Compositional Flows for 3D Molecule and Synthesis Pathway Co-design
Authors: Tony Shen
Seonghwan Seo
Ross Irwin
Kieran Didi
Simon Olsson
Woo Youn Kim
Martin Ester
Venue: ICML 2025 poster (2025)
Keywords: drug discovery
synthesizable molecular design
GFlowNets
flow matching
Primary area: applications->chemistry_physics_and_earth_sciences
TL;DR: GFlowNets meet flow matching for 3D molecules generation via synthesis pathways.

Abstract: Many generative applications, such as synthesis-based 3D molecular design, involve constructing compositional objects with continuous features.
Here, we introduce Compositional Generative Flows (CGFlow), a novel framework that extends flow matching to generate objects in compositional steps while modeling continuous states. 
Our key insight is that modeling compositional state transitions can be formulated as a straightforward extension of the flow matching interpolation process.
We further build upon the theoretical foundations of generative flow networks (GFlowNets), enabling reward-guided sampling of compositional structures. 
We apply CGFlow to synthesizable drug design by jointly designing the molecule's synthetic pathway with its 3D binding pose.
Our approach achieves state-of-the-art binding affinity and synthesizability on all 15 targets from the LIT-PCBA benchmark, and 4.2x improvement in sampling efficiency compared to 2D synthesis-based baseline.
To our best knowledge, our method is also the first to achieve state of-art-performance in both Vina Dock (-9.42) and AiZynth success rate (36.1\%) on the CrossDocked2020 benchmark.

Compositional Flows for 3D Molecule and Synthesis Pathway Co-design
Tony Shen
Seonghwan Seo 22 Ross Irwin
Kieran Didi 56
Simon Olsson
Woo Youn Kim Martin Ester'
Abstract
sequence of compositional reaction steps and predict their continuous 3D conformations relative to protein target (Li et al., 2022). To this end, we propose a bow-based generative framework that jointly models the compositional structure and continuous state of objects.
Many generative applications, such as synthesis- based 3D molecular design, involve construct- ing compositional objects with continuous fea- tures. Here, we introduce Compositional Gener- ative Flows (CGFlow), a novel framework that extends flow matching to generate objects in com- positional steps while modeling continuous states, Our key insight is that modeling compositional state transitions can be formulated forward extension of the flow matching interpo- lation process. We further build upon the theo- retical foundations of generative flow networks (GFlowNets)), enabling reward-guided sampling of compositional structures. We apply CGFlow to synthesizable drug design by jointly design- ing the molecule's synthetic pathway with its 3D binding pose. Our approach achieves state-of- the-art binding affinity and synthesizability on all 15 targets from the LIT-PCBA benchmark. and 4.2x improvement in sampling efficiency compared to 2D synthesis- based baseline. To our best knowledge, our method also the first to achieve state df-art-performance in both Vina Dock (-9.42) and AiZynth success rate (36.1%) 1%) the Cross CrossDock002020 benchmark.
Diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2021) and flow matching models (Lip- man et al., 2023) have achieved state-of-the-art performance in high-dimensional modeling tasks such as 3D molecule generation and protein structure design (Hoogeboom et al., 2022; Campbell et al., 2024; Schneuing et al., 2024a). How- ever, standard diffusion and flow matching are restricted to modeling all the dimensions of the object at once (Chen et al., 2024). This results in an inability to model the compo- sitional structure of objects through sequential construction steps. As consequence, two main limitation arise: (1) the validity of compositional objects cannot be ensured, as invalid generative actions cannot be masked, and (2) the potential for efficient reward credit assignment in the com- positional space is restricted (Bengio et al., 2021: Hansen et al., 2022; Yao et al., 2023). In drug design, where syn- thesizability is crucial for wet-lab validation, molecules can be naturally viewed compositional objects constructed through sequential synthesis steps. Unfortunately, exist- ing diffusion and flow matching models lack the ability to effectively model and respect the compositional nature of synthesis constraints when generating molccules.
straight-
Sequential models are a natural fit for generating composite objects. For instance, autoregressive models have been ap- plied for 3D molecular design (Peng al., 2023; Gebauer et al., 2020). However, current autoregressive models lack mechanisms to correct eтrors from earlier steps, causing slight errors in early position predictions to cascade (Jin et al., 2022). Generative flow networks (GFlowNets; Ben- gio et al., 2021) have recently shown success in sampling compositional structure for synthesis- molecule design (Koziarski et al., 2024; Cretu et al., 2024; Seo et al., 2024), but remain limited to 2D molecules.
1. Introduction
Sampling objects through compositional steps while model- ing continuous state is essential for a wide range of scientific applications (Jain et al., 2023a; Wang et al., 2023). One such important application is synthesizable targer-based drug de- sign, which aims to jointly generate molecules through
"Equal contribution 'School of Computing Seience, Simon Fraser University, Canada 'Deparmment of Chemistry, KAIST, Re- public of Korea 'Molecular AI, Discovery Sciences. R&D, As- traZeneca 'Department of Computer Science and Engineering, Chalmers University of Technology. Sweden 'Department of Com- puter Science, University of Oxford, UK "NVIDIA. Correspon- dence to: Tony Shen <tsa87 @sfu.ca>..
In this paper, we identify the key gap in standard flow match- ing and sequential models when generating compositional objects with continuous properties. To address this lim- itation, we introduce Compositional Generative Flows (CGFlow), novel generative framework that enables flow-
Proceedings of the 4dnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Object æt (3D molecule)
Ct=0
0.225
0t=0.5
0
1t=1
Composition C (Synthetic pathway)
Reductive Amination
Amine Condensation
Amination
Ct=0
00
Ct=
Ct=0.75
Ct=1
HN
Figure 1. Overview of 3DSynthFlow generation. 3D Molecule x (C, S) consisting of its synthesis pathway and 3D conformation (visualized using æ). CGFlow generation interleaves 1). the continuous process for modeling position S, and 2). the sequential sampling of synthesis steps discrete intervals (t=(0, 0.25, 0.5, 0.75 The modeling of synthesis pathways and position are both dependent on the object æ, {Se, C. h. ensuring the interplay between the two processes.
based compositional generative modeling. Our key insight is that compositional generation in flow matching can be realized through straightforward extension of the interpola- tion process to accommodate compositional state transitions. CGFlow represents a new generative modeling paradigm that combines the strengths of flow matching models for high-dimensional data while respecting the innate composi- tional nature of objects.
interdependence throughout the generative process.
As an application of the CGFlow framework, we present 3DSynthFlow, the method for target- based drug design en- suring synthesizability. We combine flow matching- -based 3D structure generation with the GFlowNet- synthesis- aware molecular generative model developed by Seo et al. (2024). Fig. illustrates how 3DSynthFlow jointly gener- ates the synthesis pathway (compositional structure) and 3D conformation (continuous state) of molecules. Previ- ous flow-based generative models focused on generating either the 3D molecular structure or the synthesis pathway, but not both (see Sec. 5). 3DSynthFlow can jointly gener- ate synthesis pathways and 3D molecular structures. This enables effective modeling of protein-ligand interactions and ensures synthesizability, both of which are essential for target-based drug discovery.
CGFlow consists of two interleaved flow processes: (1) Compositional Flow for modeling the probability path of compositional structure from data distribution to empty structures, and (2) State Flow for transporting the state variables associated with the compositional structure from data distribution noise distribution.
To generate the interpolation path from data to noise, Com- positional Flow progressively dismantles the compositional structure until it reaches an empty state. State Flow follows the standard optimal transport interpolation of flow match- ing, with the distinction that it assigns higher noise levels to the states of components removed earlier in the process, as described in Ruhe al. (2024).
In our experiments, we evaluate 3DSynthFlow on the task of designing synthesizable drugs directly within protein pockets. 3DSynthFlow achieves 4.2x sampling efficiency improvement, and state-of-the-an performance across all 15 targets in the LIT-PCBA benchmark (Tran-Nguyen et al., 2020) for binding affinity. 3DSynthFlow can be extended to pocket-conditional setting and achieve state perfora-erfoomancce in both Vina Dock (-9.42) and AiZynth success rate (36.15 %)) on the CrossDocked benchmark.
To generate compositional structures from the empty state, CGFlow samples constructive compositional steps with the generative policy, which can be modeled using distribution learning approaches, reinforcement learning, or GetowNets. In particular, GFlowNets is used to prompt efficient explo- ration of compositional state spaces by soward-guides sam- pling (Bengio al., 2021). The conditional flow matching (CFM) objective (Lipman al., 2023) is used to estimate the vector field for generating state variables. Both composi- tional structure and state variables serve as inputs, ensuring
Our contributions are summarized as follows:
We propose Compositional Generative Flows (CGFlow), flow-hased framework that enables generation of com- positional objects while modeling continuous states.
We incorporate GFlowNets in CGFlow enable effi-
2

