter, we further optimize the structure with a rhotheta relaxer and compute the corresponding rhotheta score. Our findings indicate that 85.54% of the target peptides achieve a negative rhotheta score, signifying an energetically favorable state. The rhotheta score is a widely used metric for peptide evaluation, providing an efficient method for assessing large sample sizes.\n\n> Q2: The paper does not clarify whether test-time cyclization strategies (e.g., disulfide bonds) involve constraints entirely absent from training. If training data includes residues like cysteines (common in disulfide bonds), the \"zero-shot\" claim might overstate novelty.\n\nSorry for the confusion. Here \"zero-shot\" means that the specific combination of constraints required for cyclic peptides is not present during training. While the training data includes individual unit constraints (e.g., cysteine residues), the exact combination needed for cyclization is not observed. Our method learns combinations of constraints in linear peptides during training and generalizes to their combinations during inference to generate cyclic peptides.\n\n> Q3: The theoretical claims are mathematically correct under ideal assumptions, but practical implementations introduce approximations (finite RBFs) that weaken injectivity guarantees. The reliance on external proofs for equivariance is acceptable but leaves a minor risk of inherited errors. Overall, the proofs are valid but lack robustness analysis for real-world settings... The experimental design adequately addresses core claims but lacks rigor in validation: ... missing ablation studies.\n\nWe evaluate the influence of the RBFs to the quality of the generation of peptide under most difficult setting: Bicycle peptide(26 samples in test set):\n\n|  Succ.(w=2) | Bicycle peptide | \n|-------|-----------:|\n| RBFs=0  |26.92%   | \n| RBFs=16 | 30.76% |\n| RBFs=32 | 30.76% |\n\nBased on the validation and parameter sensitivity study, we can conclude the necessity of RBF design to support the distance control. Further, an saturation beyond 16 channels is observed, indicating that finite RBFs is enough for empirical performance.\n\n> Q4: Reproducibility: While code is provided, computational resource requirements are underspecified.\n\nWe train CP-Composer on a 24G memory RTX 3090 GPU with AdamW optimizer. More details can be found in Section C.4.\n\n> Q5: Add runtime metrics (e.g., seconds per peptide generation) to Appendix C.4 for scalability assessment.\n\nHere we show the runtime comparison between our method and the baseline method when they both use a 24GB RTX3090 GPU.\n\n|       | CP-Composer | DiffPepBuilder | \n|-------|-----------:|-----------:|\n| second per peptide | 1.42s     | 29.94s     |\n\n> Q6: Were generated peptides assessed for chemical synthesizability (e.g., using SAscore or RAscore)? If not, how might impractical structures affect real-world utility?\n\nThe SA score is primarily designed for assessing the synthesizability of small molecules and is not directly applicable to peptides, which follow a distinct synthesis methodology. For peptides, higher hydrophobicity can lead to aggregation and hinder synthesis. Thus, we analyze the distribution of GRAVY scores [1], which measure peptide hydrophobicity. The results, provided in the linked analysis（https://anonymous.4open.science/r/Rebuttal-68EF/readme.md), demonstrate that the generated peptides exhibit a hydrophobicity distribution similar to that of natural peptides, suggesting that they are likely to be synthesizable.\n\nReference：\n[1] Kyte, Jack, and Russell F. Doolittle. \"A simple method for displaying the hydropathic character of a protein.\" Journal of molecular biology 157.1 (1982): 105-132.", "claims_and_evidence": "These claims are supported by convincing evidence, both theoretical and empirically validated. However, there are some small holes in the validation (robustness of MD and ablation studies) that slightly weaken the argument.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are largely appropriate and well-aligned with the problem of cyclic peptide design, but certain aspects could be strengthened.\n- Limited MD Validation: Only two test cases are simulated. A larger sample size and error analysis (e.g., standard deviations across replicates) would improve confidence.\n- The paper does not clarify whether test-time cyclization strategies (e.g., disulfide bonds) involve constraints entirely absent from training. If training data includes residues like cysteines (common in disulfide bonds), the \"zero-shot\" claim might overstate novelty.", "theoretical_claims": "The theoretical claims are mathematically correct under ideal assumptions, but practical implementations introduce approximations (finite RBFs) that weaken injectivity guarantees. The reliance on external proofs for equivariance is acceptable but leaves a minor risk of inherited errors. Overall, the proofs are valid but lack robustness analysis for real-world settings.", "experimental_designs_or_analyses": "The experimental design adequately addresses core claims but lacks rigor in validation: small MD sample size and missing ablation studies.", "relation_to_broader_scientific_literature": "CP-Composer addresses the unique challenges of cyclic peptide design through composable constraints and zero-point learning, providing a new paradigm for customizable molecule generation with broad scientific and industrial relevance,", "essential_references_not_discussed": "No essential references have been omitted.", "other_strengths_and_weaknesses": "## Weaknesses:\n- Method: lack of ablation studies.\n- Validation: Small MD Sample Size: Only two test cases are simulated, reducing confidence in stability claims. Diversity metrics are missing.\n- Synthesizability: No discussion of whether generated peptides are chemically feasible or compatible with synthesis pipelines.", "other_comments_or_suggestions": "Add runtime metrics (e.g., seconds per peptide generation) to Appendix C.4 for scalability assessment.", "questions_for_authors": "Were generated peptides assessed for chemical synthesizability (e.g., using SAscore or RAscore)? If not, how might impractical structures affect real-world utility?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper introduces CP-Composer, a novel framework for zero-shot cyclic peptide design using composable geometric constraints. The work addresses the challenge of designing cyclic peptides with minimal training data by leveraging a diffusion model and geometric conditioning. The paper is well-received, with notable strengths in its innovative approach, solid experimental results, and clarity in presentation.

Reviewer scores initially varied with scores of 2, 3, and 3 (only 3 reviews were received), reflecting a range of opinions primarily concerning baseline comparisons and theoretical grounding. Post-rebuttal discussions involved authors addressing all major concerns, such as conducting extensive experiments against additional baselines like CADS and DiffPepBuilder, and explaining the connection between the guided and conditional scores more clearly. These clarifications were well-received by reviewers who engaged with the discussion, with one reviewer improving their score from 3 to 4. Note that the reviewer who scored 2 did not respond to the rebuttal despite repeated prompting.

The work's strength lies in its innovative design and potential application to drug discovery. However, the reviewers highlighted that additional baseline comparisons and further theoretical backing for guidance mechanisms would strengthen the claims. The rebuttal addressed these points effectively, reinforcing the paper's validity. The authors also did a good job of acknowledging the limitations of the approach and identifying avenues for future work.

Overall, the paper presents valuable contributions to the field of peptide design and constrained generative modelling, and I recommend accepting it as a solid addition to ICML.
Decision: Accept (poster)