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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
cient exploration of compositional state-space for high- rewarded samples.
3. Compositional Generative Flows
CGFlow is generative framework for modeling composi- tional objects with continuous states. The framework con- sists of two interleaved flows: the Compositional Flow for modeling compositional structures and the State Flow for modeling continuous states.
We use our compositional framework to develop 3DSyn- thFlow for 3D molecule and synthesis pathway co-design. 3DSynthFlow achieves x.2x improvement in sampling efficiency and demonstrate significant improvements in binding affinity and ligand efficiency on the LIT-PCBA benchmark.
Data representation. Many applications naturally re- quire compositional structure modeling, such as composing molecules via synthesis pathways (Gao et al., 2022) or con- structing a causal graph (Nishikawa-Tonn Toomay et al., 2024).
To the best of our knowledge, 3DSynthFlow is the first model to achieve state-of-the-ar performance in both binding aftinity and synthesis success rate on Cross- Docked2020.
Here, we represent an object x tuple (C, where C denotes the compositional structure and S represents the associated continuous states. For given object, the compositional structure is defined as an ordered sequence C = (C()) )= where n denotes the number of its compo- sitional components (e.g., molecular building blocks). The i-th component C(i) is added at the i-th generative step of the trajectory (e.g., synthesis pathway).
2. GFlowNets preliminary
Generative Flow Networks (GFlowNets; Bengio et al., 2021) are family of probabilistic models that learn a stochastic policy to construct compositional objects x E X proportional to the reward of terminate state R(x), i.e., p(z) x R(x). Each object æ is constructed through a trajec- tory 7 (su - ... - 8n = x) E 'T from the initial state so and series of state transitions s + s', where the terminate state is the object sn = x E X.
Each compositional component Cl) contains m, points (e.g,, atoms) and my may vary across components. Each point has an associated continuous state of dimension d (e.g,, atom position). (t()) represents the states associated with component i and is of size (m,, The continuous state S is defined as an ordered tuple of all states from each component S (S y
A GFlowNet models a flow F as an unnormalized density function along a directed acyclic graph (DAG) g = AS, where S denotes the state space and A represents transitions. We define the trajectory flow FT) as a flow through the trajectory T. The node flow Fss) is defined as the sum of tra- jectory flows through the node 8, i.e., F(s) Ever F(T), and the edge flow F(s- - s') is defined as the total flow along the edge + 8', i.e., F(s 8') (o--s-) F(T).
This representation differs from standard flow matching, which models only state variables while ignoring the com- positional structure and generation order of the object. In CGFlow, the compositional structure and state variables of an object are modeled jointly, ensuring the validity of the composition in generated objects.
From the flow network, we define two policy distributions. The forward policy (s)(s) executes the state transition 8 + of from the flow distribution, i.e., (=(''|s) = F(s + s') Fs). Similarly, the backward policy (B s') dis- s',
3.1. Joint conditional flow process
We first define a joint conditional flow (Lipman et al., 2023) consisting of two components, the compositional flow and state flow. The joint conditional flow Peji (=|aa) interpo- lates the object æ from an initial state Do to the final object Φ1. At the initial state, xo = So), the compositional structure is represented as an empty graph, Co = 0, and the continuous state Sy = [] has no dimension. The final object æ = (C,,S) consists of its complete structure C₁ and its continuous states Sj. Our proposed flow must satisfy the following boundary conditions:
tributes the node flow F(s) to reverse transitions ie., Pp(sss')= F(s' + F)s((s).
To match the likelihood of generating I E X' with the re- ward function Rt two boundary conditions must be achieved. First, the node flow of each terminal state x, which repre- sents the unnormalized probability of sampling the object x, must equal its reward, i.c., F(x) = R(x). Second, the ini- tial node flow $o, which represents the partition function Z, must equal the sum of all rewards. i.c., Z Evex R(x). One such objective to satisfy these conditions is trajectory balance (TB; Malkin et al., 2023), defined as follows:
t= 0, 66(z) x1), t= 1.
60(z = zo),
P (1
(2)
Ze IT__ P=(8(18(-150) )
(TB(T) = log R(xx) II:-, Piz (1
(I)
where the PF. PB. and Z are directly parameterized to minimize the TB objective.
which ensures that at t = 0, the flow starts at the initial state No, and at = 1, it reaches the final state 21.
3

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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
3.1.1. COMPOSITIONAL FLOW
State flow interpolation
Contnouus states
1.0
0.6
Compositional Flow defines conditional probability flow over the compositional structure C, progressively transition- ing it from an empty graph Co to complete structure C1- Components are added sequentially in predefined valid or-
5
5/4
0.4
0.5
Local time
5:4
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Global time (t)
der, where C(2) is the first component added. The function k(t) determines how many components have been added at time t, defined as:
Figure 2. Local time for each component over time, with n 4.
= 0.2, and bwindow = 0.4. ( yel been initialized.
foont = indicates 5(1) has not
k(t)
0,
1= 0, min (Lt// + 1,n), t> O,
[0, 1J. Intuitively, Giecal 0 when the current time is 'gen- and (6) local = 1 when the current time surpasses (1)
''ge + wwindow
where A defines time interval between adding each compo- sitional components, At time i, the compositional structure C, includes the first (t)) components from this order. k(t) increases in discrete steps as & progresses, starting from (0) = 0 and ensuring (1) = n, such that all compo- nents are added by t 1. Each component C(i) is generated at time k = A (i - 1). To ensure that all components are generated within the valid time range, we require À < 1/n for all datapoints, satisfying 'gen S 1- The compositional structure at time / is then given by:
State flow is modeled as a linear interpolation based on Ineal combined with Gaussian noise applied throughout:
S 1)) [N(1 s + [1I
(
(i) ,0²), if )
(i)
gen
else.
(6)
where 5 represents the fully noisy initial state, and S the final refined state. The continuous state s exists only if the corresponding component C has been generated, i.e., ((() > gen-- To summarize, state flow enables the interpolation of continuous states when their associated compositional components are generated sequentially.
C = (C (1) k(t)
1==1
(4)
This formulation guarantees a gradual and sequential con- struction of C, transitioning from the empty state Co to the fully constructed structure C₁ at fixed intervals.
3.2. Sampling
During the sampling process, objects are generated by in- terleaving the integration of the state flow model pf and sampling actions using the compositional flow policy x², The process alternates between refining continuous states S₁ and sequentially constructing the compositional structure C2 at fixed time points.
Previous work models transitions across dimensions diffu- sion processes using a rate function (Campbell et al., 2023). In contrast, we formulate transitions fixed discrete inter- vals. Our approach retains key advantages of autoregressive generation, including simplified likelihood evaluation and learning objectives.
For state flow, the vector field governing the continuous states for the i-th component S is defined as 5 - s where S(3) the predicted clean state by p as formulated in previous works (Le al., 2023). The rate at which step in this vector field (()) is determined by the time remaining in the interpolation process for the state S
3.1.2. STATE FL.W
State flow defines a conditional probability path over the continuous states S = ( Each continuous state ((i) is initialized only when its corresponding compositional component (+) is generated, and components are generated at different times. Intuitively, we have greater uncertainty in the continuous states of recently added components than those generated earlier. Therefore, we introduce a temporal bias similar to that used diffusion-based video generation (Ruhe et al., 2024): the global time t is reparameterized into a component-wise local time locall defined as:
min(t
(+) end - t, At)
twindow
where (0] = ggn + bwindow is the time at which the inter- polation for component is completed, and twindow is the interpolation window. The state values 5(i) are updated using Euler's method:
(())
local = clip
t
-gen
(5)
S = S + (S()) - -(()) (
(8)
twindow
Intuitively, if 2 (1)) the state s( is directly set to the predicted clean value (((i), ensuring the coherence of the continuous state.
where Egon is the generation time of component ( twindow the interpolation time window, and clip(ar) ensures pocal E
(4)
4

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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
31
already been generated the sampled time t:
Reward Calculation R((r)
k(t)
1 -f (9)
Lstate = 1B (m) (a((()
Pije
Reach at 1-1
Train Generative Palicy
where k<(t) represents the number of components generated at time t. The refinement model (xx) predicts $
the clean continuous states for component i, and we compute the MSE loss compared to the ground truth s
Sample Component
Update until = (i+ 1)A
3.3.2. COMPOSITIONAL FLOW Loss.
C
T T )(0)
Given a pre-trained state flow model pîje- the compositional flow model T samples a trajectory T by sequentially adding a component C at i', conditioned on the current state De and self-conditioning éं. This strategy allows the compositional flow model to make decisions using less noisy estimate 2i, which is particularly advantageous in protein-ligand interaction modeling (Harris et al., 2023).
Set Noise State Sij" for the Component
Figure 3. Overview of sampling and training using the pre- se-trrined state flow model plje- A i', compositional flow model л samples a component (*))) based on the state Te and its previous prediction #9. Then, the transition function T' incorporates the component C+) into the object. At ( = L, the compositional flow model trained based on the reward of the generated object æ1.
Inspired by GFlowNets (Bengio et al., 2021), we optimize the compositional flow model such that the probability of sampling a compositional structure for 21 is proportional to its reward R(x1), ). using the trajectory balance (TB; Eqq (I)) objective. However, the object æ; S,) from trajec- tory is stochastic due to the transition function T, which samples the initial state 56") from a noise distribution. To ensure deterministic transition T(x, C(3),, we fix the random seed when sampling the initial state (
For compositional structure generation, new components C09 are sampled from the compositional flow policy x² at discrete time intervals separated by X. Transition function T(x C(O) incorporates newly sampled component (+)) into the object. T also incorporates the new component's associated state s( by sampling its value from noise distribution (typically Gaussian).
Given a deterministic transition function and fixed state flow model ODE, x, = (C,,S) is uniquely determined by given trajectory sampled from the compositional flow model क This formulation views the interpolation with the state flow model f as the transition of the state resulting from the sampled action by the compositional flow policy .de Then, TB loss is computed as:
3.3. Training objectives
We train CGFlow to jointly approximate the distribution of continuous states S and the sequential generation of the compositional structure C' with two models: (1) state flow model pf for updating continuous states, and (2) a compositional flow policy 7 for sampling compositional components. Both models are conditioned on the object a;= (C,, S.) with self-conditioning क = St) time 1, where St = ( from the previous prediction (Chen et al., 2022). This ensures their dependence on both the com- positional structure and the continuous state of the object.
LTB(T)= (10gs Zo I1:'0 PF(C()) (4 2f (0)
(10)
R(m)
)==
We provide the theoretical background in Sec.
By enabling online training, this approach generalizes be- yond the empirical data, as it can sample new data under the current policy. Alternatively, the compositional flow model can be trained using a maximum likelihood objective based on the data distribution (see Sec. A.3).
3.3.1. STATE FL.WW LOSS.
The state flow model can be trained simulation-free, and independently of the compositional flow model. For each object æ. we first assign a generation trajectory over its compositional components C. Then we can sample æ; ac- cording to the joint interpolation process (see Sec. 3.1).
We refer readers to Sec. A. for a summary of the key steps in applying CGFlow next section, we demonstrate CGFlow's application to 3D molecular generation and synthesis pathway design.
new data domain. In the
The state flow model pft takes the entire object at St) input and outputs Št+11 the predicted clean continuous states. The objective sums over the continu- ous states S(6) corresponding to components Ct+) that have
"Conceptually, it resembles an internal model of the world: used to predict the next state of the world as function of the current state and action (Bryson & Ho, 1969). The state flow model weights are fixed to remain faithful to the data distribution.
5

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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
HN-NH
the composition flow model consists of all valid synthetic steps for given structure C2 (see Sec. 1.1).. We modify the architecture from RxnFlow (Seo et al., 2024) to model the sampling policy for synthesis steps using 3D protein-ligamt complexes as input (see Sec. D.2.2). The compositional flow model is trained online as described in See. 3.3.2.
Compose
Decompose
Convert
Convert
b)
Compose
HN--NH
Decompose
Figure4 4. Illustration of synthesis-based composition rules. (a) reactant unit-based and (b) synthon unit-based (ours).
5. Related Work
Synthesis-based generative models. Generative models have emerged as the key paradigm for discovering candi- dates by bypassing the expensive virtual screening. How- ever, most generative models often render molecules out- side the bounds of synthesizable chemical space, limiting their practical use in real-world applications (Gao & Co- ley, 2020). To address this limitation, several studies (Shen et al., 2024; Guo & Schwaller, 2024) have employed various synthetic complexity estimation methods (Ertl& & Schuffen- hauer, 2009; Coley et al., 2018; Kim et al., 2023; Neeser et al., 2024; Genheden et al., 2020) as the reward function.
4. 3D Molecule and Synthesis Pathway Co-design within Protein Pockets
Synthesizability is a critical factor for ensuring molecules can be readily made for wet lab validation. Recent works have incorporated combinatorial chemistry principles into generative models to respond to this challenge (Koziarski et al., 2024; Cretu et al., 2024; Seo et al., 2024). Despite these advancements, these synthesis-based generative mod- els are restricted to 2D molecular graphs, limiting their ability to capture the 3D protein-ligand interactions that are essential for biological efficacy.
Another promising direction is to design molecules by as- sembling purchasable building blocks under predefined syn- thesis protocols. (Gao et al., 2022; Li al., 2022; Seo et al., 2023; Swanson et al., 2024; Gao et al., 2024). This strategy explicitly constrains the sample space to synthesiz- able chemical space. More recently, Koziarski et al. (2024); Cretu et al. (2024); Seo et al. (2024) have extended this strategy using GelowNets, formulating synthesis pathway generation as trajectories of GFlowNets. This effectively explores the chemical space to discover diverse candidate molecules while balancing exploration and exploitation.
To address this limitation, we introduce 3DSynthFlow, a gen- erative method based on CGFlow, enabling the co-design of synthesis pathways and 3D molecular conformations. This approach facilitates effective modeling of protein-ligand in- teractions and synthesizability, which are both essential for target-based drug discovery.
State flow model predicts the docking pose of molecule within a target protein pocket. Unlike typical docking, where the full 2D molecule is provided at f = 0, the state flow model must predict the pose for the ligand that is se- quentially constructed at discrete time intervals. Molecules for training the state flow model x: are first decomposed into their compositional structure C, which represents the sequentially composed synthesis pathway using Enamine re- action rules, and their continuous state S, which represents the 3D coordinates refined over time. To ensure atoms not present in the molecule do not appear during decomposition (i.e., leaving group for reactions), we adopt synthon-base based representation rather than reactant-based representation as Fig. 4. We discuss the motivation behind this formulation in Sec. 1.2.
Diffusion for sequential data. Diffusion models have recently gained traction for generative modeling of se- quential structures in diverse domains, spanning biologi- cal sequences (Campbell et al., 2024; Stark et al., 2024), videos (Ruhe et al., 2024), and language modeling (Lou et al., 2024). Campbell et al. (2023) propose a jump pro- cess for transitioning between different dimensional spaces to address the variable-dimension nature of data. To ex- ploit the temporal causal dependency in sequences, Ruhe et al. (2024); Zhang et al. (2023) explore frame-level noise schedules for diffuuson- baseed video generation for arbitrary- length frame rollout. Wu et al. (2023); Chen et al. (2024) apply similar ideas of training next-token prediction models while diffusing past ones for applications in planning and language modeling. Most similar to our work for molecule design using diffusion models are methods that use sepa- rate diffusion process for each sequentially added fragment (Peng et al., 2023; Ghorbani et al., 2023; Li et al., 2024).
The state flow model is then trained using the objective de- scribed in Sec. 1 on the protein-ligand complex dataset, independent of the compositional flow model. The Semla architecture (Irwin et al., 2024), originally designed for 3D molecular generation, is used to parameterize the State flow model. We introduce new hierarchical Semla for memory- efficient protein encoding, and popten-lligand message pass- ing to enable protein-ligand modeling (See Sec. 1.2.
We provide an extended related works for sequential dif- fusion for molecular generation and structure- based drug design in Sec. C.
Compositional flow model generates a synthesis pathway to construct a molecular structure. The action space for
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Table 1. Average Vina docking score of Top-100 diverse modes. We report two versions of SynFlowNet (v2024.05* and v2024. 1444,10),, Avg. and Med. are the average and median values over the average docking scores for all 15 LIT-PCBA protein targets. The results for the remaining target proteins are reported Appendix. 17 The best results are in bold.
Average Vina Docking Score (kcal/mol, 4
Category
Method
ADRB2
ALDHI
_sR_ago
_aR_an
FENI
Avg.
Med.
FragGFN
-10.19 (= 0.33)
-10.43 (# 0.29)
-9.81 (# 0.09)
-9.85 (# 0.13)
-7.67 (# 0.71)
.9.58
-985
Fragment
FragGFN+SA
-9.70 0.61)
-9.83 (# 0.65)
-9.27 (#: 0.95)
-10.06 (#: 0.30)
-7.26 (#: 0.10)
-9.22
-9.58
SynNet
-8.03 (=: 0.26)
-8.81 (# 0.21)
-8.88 (+: 0.13)
-8.52 (#: 0.16)
-6.36 (#: 0.09)
-8.12
-8.52
BBAR
-9.95 (= 0.04)
-10.06 (#: 0.14)
-9.97 (+: 0.03)
-9.92 (#: 0.05)
-6.84 (:: 0.07) 0.07)
-9.35
-9.84
SynFlowNett
-10.85 (= 0.10)
-10669 (# 0.09)
-10.44 (#: 0.05)
-10.27 (# 0.04)
-7.47 0.002)
-9.95
-00.34
Reaction
SynFlowNet
-9.17 (= 0.68)
-9.37 0.229
-9.17 (t: 0.12)
-9.05 (2: 0.14)
-6.45 (# 0.13)
-8.78
-9.17
RGFN
-9.84 0.21)
(499
-9.72 (2: 0.14)
-6.92 (#: 0.06)
-9.08
-9.11
RxnFlow
-11.45 (== 0.05)
-11.26
-11.15 0.002)
-10.77 (# 0.04)
-7.66 (# 0.02)
-10.46
-10.84
3D Reaction 3DSynthFlow
-11.96 (:L: 0.12)
-11.82 (1: 0.03)
-11.58 (1: 0.07)
-11.23 (dL: 0.08)
-7.79 (1: 0.01)
-10,89
-11.26
6. Experiments
model to intermediate states allowing it to predict their poses for partial structures during compositional flow model training (see Sec. 1.1.2 for motivation).
Overview We evaluate 3DSynthFlow for synthesizable target-based drug design in two common settings: pocket- specific optimization (Sec. 6.1) and pocket-conditional generation (Sec. 6.2). Our experiments aims to address three main key questions: (1) Does 3DSynthFlow generate molecules with improved binding affinity and ligand effi- ciency compared to existing synthesis-baud based baselines? (2) Does co-designing 3D structures improve the sampling effi cieney in discovering diverse high-reward modes? (3) How does 3DSynthFllw generalize to the pocket-conditionll set- ting, and how does it compare to existing SBDD baselines?
6.1. Pocket-specific optimization
Setup. We follow Seo et al. (2024) in both the reward function and evaluation protocol. To estimate the binding affinity, we use the GPU-accelerated docking tool UniDock (Yu et al., 2023). Each method generates up to 64,000 molecules for each protein target. To prevent reward hack- ing by increasing molecular size to improve the docking score, QED (Bickerton et al., 2012) is jointly optimized, and we set generation of 40 heavy atoms. The reward function for multi-objective optimization is described in Sec. F.2.
To answer these questions, We first apply 3DSynthFlow to optimize for targets in the LIT-PCBA benchmark (Tran- Nguyen et al., 2020). We evaluate the affinity, ligand ef- ficiency, synthesis success rate and pooein-liiande interac- tions of generated molecules. Then, we compare the sam- pling efficiency of 3DSynthFlow against 2DD-based baseline. Lastly, we comapre 3DSynthFlow against SBDD methods in the pocket-conditional setting on the CrossDocked dataset (Francoeur et al., 2020).
Generated molecules are filtered based on property con- straints (QED > 0.5), and the top 100 diverse modes are selected according to docking scores, ensuring structural di- versity with a Tanimoto distance threshold of 0.5 1, Finally, we evaluated the average Vina docking score and AiZyn- thFinder Success Rate of the selected molecules. Ligand effiency computed by (Vina / number of heavy atoms) is also reported to confirm the docking score improvement do not arise from simply increase in molecular size.
Setup. To construct synthetic pathway, we utilize 38 bimolecular Enamine synthesis protocols from Gao et al. (2024). We use Enamine's 1.2M-size catalog set and 300k- size stock set in Sec. 6.1 and Sec. 6.2 respectively. For stock set, filtered out molecules with drug-likenes,, score lower than 60 (Lee et al., 2022). To ensure tractability, molecular generation is limited to two synthesis steps, consistent with Enamine REAL Space (Grygorenko et al., 2020). To esti- mate synthesizability, we employ the retrosynthetic analysis tool AiZynthFinder (Genheden et al., 2020).
Baselines. We compare our approach against several synthesis-based methods, including a genetic algorithm SynNet (Gao et al., 2022), a conditional generative model BBAR (Seo al., 2023), and multiple GFlowNets. We consider two settings of fragment- based GFlowNets, with and without synthetic accessibility score (SA; Ertl & Schuf- fenhauer, 2009) objective (FragGFN. FragGEN+SA), and three different synthesis- based GFlowNets (RGEN, Syn- FlowNet, RxnFlow) (Koziarski et al., 2024; Cretu et al., 2024; Seo et al., 2024).
We pre-train the state flow model for 3D pose prediction on the CrossDocked dataset (Francoeur et al., 2020) with LIT-PCBA targets removed (see Sec. E.3.2). We sample synthesis pathway for each ligand using reaction rules to fragment the ligand (see Fig. 4). This exposes the state flow
SSince we select top 100 modes filtering for similarity, diversity is not reported in this section.
7

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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
ADRB2
ALDH1
ESR, ago
ESR antago
5000
6000
3000
Discovered modes
20
20
20
4000
3000
4000
2000
3000
2000
2000
2000
1000
1000
0
20000
40000
60000
20000
40000
60000
20000
40000 Sampling budget
60000
20000
40000
60000
Sampling budget
Sampling budget
Sampling bud
Figure 5. Number of discovered modes (satisfying Vina <-10 kcal/mol, QED >0.5, Sim <0.5) as a function of sampling budget for the first four LIT-PCBA targets for 3DSynthFlow (3D) vs RxnPlow (2D) across seeds. Higher is better.
Table 2. The average success rate and synthetic steps estimated from AiZynthFinder for 15 LIT-PCBA protein targets.
Table 3. PoseCheck Averages and standard deviations over 4 runs, the top 100 diverse modes the first 5 LIT-PCBA pocket. The results for all protein-ligand interactions are reported in Ap- pendix. F.5. The best results each column are in bold.
Method Success Rate (%, t) Synthesis Steps (L)
FragGFN+SA
3.52
3.74
SynNet
47.50
3,45
Method
H-Bon H-Bond Acceptors
H-Bond Donors
Sum
BBAR
17.92
3.68
SynFlowNet
0.22 (d: 0.01)
0.11 (1 0.01)
0.33
SynFlowNet"
54.60
2.55
SynFlowNet
0.22 (1: 0.03)
0.10 (1 0.01)
0.32
SynFlowNet
58.38
2.47
RGFN
0.19 (1: 0.01)
0.11 (1 0.01)
0.30
RGFN
47.43
2.46
RxnFlow
0.22 (d: 0.00)
0.10 (1L 0.01)
0.32
RxnFlow
65.35
2.17
3DSynthFlow
0.33 (#: 0.06)
0.17 (#: 0.03)
0.50
3DSynthFlow
68.58
2.39
Finally. we conduct extensive ablation studies on the var- ious technical decisions regarding: flow matching steps (Sec. F.2), time scheduling (Sec. F.3), and use of pose-based rewards (Sec. F.1). Analysis on training efficiency can be found Sec. E.1.3.
Results. Table. 1 presents the Vina results for the first five targets, while the full property results for all targets are in Sec. F.7. 3DSynthFlow consistenlly outperforms all baselines across LIT-PCBA targets in affinity and ligand efficiency, demonstrating that co-designing 3D molecular structures alongside synthesis pathways enhances the dis- covery of high-affinity molecules. Table. 3 shows molecules generated by 3DSynthFlow also exhibit a higher number of pootein-ligand interactions, as quantified by PoseCheck, highlighting the benefits of 3D-aware modeling for target- aware drug design (see full results in Sec. F:5).
6.2. Pocket-conditional generation.
Setup. Our method generalizes to pocket-conditional gener- ation problem setting (Peng et al., 2022: Guan al., 2023; Schneuing et al., 2024a), enabling the design of binders for unseen pockets with a single model and no additional oracle calls. We follow the same pocket-conditional experi- mental setup and reward function used in TacoGFN (Shen et al., 2024) and RxnFlow (Seo et al., 2024) (see Sec. E.2. 3DSynthFlow adopt the pre-trained proxy from TacoGFN trained on CrossDock2020 train set, which leverages phar- macophore representation (Seo & Kim, 2024), to compute rewards for training pocket-conditional policy.
Furthermore, Fig. 5 and Table. 16 presents the sampling efficiency for the first 5 LIT-PCBA targets. Diverse high- scoring modes were defined by QED>0.5, Vina<-10 kcal/- mol', and Tanimoto similarity-c0.5 to any other mode. After sampling 64,000 molecules, 3DSynthFlow identified 4.2x number of diverse high-scoring modes compared to Rxn- Flow (4432.3 1062.6). This enhanced sampling efficiency validates the effectiveness of 3DSynthFlow framework, and suggests a higher probability of experimental success.
Each method generates 100 molecules for each of the 100 test pockets the CrossDocked22200 benchmark (Francoeur et al., 2020) and are evaluated on these additional metrics compared to pocket-specific setting: Diversity repre- sents the average pairwise Tanimoto distance computed from ECFP4 fingerprints (Morgan, 1965). We also report Validity ( (%). ). the proportion of unique molecules that can be parsed by RDKit, and Time (sec.), the average duration required to sample 100 molecules.
Table. 2 shows that 3DSynthFlow attains comparable syn- thesizability compared to its 2D baselines, demonstrating its generated molecules is likely to be synthesizable. This ensures that the high-affnity compounds identified by our model are not merely theoretical but represent viable candi- dates for experimental validation and further development.
'Exeept for FENI, where we Vina helow -7 kcal/mol to maintain similar number of modes compared to the other targets.
Baselines. We compare 3DSynthFlow with state-of-the the art distribution deaning-based models trained on a syn-
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Table 4. Benchmark Results for Generative Methods. We report the average (Avg.) and median (Med.) values for each metric when
available. Time indicates the average duration to generate 100 molecules. Reference denotes known actives. For methods where only value is available, the median is indicated as "-".
Validity (t)
Vina (1)
QED (1)
AiZynth. Suce Rate (1)
Div (t)
Time (L)
Category
Method
Validity
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Avg.
Reference
-7.11
-7.80
0.48
0.47
36.1%
Pocket2Mol
98.3%
-7.60
-7.16
0.57
0.58
29.1%
22.0%
0.83
2504
TargetDiff
91.5%
-7.37
-7.56
0.49
0.49
9.9%
3.2%
0.87
3428
DecompDiff'
66.0%
-8.35
-8.25
0.37
0.35
0.9%
0.0%
0.84
6189
Atom
DifSSBDD
76.0%
-6.95
-7.10
0.47
0.48
2.9%
2.0%
0.88
135
MoICRAFT
96.7%
-8.05
-8.05
0.50
0.50
16.5%
9.1%
0.84
141
MoICRAFT-large
70.8%
-9.25
-9.24
0.45
0.44
3.9%
0.0%
0.82
>> 141
Fragment
TacoGFN
100.0%
-8.24
-8.44
0.67
0.67
1.3%
1.0%
0.67
4
2D Reaction
RxnFlow
100.0%
-8.85
-9.03
0.67
0.67
34.8%
34.5%
0.81
4
3DSynthFlow (low ()
99.9%
-9.14
-9.38
0.69
0.69
36.2%
37.0%
0.78
6
3D Reaction
3DSynthFlow (med (8)
99.9%
-9.30
-9.62
0.72
0.71
35.1%
36.0%
0.74
6
3DSynthFlow (high (3)
100.0%
-9.42
-9.61
0.73
0.73
36.1%
36.0%
0.69
6
thesizable drug set, including the autoregressive model Pocket2Mol (Peng et al., 2022), and diffusion- based meth- ods: TifgetDiff (Guan et al., 2023), DiffSBDD (Schneuing et al., 2024b), DecompDiff (Guan et al., 2024), and Mol- Craft (Qu al., 2024). We further include comparisons with optimization- based approaches: the fragment- based method TacoGFN (Shen et al., 2024) and the daction-based method RxnFlow (Seo et al., 2024). To ensure a fair eval- uation of distribution bearning-based methods, we use the docking proxy trained on CrossDocked training set. To bal- ance exploration and exploitation during sampling, we vary the reward exponentiation parameter / of 3DSynthFlow: medium 3 (1/(16, 64)),
SBDD methods such as MolCRAFT-large can attain strong binding affinity (-9.25) similar to 3DSynthFlow (-9.42), however their synthesis success rate is much lower (3.9% vs 36. 1)). The main contribution of 3DSynthFlow is represent- ing both the compositional nature for synthesis constraints and modeling 3D poses for binding.
7. Discussion
Limitations. Our synthesis- based action space based on arm and linker synthons does not yet explore certain nonlin- ear synthesis pathway such as ring-forming reactions. This synthon-based generation is chosen prevent the leaving group atoms of intermediate states being lost forming new rings - which would degrade the accuracy of pose pre- diction for intermediate states. However, this constraint can be substantially mitigated by expanding the chemical search space through incorporating a larger building block library. For example, Sadybekov et al. (2021) successfully achieved notable hit rate of 33% with arm-and-linker design.
low 3 (sampled from and high 3 (32, 64)).
Results. As shown in Table. 4, 3DSynthFlow achieves improvements in pocket-conditional generation in synthesiz- ability and docking scores. In particular, 3DSynthFlow- high 8 attains an average docking score of -9.42 kcal/- mol, outperforming RxnFlow (-8.85) and state-of-the-art diffusion- based methods like MoICRAFT-large (-9.25) and DecompDiff (-8.35). We attribute this improvement largely to our explicit consideration of 3D co-design in the reaction- based generation framework. However, due to the limited accuracy of the pre-trained proxy model for docking score reward, we find the improvement in docking score less sig- nificant than the pocket-specific setting.
Conclusion. In this work, we introduce Compositional Gen- erative Flows (CGFlow), flexible generative framework for jointly modeling compositional structures and continuous states. We introduce a simple extension to the flow match- ing interpolation process for handling compositional state transition. CGFlow enables the integration of GFlowNets for efficient exploration of compositional state spaces with flow matching for continuous state modeling. We apply CGFlow to 3D molecule and synthesis pathway co-design and develop 3DSynthFlow, which achieves state-of-the-art performance on both LIT-PCBA and CrossDocked bench- mark. Future work includes using more expressive model for pose prediction and developing more inlliiaationsspccinn methods using CGFlow.
3DSynthFlow surpasses the 2D reaction- based GFlowNets, TacoGFN and RxnFlow, while maintaining highly compa- rable computational cost. We attribute this to a fundamental design difference: while the 2D baselines are conditioned on ID sequence-basee representations, 3DSynthFlow leverages the full 3D geometry of the binding site. This result indi- cates that 3D interaction modeling is essential, particularly for achieving robust performance across diverse targets.
9

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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Impact Statement
pdf.
In small-molecule drug discovery, it crucial to design molecules that possess both high binding affinity and syn- thesizability. Despite the clear importance of these goals, ef- forts achieve them simultaneously have been constrained by the distinct nature of each objective. To address this challenge, we propose a generative modeling framework for compositional and continuous data. Our approach en- ables the joint generation of 3D binding poses within protein binding site and their synthetic pathways, addressing key challenges in target-based drug discovery. By improving the integration of synthesis constraints and structural modeling, this work has the potential to accelerate the development of novel therapeutics, ultimately benefiting public health. At the same time, generative models for molecular design carry inherent risks, including the potential for misuse in design- ing harmful substances. To promote responsible use, we focus on applications that align with therapeutic discovery.
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Appendix to:
Compositional Flows for 3D Molecule and Synthesis Pathway Co-design
A. CGFlow details
All code is provided in supplementary material.
A.1. CGFlow recipe
We now summarize the key steps for implementing CGFlow for generative tasks which constructs compositional structures with continuous states.
1. Decompose the object into its compositional and continuous part (c.g., 2D structure and 3D coordinates) (See Sec. 3).
2. Define action space for additive composition steps.
3. Define a function for sampling action sequence for constructing the compositional structure (e.g. synthesis order).
4. Train State Flow model on existing datasets (e.g. 3D protein-ligand complexes) (Sec. 3.3.1).
5. Train the compositional flow model using GFlowNets-basse Compositional Flow loss, if reward function R(xx) (docking score) is available, else use cross-entropy loss (Sec. 3.3.2).
6. Run sampling using trained state flow and compositional flow model (Algorithm 1).
A.2. Sampling Algorithm
Algorithm Compositional Flow Sampling with CGFlow
Require: step size Al, interval X, time window wwnddw
1: init t = 0, = O,C, = Co. So So. S = Sg
2: while f < 1 do
3: Iy + (C,, Si)
b Use self-conditioning.
4:
mod \= = 0 then
5:
it i+tt
6:
C(I Tx()))
Compositional flow model: Sample the next compositional component i. b Initialize new state values for component under the fixed seed Transition with sampled composition and state value.
5(0) ~ 1)
7:
De T( C(.) ((())
8:
(()
9:
geen +t t
end if
11:
(0)
local f clip
1- (3)
Si
Eviston
5(5) ( local). Si
State flow model: Predict final state values.
56) + s(1) + +S()) -S 600 At, Vi
13:
Step according to the predicted vector field.
t +-t+ At
end while
16: return 111
A.3. Alternative training objectives
There may be cases where reward function R(x) is not available, or the goal is to model the data distribution instead. In these settings, the compositional flow model can adopt cross-entropy loss to maximize the log-likelihood of sampling ((::) at each step i, aligned with the valid generation order σ. The loss is:
Ccomp = (w.) Σ log " (c (2))))))))))) (a))
(11)
gen
where (C(())) (z;) represents the policy model for generating the next compositional component C(a)), conditioned on the entire object Zt..
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
B. Theoretical background
The object i = () is sequence data where = )= and S (S Y=1 Therefore, we formulate the generative process as an regressive process, i.c., (- 1.0.
To train the compositional flow model with the trajectory balance (TB) objective, must estimate forward transition probabilities along the trajectory
(æy 2AA + 2nd #1), where À is the time interval between successive
components CO), and < 1/A is the total number of components.
Since the state flow model pl introduces randomness in the initial state 56¹² NO o²), estimating the forward transition probability involves integrating over this noise distribution as follows:
Pp 2ar, Pr (c
BiA. BiA zf:0) / (ESA (0 (:
)dsk
Pp (c ass, 2f:0) (00 (T(E,.C0,
(TT,T)), ),,,,, - *((+1))) ) pl pl5 )
(12)
where Φ" the ODE solver of the state flow model p/p-- This integration induces a Dirac delta term, making direct probability estimation challenging.
Proposition B.1. Let the initial state 5 be fixed Then, the object æ, Sc), uniquely determined by given trajectory sampled from the compositional flow model n
Proof. When ( is fixed, the ODE solver fully specifies ((4+1)A based on Six, the self-conditioning æi. and the sampled component (+), Consequently, the sequence (C(1) ..... ((k(t)) directly determines S,. Given that the generative progress auto-regressive, there is one-to-one correspondence between æ, and (C(() ,..., ((k())))(() for every
Building on this determinism, simplify the forward transition probability PF PF (1(41))) ( [ssspep ) as:
0. L.a. 2i: Mx: = PF (c10)
PF
(13)
This allows to write the TB objective in tractable form:
P P(a 2
Zo I Pe ( p.P
LTb(T)=
log
[(x )] 1=00
m-1 Pr
P P(
2
2g 11:00 (F (rxx Φ)) R(x1)
log
(14)
By enforeing trajectory balance under these conditions, we ensure that the likelihood of sampling a final object æ1 is proportional its reward R(x1), while sidestepping the complexities introduced by the continuous noise integration.
C. Extended related works
Sequential diffusion for molecular generation Peng et al. (2023); Ghorbani et al. (2023); Li et al. (2024) sequentially generate molecules fragment by fragment using diffusion models. These methods use a separate diffusion process to generate each 3D fragment graph, with atomic positions fixed post-generation. They also lack the ability to enforce compositional synthesis constraints during the generation process. Instead, 3DSynthFlow formulates a joint flow process: state flow refines all atomic positions throughout, mitigating the issue with cascading error in position prediction; composition flow sequentially constructs the synthesis pathway, effectively enforcing the synthesis constraint.
'To minimize the influence of the fixed initial state value, sample the initial state from the noise distribution using the manual random seed which is equal the size of the current object, such as the number of atoms.
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Structure-based drug design We categorize structure-based drug design (SBDD) in main categories: pocket-specific and pocket-conditional following Seo et al. (2024).
The first approach optimizes docking scores for a target. Methods include evolutionary algorithms (Reidenbach, 2024), reinforcement learning (RL) (Zhavoronkov et al., 2019), and GFlowNets (Bengio et al., 2021; Pandey et al., 2025; Koziarski et al., 2024). The drawback of this approach is that each pocket must be optimized individually, which can restrict scalability.
In contrast, the pocket-conditional generation approach produces molecules tailored to any given pocket without the need for extra training. This strategy leverages distribution-base generative models (Ragoza et al., 2022; Peng et al., 2022; Guan al., 2024; Schneuing et al., 2024b; Qu et al., 2024) that are trained protein-ligand complex datasets to learn the distribution of ligands suitable for different pockets. Recently, Shen et al. (2024); Seo et al. (2024) adopted pocket-conditioned policy for GFlowNets that generates samples from reward-biased distributions in zero-shot setting.
D. 3DSynthFlow details
D.1. Action space
Following Cretu et al. (2024); Koziarski et al. (2024); Seo et al. (2024), we treat chemical reactions as forward transitions and synthetic pathways trajectories for molecular generation.
Compared to previous methods, we represent building block as synthon, which is not complete molecule. The synthons can be connected at the altachment point according the pre-defined connection rules, i.e., reactions R. (See Fig. 4). To prevent generation trajectory terminating at an incomplete structure, we define two types of synthon according to Liu et al. (2017): brick is the synthon including one attachment point, and linker is the synthon including two attachment points.
Brick
Linker
Figure 6. Examples of brick and linker synthons.
We define B as the entire synthon set, B' C B as the brick synthon set, and B, S B as the allowable synthon set for reaction r E R.
At the initial state Co, the model always selects First which samples a brick synthon b from the entire brick synthon set B3' to as the starting molecule. For subsequent states C., the model chooses AddSynthon, which firstly identifies the available reaction set R(C,) R and then samples the synthon from the available synthon set Urer(e,) B,. If the brick synthon is selected, the trajectory is terminated. When the trajectory reaches the maximum length, the model always selects a brick synthon.
In summary, the allowable action space A(C) for a given compositional state C is:
ift= 1, otherwise,
A(C)
(15)
Ur
D.2. 3DSynthFlow Model architecture
1.2.1. STATE FLOW MODEL
To model state flow for predicting ligand docking poses in 3DSynthFlow, we extend the Semla architecture introduced by Irwin al. (2024). Semla is scalable, -qqivaaaia model originally designed for 3D molecular generation; We refer reader to the original paper for full details for SemlaFlow. We make the following modifications to adapt Semla for 3D protein-ligand modelling:
Hierarchical pocket encoding: Inspired by AlphaFold3 (Abramson et al., 2024), which models protein at both atom level and token level. we propose a hierarchical encoding strategy HierSemla which first encodes each residues at atom level and aggregates atomic representation to residue level. More specifically, we introduce a Residue Encoder based on the
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Semla architecture, and apply it independently to encode each of its atom type, connections and position first. Then we perform mean pooling over the invariant and equivariant features within each residue, obtaining residue-level embedding (h! (h(")) .r. ) ). This hierarchical design enables all-atom resolution modeling of the protein pocket while significantly improving memory efficiency: by restricting full attention to within-residue interactions, we avoid the ((N2) memory cost of full atom-level attention across the entire protein, which can contain up to 2000 atoms.
Synthon attachment point information: In addition to the original atomic input features (atomic type and charge), we further provide the boolean feature IS ATTACHMENT POINT indicating whether this atom is the attachment point for new synthon. Intuitively, this hints the model where the future synthon will be added in next reaction and bias the model to leave space for the future synthon in the intermediate state pose prediction. We find this additional feature lead to better pose prediction performance in practice.
(pro) Protein-ligand attention layer: The protein residue embeddings (h!"T)) x (z!"" _e!""))) along with their original positions x; are combined with the ligand atom embeddings (h (lis) (i,5) E V x P, defined as:
(h. xx (lie)) for pairwise message passing at each modified Semla layer (m
iny
equi) = 966m (iforo-lig) h. h2, ã; T.,z)) 2z).
(16)
where h; and ã; are normalized linearly projected features. The protein-ligand messages are aggregated with the original ligand-ligand messages and used for attention-based updates. This formulation enables message exchange between residue nodes and atom nodes, ensuring that the model effectively learns protein-ligang interactions critical to binding.
Modification to prior: Since the atom type and bond connections are generated by the compositional flow model instead of the state flow model, therefore they remain fixed throughout the process. This means we cannot use techniques such as equivariant-OT to reduce the transport cost (Klein al., 2023; Song et al., 2023), since they assume interchangeability between newly initialized nodes. We have also tried using harmonic prior from Jing al. (2023); Stärk et al. (2024) to initialize position with bonding information as prior. We observed improved pose prediction with Gaussian noise during initial training, but no advantage of the harmonic prior over the Gaussian prior at convergence.
D.2.2. COMPOSITIONAL FLOW MODEL
We adopt a model architecture inspired by Bengio et al. (2021); Cretu et al. (2024); Seo et al. (2024), using a graph transformer (Yun et al., 2022) as the backbone fa. and a multi-layer perceptron (MLP) go for action embedding. The graph embedding dimension is d1 and the synthon embedding dimension is d2. The GFlowNet condition such as temperature / or multi-objective weights are encoded in condition vector c.
To capture spatial relationships between the protein and ligand, the model uses 3D protein-ligand complex graph for each state. The protein is represented as a fully-connected residual graph, where each node corresponds to Ca atom. The ligand is also connected to all protein nodes. All pairwise distances between nodes are encoded in the graph edges, enabling the model to reason about the 3D structure. We represent each state s as an input of GFlowNet.
Initial synthon selection. For the initial state s = 8p. the model always selects Fi rstSynthon to sample brick synthon b E B' for the starting molecule with MLP Raddyytthon Rdd + Rdd..
Fo c) MLP Myppsestsyathon (fo, (Su, c)) (b)
(17)
Adding synthon selection. For the later states s + sp, the model selects AddSynthon to sample allowable brick or linker synthon 6 E Br with MLP AadSyathonn _dd Rdd. We note that the reaction type information is included in synthon embedding:
Fr,s,(r,b).c) = MLP Adddyyasoon (f c)) 2 ge(r,
(18)
Synthon masking. The state flow model is trained on the data distribution of active ligands. This may sometimes not work well for dittr---istiibttion molecules that are much larger than the training data. Therefore, we restrict the actions which make the state to have more than 40 atoms. This process can be performed simply in synthon- based action space.
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
E. Experimental details
E.1. Training details
E.I.I. 3DSYNTHFLOW HYPERPARAMETERS
Table
Default hyperparameters used for compositional structure.
Hyperpaaameterss
Values
Time per action
0.3
Interpolation window Ewindow
1.0
Maximum decomposed part
3
Minimum decomposed fragment size
5
Minimum trajectory length
(minimum reaction steps:
Maximum trajectory length
3 (maximum reaction steps: 2)
Here we define the hyperparameters used for 3DSynthFlow:
1. Time per action (A): Defines the time interval between adding each additional synthon.
2. Interpolation window (fwindow): Specifies the fixed time window that affects the noise scheduling of the continuous states of each component.
3. Maximum decomposed part: Determines the maximum number of synthons a molecule can be decomposed into, preventing molecules from being associated with excessive synthesis steps.
4. Minimum decomposed fragment size: Specifies the minimum number of atoms that each synthon product must contain when a molecule decomposed according reaction rules. This ensures that synthons are of realistic size when decomposing CrossDocked ligands for training pose prediction model.
5. Minimum trajectory length: Defines the minimum trajectory length for sampling composition steps in 3DSynthFlow.
6. Maximum trajectory length: Specifies the maximum trajectory length that can reached.
We further exam the effect of performance for different setting of time scheduling, varying À and twindow in Appendix F.3.
Table 6. Default hyperparameters used for State flow model.
Hyperparameters
Values
Number of protein layers
Number of ligand layers
Noise prior Time distribution
Gaussian Beta(1.0, 1.0)
the same hyperparameter from the official repository 9 We show the additional hyperparameters in Table. 6 and provide explanation for each below:
For parameterizing the state flow model for pose prediction,
1. Number of protein layers: the number of layers with protein-protein message passing.
2. Number of ligand layers: the number of layers with pootein-ligand message passing.
3. Noise prior: Defines the noise distribution which initial state values drawn from.
4. Time distribution: Defines the time distribution
Follow SemlaFlow's hyperparameter settings in train.py https://githhei http:tthw...oom/sss///eeeeeeee flow/blob ma h semla ww/ctt/rrae tttttraiii prain.py
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Composition flow model In this work, we most parameters to the default values for all GelowNet baselines (Some of the parameters are in Table. 7). However, since 3DSynthFlow is built from RxnFlow, it follows some important parameters of RxnFlow except for maximum trajectory length and state embedding size. We note that our state embedding dimension is smaller than other GFlowNet baselines.
Table Default hyperparameters used in all GFlowNets. The settings are from fra. py (Bengio et al., 2021)
Hyperparameters
Values
GFN temperature 3 Sampling tau (EMA factor)
Uniform(0, 64)
0.9
Learning rate (2)
10 10-3
Learning rate (Pp)
10-4
State embedding dimension
64
Table Specific hyperparameters used in 3DSynthFlow training. The parameters are from RxnFlow (Seo et al., 2024), except for the maximum trajectory length (4 for RxnFlow) and state embedding size (128 for RxnFlow and other GFlowNets).
Hyperparameters
Values
Minimum trajectory length Maximum trajectory length
2 (minimum reaction steps: 1)
(maximum reaction steps: 2)
State embedding dimension
64
Action embedding dimension
64
Action space subsampling ratio Train random action probability
1%
5%
For action space subsampling, we randomly subsample 1% actions for FirstSynthon and each bi-molecular reaction template r E R2. However, for bi- molecular reactions with small possible reactant block sets B, E B, the memory benefit from the action space subsampling is small while variance penalty is large. Therefore, we the minimum subsampling size to 100 for each bi-molecular reaction, and the action space subsampling is not performed when the number of actions is smaller than 100.
The number of actions for each action type is imbalanced, and the number of reactant blocks (B,) for each bi-molecular reaction template is also imbalanced. This can make some rare action categories not being sampled during training. We empirically found that React action were only sampled during 20,000 iterations (1.28M samples) in a toy experiment that uses one bi-molccular reaction template and 10,000 building blocks in some random seeds. Therefore, we set the random action probability the default of 5%, and the model uniformly samples each action category in the random action sampling. This prevents incorrect predictions by ensuring that the model experiences trajectories including rare actions. We note that this random selection is only performed during model training.
1.1. DETAILS OF STATE FLOW MODEL TRAINING
To expose the state flow model realistic partial ligand structures, we decompose each CrossDocked ligand into up to three fragments using 38 bimolecular Enamine synthesis protocols, defined by reaction SMARTS patterns. For each molecule, we randomly select fragment ordering and sample time step t. so the model observes the molecule varying stages of assembly (e-g., only fragment A at f 1, fragments A and B at = etc.). This mimics the compositional assembly process used during generation and teaches the model to predict physically plausible docking conformations for incomplete ligands.
Importantly, the decomposition is not intended to yield commercially purchasable Enamine synthons. Instead, the use of Enamine protocols ensures the resulting fragments are chemically meaningful and synthetically relevant, even they do not match existing catalog synthons. This allows us to use any CrossDocked molecule for training while staying aligned with the synthetic priors used at generation time.
Across the CrossDocked dataset, we find that over 93% of molecules can be decomposed into at least two fragments using
Follow default hyperparameter settings in seh_frag.py and seh_frag.moo.pp py https: ftttp:://gthub.com recursiongs httprssiooaaaaaaaaagaaaaaaaa http:///tttottttt////////c////// http://///////g/ooo///////a/////
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Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
this protocol, and over 87% be decomposed into three. This high decomposition rate enables robust learning from partially constructed molecules and ensures strong coverage of fragment combinations encountered during inference.
E. 1.3. TRAINING TIME AND COMPUTATIONAL EFFICIENCY
The state flow model (i.e., the pocket-conditional pose predictor) was trained for 30 epochs on 8 A4000 GPUs (I6GB), requiring a total of 26 hours. Since the state flow model is trained on the CrossDocked dataset and is reused across different test pockets, it incurs only a one-time computational cost. We plan to release the pretrained weights, so that users will need to train only the composition flow model tailored to their custom reward function and target.
In contrast, the composition flow model is trained for 1,000 iterations under 20 flow matching steps. Training with GPU- accelerated docking (UniDock; balance mode) takes between 7 and 12 hours (depending the target) single A4000 GPU (16GB), making the computational requirement accessible for most practical drug discovery campaigns. Moreover, the composition flow model can be trained in a pocket-conditioned manner to enable zero-shot molecule sampling for any target pocket, thereby converting the training into a one-time cost this setting.
Table Summary of Training Time for 3DSynthFlow Components.
Model Component
Hardware
Batch Size
Number of Iterations
Training Time
State Flow Model
x A4000 (16GB)
dynamic 64
30 epochs
26 hours
Composition Flow Model
x A4000 (16GB)
1,000 steps
7-10 hours
E.2. Reward function
To train GFlowNet models, we employ the same reward function proposed in RxnFlow (Seo et al., 2024) and TacoGFN (Shen et al., 2024).
Pocket-specific optimization
To optimize both QED andd Vina docking score, we set the reward function as:
R(x)= ui QED(x) + w2 Vina
(19)
where Vina(x) is normalized docking score. The parameters wi and wa serve conditions of multi-objective GelowNets (Jain et al., 2023b), and are set to 0.5 for non-GFlowNet baselines.
Pocket-conditionall optimization We use the the modified reward function proposed by Shen et al. (2024). According to Seo et al. (2024), we remove SA score term (Ertl& & Schuffenhauer, 2009) from the reward functions since 3DSynthFlow explicitly generate synthetic pathway:
0
0 < Proxy(x:
0.00 x Proxy(#)
if - < Proxy(x) 50 if 13 & Proxy(z) S if Proxy(#) < -13
Caffinity (x)
0.2 x Proxy(x) 1.28
1.32
TQED(x)= = QED(x)/0.7 if QED(2) s 0.7
otherwise
(x)(x)= (A(x))0088 if $.0
otherwise
Taftinity (x) x (QED(2) x (x)
TacoGFN-Rewarte =
(20)
/HeavAtommCountt(r
Fallinity (x) (2))(z)
SknFlow-Rewarde / /HeavyAtomCountts
(21)
20

---

Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
E.3. Datasets
E.3.1. LIT-PCBA POCKETS
Table. 10 describes the protein information used pocket-specific optimization with UniDock, which performed on
Sec. 6. We follow the same procedure used in pocket extraction for the CrossDock dataset: taking all residue of the protein within 10 Á radius to the reference ligand as the binding pocket.
Table 10. The basic target information of the LIT-PCBA dataset and PDB entry used in this work.
Target
PDB
Target name
ADRB2
4ldo
Beta2 adrenoceptor
ALDHI
512m
Aldehyde dehydrogenase
ESR_ _goa
2p15
Estrogen receptor with agonist
ESR antago
2iok
Estrogen receptor with antagonist
FENI
5fv7
FLAP Endonuclease 1
GBA
2v3d
Acid Beta- Cl--uoooeerrbbosdaasee
IDHI
4umx
Isocitrate dehy drogenase 1
KAT2A
5h86
Histone acety Itransferase KAT2A
MAPK1
4zzn
Mitogen-activated protein kinase 1
MTORCI
4dri
PPlasc domain of FKBP51, Rapamyein
OPRKI
6b73
Kappa opioid receptor
PKM2
4jpg
Pyruvate kinase muscle isoform M1/M2
PPARG
5y2t
Peroxisome troliferator-activate receptor
TP53
3zme
Cellular tumor antigen p53
VDR
3a2i
Vitamin receptor
E.3.2. CROKSDDOK
We train the State flow model of 3DSynthFlow on the commonly used CrossDocked dataset (Francoeur et al., 2020). We apply the splitting and processing protocol on the CrossDocked dataset to obtain the same training split of pooein-llgandd pairs as previous methods (Luo al., 2021; Peng et al., 2022). We use 99,000 complexes as the training and remaining 1,000 complexes the validation set. Since co-design 3D binding pose and synthesis pathway, unlike the pervious 2D-based methods, we can leverage this dataset for training the auxiliary State flow pose prediction model.
E.4. Baselines
SynNet, BBAR
We reused the values reported in Sco et al. (2024).
FragGFN, RGFN, RxnFlow. All GFlowNet baselines share the same training parameters under the multi-objective GFlowNet (Jain et al., 2023b) setting. We also reused the values reported in Seo al. (2024).
SynFlowNet. There are two versions for SynFlowNet (Cretu et al., 2024): 2024.3 and 2024.8. For version 2024.3, we reused the values in Seo et al. (2024). For version 2024.8, we followed the processes and settings according to the original paper and official code repository "* To construct the action space, we randomly selected 10,000 building blocks from Enamine Global Stock (v2025.01.11) with 105 reaction templates. We trained SynFlowNet using backward policy learning maximum likelihood, maximum trajectory length to 3, and action embedding with Morgan fingerprint (Morgan, 1965). Finally, we set the training parameters used in other GelowNet baselines (See Table. 7). The training code and data used in the benchmark study are included in the supplementary materials.
F. Additional results
F.1. Reward computation without full docking
The most computational and time-intensive process in the training process is often docking the generated candidates with molecular docking for evaluation. Glide, standard docking software the industry, takes around 6 minutes per compound
"Follow SynFlowNet's hyperparameter settings in reacti iosutiinnstast .yy https: / httg/gttttutt com /mi runacrt/ 6b7 1344688
synflownet/trree/ 4aa httee//aaaacca225eeeeeea
21

---

Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Table 11. Ablation study on reward setting for Vina docking scores. Evaluated on the ADHI pocket. Results are averaged over 3 runs.
Method
Reward setting
Docking score (L)
RxnFlow
Full docking
-11.26 (# 0.07)
3DSynthFlow
Full docking
-11.82 (4: 0.07)
3DSynthFlow
Local opt.
-11.44 (#: 0.06)
3DSynthFlow finetuned
Local opt.
-11.62 (#: 0.02)
in its most accurate setting (Friesner et al., 2004). This constraint necessitates either reducing the number of Oracle queries or trading speed for less accurate docking settings. Docking scores are typically computed via Full docking, which performs full search for the optimal binding pose at high computational cost. However, it can also be computed via Local optimization for significantly faster computation, if an existing binding pose is available. f1
In this setting, we investigate directly using the final predicted pose from 3DSynthFlow to compute reward using local optimization compared using the full docking score. In the 3DSynthFlow finetuned setting for local opt., we first finetune the pose predictor on re-docked poses from the first 9,600 sampled molecules to improve binding pose prediction, thereby enabling accurate local optimization docking scores.
From Table. 11, we see that regardless of the scoring function used or whether perform fine tuning, 3DSynthFlow outperformed the best 2D baseline RxnFlow, confirming the benefit of 3D structure co-design. Interestingly, 3DSynthFlow using local opt. do not perform as well as 3DSynthFlow trained with signals from full docking in both settings. While fine tuning the pose prediction module helps, the gap between full docking and local opt. is not fully closed. Empirically, we find the poses predicted from 3DSynthFlow sometimes contain steric clashes, leading to inaccurate estimation of the reward signal. Accordingly, improving the pose prediction module emerges as key next step to reduce steric clashes and enhance the accuracy of local optimization docking scores, as disccussed in Sec. 7.
By co-designing binding pose and molecule, 3DSynthFlow using local opt. can bypass the computational burden of full docking which 2D generative methods are subjected to. while surpassing their performance. This is key advantage for 3DSynthFlow in cases where accurate full docking is prohibitively expensive for a large number of ligands.
F.2. Effect of Flow Matching Steps
Table 12. Effect of flow matching steps on performance for the AL.HI target with the Vina reward. We report both the average docking score (Avg Vina) over all generated molecules and the top 100 docking scores (Top 100 Vina), with lower values indicating better binding. Training time is reported in seconds per iteration, and sampling time is reported in seconds per molecule.
Flow Matching Steps
Avg Vina (L)
Top 100 Vina (4)
Training Time (sec/iter)
Sampling Time (sec/mol)
20
-8.55 + 0.18
-12.86 + 0.22
16
0.058
40
-8.57 + 0.13
-13.03 + 0.27
22
0.086
60
-8.84 1 0.14
-13.50 1 0.24
24
0.115
80
-8.47 + 0.18
-13.15 1 0.16
27
0.153
We further analyzed how the number of flow matching steps impacts performance using the ALDHI target with the Vina reward. As shown in Table 12, performance slightly improves with increasing flow matching steps and appears to saturate around 40-60 steps. This marginal improvement may stem from the fact that the pose prediction module's 's primary role is to provide a spatial context between intermediate molecules and the pocket; hence, extremely precise pose predictions have limited additional impact on model decisions.
F.3. Ablation study on time scheduling of 3DSynthFlow
We conducted an ablation study to assess the effect of time scheduling in state flow training. Specifically, we compared three scheduling strategies:
No overlap: strictly autoregressive denoising each synthon denoised after the previous one is completed. (A 0.33, twindow 0.33).
"Scoring predicted pose using the local-optimization setting in AutoDock Vina is 7x faster than performing full docking. This speedup is even greater for more accurate docking programs, since the vast majority of time is spent on pose searching rather than scoring.
22

---

Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Overlapping: partial overlap of synthon denoising (A 0.3, wwindwww -0.4).
Till end: all synthons are denoised jointly until 1 (A 0.33, wwindow 1.0).
To highlight the impact of noise scheduling on the final pose, we report the average local-optimized Vina docking scores across different training iterations for the ALDHI target over seeds:
# of mol explored
10,000
20,000
30,000
No overlap
5..68 + 0.29
-6.33
0.34 -7.22
-7.02
Overlapping
-6.28 + 0.22
-7.28 7.28::0.21
0.12
Till end
-7.15 + 0.40
-7.60 0.29
-7.79 0.12
Table 13. Ablation study on time scheduling for state flow training on the ALDHI target.
We find 3DSynthFlow 's Till end strategy, where all positions are refined until time = 1, clearly outperforms conventional
autoregressive approaches No overlap, adopted in previous works (See Appendix C). Our framework enables tuning of hyperparameter and twidow to accommodate varying data problems.
E4. State Space Size Estimation
We estimate the sample space size based on the number of synthetic steps: 10 molecules with a single reaction step, 10 molecules with two reaction steps, and 20 molecules with three reaction steps. In our experiments, we employed up to two reaction steps according to Enamine REAL. The resulting state space size is comparable to RGFN (up to 4 steps with 8,350 blocks) and SynFlowNet (up steps with 200k blocks).
To assess the breadth of building block (BB) exploration, we analyzed the number of unique BBs encountered during training across the first five LIT-PCBA targets. Our model explored average of approximately 55,000 unique BBs within 1,000 training iterations using a batch size of 64. This indicates significantly broader exploration compared to SynFlowNet, which reported around 15,000 unique BBs over 8,000 iterations with a batch size of 8.
Table 14. Number of unique building blocks explored during training across 5 LIT-PCBA targets.
Target
ADRB2
ALDHI
ESR ago
ESR antago
FEN1
Number of Unique BBs
45520 + 7876
48644 + 1983
55211 = 5611
58097 + 8529
69400 + 5259
F.5. PoseCheck protein-ligand interactions
Table 15. PoseCheck protein-ligand interactions. We report two versions of SynFlowNet (v2024.05* and v2024. Averages and standard deviations over 3 runs, for the top 100 diverse modes per LIT-PCBA pocket. The best results in each column are in bold.
PoseCheck Metries (t)
Method
H-Bond Acceptors
H-Bond Donors
Van der Waals
Hydrophobic
Sum
SynFlowNet
0.22 (=: 0.01)
0.11 (# 0.01)
9.31 (1 0.05)
10.41 (# 0.05)
20.05
SynFlowNet
0.22 (# 0.03)
0.10 (# 0.01)
8,38 (1: 0.05)
9.44 (2 0.06)
18.14
RGFN
0.19 (#: n.01)
0.11 (#: 0.01)
9.19 (4: 0.28)
10.25 0.12)
19.73
RxnFlow
0.22 (=: 0.00)
0.10 (#: 0.01)
9.63 (1: 0.09)
10.67 (#: 0.10)
20.62
3DSynthFlow
0.33 (+:: 0.06)
0.17 (4: 0.03)
11.04 (1: 0.37)
10.79 (+ 0.21)
22.32
Lastly, evaluate the protein-ligand interactions of the top 100 generated molecules using PoseCheck (Harris et al., 2023).
Since baselines do not generate 3D poses, we assess all methods using their redocked structures for consistency. PoseCheck evaluates four key protein-ligant interactions: H-bond acceptors, H-bond donors, van der Waals contacts, and hydrophobic effects.
Hydrogen bonds (H-bonds) are the most important specific interactions protein protein-ligand ligand recognition (Bissantz et al., 2010) and require precise geometric alignment form (Brown, 1976). Unlike hydrophobic and van der Waals interactions, which
23

---

Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
non-directional and broadly applicable, H-bonds require strict atomic alignment, reinforcing the need for accurate 3D molecular modeling.
Notably, 3DSynthFlow achieves the highest H-bond acceptor and donor counts, outperforming all baselines. This improve- ment suggests that co-designing 3D structure and synthesis pathways enhances the geometric alignment of polar functional groups, leading to more stable and specific protein-ligand interactions. addition, 3DSymthFlow-geneee result in more hydrophobic and van der Waals interactions to baselines, as shown in Table. 15, further enhancing binding stability.
molecules also
F.6. Full sampling efficiency results
Table 16. Average number of diverse modes discovered versus the number of molecules explored. The best results are bold. Results are computed over 2 seeds.
Number of Molecules Explored
Target
Method
1,000
5,000
10,000
30,000
64,000
RxnPlow
3.0
21.5 (+4.9)
52.0 (+24.0)
500.0 (#137.2)
1282.5 (#234.1)
ADRB2
3DSynthFlow
5.5 (46.4)
70.5 (+41.7)
307.0 (=158.4)
2198.5 (454.5)
5145.5 (+62.9)
RxnFlow
4.5 (=2.1)
26.5 (27.8)
73.5 (133.2)
472.5 (299.7)
1240.0 (275.0)
ALDHI
3DSynthFlow
18.5 (+14.8)
112.0 (494.8)
326.5 (#316.1)
1789.5 (4989.2)
5701.0 (+1328.4)
RxnFlow
5.0 (a4.2)
17.0 (a4.2)
44.0 (a8.5)
440.5 (a60.1)
1174.0 (a100.4)
ESR ago
3DSynthFlow
5.0
55.0 (243.8)
229.5 (=200.1)
1742.0 (a881.1)
5015.5 (=1680.7)
RxnFlow
3,0 (=2.8)
14.5 (a0.7)
28.0 (20.0)
218.0 (a21.2)
559.0 (+50.9)
antago
3DSynthFlow
6.5 (a4.9)
60.0 (=11.3)
172.5 (a40.3)
1020.5 (a24.7)
2977.5 (4577.7)
RxnFlow
3.5 (20.7)
29.0 (+18.4)
75.5 (#57.3)
372.0 (a46.7)
1057.5 (438.9)
FEN1
3DSynthFlow
12.5 (#9.2)
58.5 (+29.0)
176.5 (195.5)
852.0 (463.6)
3322.0 (s49.5)
RxnFlow
3.8
21.7
54.6
400.6
1062.6
Average
3DSynthFlow
9.6
71.2
242.4
1520.5
4432.3
24

---

Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
E.7. Full results for LIT-PCBA target
Table 17. Average Vina docking score for top-100 diverse modes generated against 15 LIT-PCBA targets. The best results are in bold.
Average Vina Docking Score (kcal/mol, ()
Category
Method
ADRB2
ALDHI
ESR
ESRaantago
FEN1
FragGEN
-10.19 (# 0.33)
-10.43 (#: 0.29)
-9.81 (# 0.09)
-9.85 (# 0.13)
-7.67 (#: 0.71)
Fragment
FragGFN+SA
-9.70 (#: 0.61)
-9.83 (#: 0.65)
-9.27 (# 0.95)
-00.6 (# 0.30)
-7.26 (# 0.10)
SynNet
-8.03 (#: 0.26)
-8.81 (#: 0.21)
-8.88 (# 0.13)
-8.52 (#: 0.16)
66.36 0.09)
BBAR
-9.95 (#: 0.04)
-10.06 0.14)
-9.97 (# 0.03)
-9.92 (#: 0.05)
-6.84 (#: 0.07)
SynFlowNer
-10.85
-10.69 0.09)
-10.44 0.05)
-00277 0.04)
-7.47 (#: 0.2)
Reaction
SynFlowNet*
-9.17 (#: 0.68)
-9.37 (#: 0.29)
-9.17 (# 0.12)
-9.05 (# 0.14)
-6.45 (6
RGFN
-9.84 (#: 0.21)
-9.93 0.11)
-9.99 (# 0.11)
-9.72 (# 0.14)
-6.92
RxnFlow
-11.45 0.05)
-11.26 0.07)
-11.15 0.02)
-10.77 (# 0.04)
3D Reaction
3DSynthFlow
-1..97 (d: 0.12)
-1.82 0.04)
-11.58 (#: 0.07)
-11.23 (#: 0.08)
-7.79 0.01)
GBA
IDHI
KAT2A
MAPK1
MTORCI
FragGFN
-8.76 (#: 0.46)
-9.91 (# 0.32)
-9.27 (# 0.20)
-8.93 (# 0.18)
-10.51 (#: 0.31)
Fragment
FragGFN+SA
-8,92 (+: 0.27)
-9.76 (#: 0.64)
-9.14 (#: 0.43)
-8,28 (:: 0.40)
-10144 (#: 0.30)
SynNet
-7.60 (+: 0.09)
-8.74 (:: 0.08)
-7.64 (#: 0.38)
-7.33 (d: 0.14)
-9.30 (:: 0.45)
BBAR
-8.70 (+: 0.05)
-9.84 (:: 0.09)
-8.54 (#: 0.06)
-8.49 (1: 0.07)
-10.07 (#: 0.16)
SynFlowNer
-9.27 (+: 0.06)
-10.40 0.08)
-9.41 0.04)
-8.92 0.05)
-10.84 (1: 0.03)
Reaction
SynFlowNer'
-8.28 (+: 0.15)
-9.18 0.35)
-8.06 (2: 0.15)
-7.89 0.13)
-9.60 (:: 0.16)
RGFN
-8.48 (+: 0.06)
-9.49 (#: 0.13)
-8.53 (:: 0.11)
-8,22 (1.05))
-9.89 (1: 0.06)
RxnFlow
-9.62 0.04)
-10.95 0.05)
-9.73 (# 0.03)
(+
-11.39 0.09)
3D Reaction
3DSynthFlow
-9.90 (1:: 0.14)
-11.28 (1: 0.15)
-10.17 (1:: 0.37)
-9.61 (L...1))
-11.91 (1: 0.01)
OPRK1
PKM2
PPARG
TP53
VDR
FragGFN
-10.28 0.15)
-11.24 0.27)
-9.54 0.12)
-7.90 (+: 0.2)
-10.96 0.06)
Fragment
FragGFN+SA
-9.58 0.44)
-10.83 0.34)
-9.19 (:: 0.29)
-7.61 (d: 0.27)
-10.66 (:: 0.61)
SynNet
-8.70 0.36)
-9.55 0.14)
-7.47 0.34)
-5.34 (L 0.23)
-10.98 0.57)
BBAR
-9.84 (1. 0.10)
-11.39 0.08)
-8.69 (1. 0.10)
-7.05 (L 0.09)
-11.07 (1: 0.04)
SynFlowNet
-10.34 (1: 0.07)
-11.98 (:: 0.12)
-9.40 (1: 0.05)
-7,90 (L 0.10)
-11.62 (1: 0.13)
Reaction
SynFlowNet
-9.36 0.25)
-10.64 0.19)
-8.25 0.10)
-6.84 (L 0.06)
-10.32 (1: 0.07)
RGFN
-9.61 (1: 0.11)
-10.96 0.18)
-8.53 (1 0.07)
-7.07 (1 0.06)
-10.86 (1: 0.11)
RxnFlow
-10.84 (:: 0.03)
-12.53 0.02)
-9.73 (# 0.02)
88,09 (t: 0.06)
-2230 (# 0.07)
Reaction
3DSynthFlow
-11.26 (1: 0.41)
-1336 (1: 0.03)
-10.00 (1: 0.04)
-8.41 (1 0.17)
-12.98 (1: 0.10)
25

---

Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
Table 18. Average ligand efficiency for top- 100 diverse modes generated against 15 LIT-PCBA targets. The best results in bold.
Average Ligand Efficiency (4)
Category
Method
ADRB2
ALDHI
ESR.ago ago
ESR antago
FEN1
FragGFN
0,410 0.006)
0.368 0.007)
0.347 (# 0.003)
0.358 (# 0.002)
0.246 0.004)
Fragment
FragGFN+SA
0.406 0.007)
0.374 (#: 0.023)
0.369 (# 0.003)
0.345 (# 0.024)
0.210 0.004)
SynNet
0,274 0.041)
0.272 (#: 0.006)
0.317 (# 0.005)
0.289 (# 0.020)
0.196 0.003)
BBAR
0.412 0.006)
0.401 (#: 0.008)
0.380 (# 0.001)
0.387 (#: 0.003)
0.257 0.003)
SynFlowNer
0,401 (#: 0.006)
0.380 (# 0.007)
0.361 (# 0.003)
0.361 (# 0.004)
0,247 (# 0.004)
Reaction
Synflownet"
0,380 0.021)
0.362 (# 0.016)
0.351 (# 0.008)
0.349 (# 0.005)
0,234 0.007)
RGFN
0.393 0.005)
0.357 (#: 0.004)
0.346 (# 0.002)
0.344 (#: 0.002)
0.241 0.001)
RxnFlow
0,412 (#: 0.005)
0.396 (#: 0.005)
0.375 (#: 0.002)
0,380 (:: 0.004)
0,246 (# 0.001)
Reaction
3DSynthFlow
0.448 0.019)
0.395 (:: 0.006)
0.391 (+: 0.005)
0.398 (:: 0.016)
0.252 0.005)
GBA
IDHI
KAT2A
MAPKI
MTTORI
FragGFN
0.333 (# 0.018)
0.367 (# 0.009)
0.322 (#: 0.008)
0.302 (# 0.002)
0.354 (# 0.005)
Fragment
FragGFN+SA
0.318 0.005)
0.369 0.020)
0.298 (#: 0.020)
0.294 (# 0.015)
0.355 0.027)
SynNet
0,244 0.013)
0.281 (# 0.016)
0.294 (#: 0.042)
0.226 (#: 0.004)
0.316 (# 0.035)
BBAR
0,336 0.002)
0.382 0.005)
0.332 (+: 0.003)
0.320 0.002)
0.385 0.004)
SynFlowNer
0,330 0.004)
0.368 (:: 0.002)
0.327 (+: 0.003)
0.305 (+: 0.002)
0.368 0.002)
Reaction
SynFlowNer
0.324 (#: 0.007)
0.360 (#: 0.013)
0.309 (#: 0.004)
0,297 (# 0.011)
0.361 (# 0.009)
RGFN
0.310 0.002)
0.351 0.003)
0.310 (:: 0.003)
0.298 (1: 0.002)
0.346 0.004)
RxnFlow
0.327 0.004)
0.378 (:: 0.001)
0.330 (+: 0.001)
0.313 (:: 0.001)
0,370 0.001)
3D Reaction
3DSynthFlow
0.340
0.388 0.007)
0.340 (:: 0.016)
0.322 (1: 0.009)
0.387 0.008)
OPRKI
PKM2
PPARG
TP53
VDR
FragGFN
0,352 (#: 0.004)
0.442 (#: 0.008)
0.319 (#: 0.077)
0.307 (#: 0.005)
0,394 (#: 0.006)
Fragment
FragGFN+SA
0.327 (#: 0.014)
0.440 (#: 0.009)
0.303 (#: 0.013)
0.248 (#: 0.025)
0.390 (# 0.020)
SynNet
0,298 (:: 0.039)
0,296 (+: 0.005)
0.253 (+: 0.051)
0,211 (:: 0.031)
0.359 (#: 0.015)
BBAR
0.370 (:: 0.006)
0.442 (+:: 0.004)
0.326 (1: 0.007)
0,288 (#: 0.005)
0,409 (1: 0.002)
SynFlowNet
0.359 0.004)
0.427 0.003)
0.317 (+: 0.002)
0.287 (:: 0.008)
0.393 0.003)
Reaction
SynFlowNer
0,355 (:: 0.008)
0,410 (+: 0.018)
0,296 (+: 0.010)
0,282 (:t: 0.005)
0,380 (#: 0.005)
RGFN
0.349 (:: 0.001)
0,405 (+: 0.002)
0.307 (1: 0.002)
0,271 (#: 0.001)
0.381 (4: 0.002)
RxnFlow
0.369 0.007)
0.436 0.005)
0.319 (1: 0.002)
0.289 (1: 0.003)
0.405 0.002)
3D Reaction
3DSynthFlow
0.389 (::: 0.006)
0.444 (:: 0.010)
0.321 (:: 0.005)
0.294 (:: 0.006)
0,416 (::: 0.009)
26

---

Compositional Flows for 3D Molecule and Synthesis Pathway Co-design
Table 19. Average success rate of AiZynthFinder for top-100 diverse modes generated against 15 LIT-PCBA targets. The best results are in hold.
AiZynthFinder Success Rate (%, 1)
Category
Method
ADRB2
ALDHI
ESR_ago
ESR _antago
FEN1
FragGFN
4,00 (#: 3.54)
3.75 (#: 192)
1.00 (#: 1.00)
3.75 (# 192)
0.25 (# 0.43)
Fragment
FragGFN+SA
5.75 (=: 1.48)
6.00 (# 2.55)
4,00 (#: 2.24)
1.00 (#: 0.00)
0.00 (+ 0.00)
SynNet
54.17 (#: 7.22)
50.00 (+: 0.00)
50.00 (:: 0.00)
25.00 (:: 25.00)
50.00 (# 0.00)
BBAR
21.25 (=: 5.36)
19.50 (=: 3.20)
17.50 (#: 1.50)
19.50 (#: 3.64)
20.00 (+ 2.12)
Reaction
SynFlowNet
52.75
1.09)
57.00 6.04)
53.75 (# 9.52)
56.50 2.29)
53.00 8.92)
SynFlowNet
56,50 r=: 6.58)
56.00 (+: 3.08)
61.00 (+ 2.74)
64.50 (#:: 9.86)
60.75 (# 3.77)
RGFN
46.75 (= 6.86)
47.50 (+ 4.06)
50.25 (# 2.17)
49.25 (#: 4.38)
48,50 ( 6.58)
RxnFlow
60.25
3.77)
63.25
3.11)
71.25 (= 4.15)
66.50 +
65.50 4.09)
3D Reaction
3DSynthFlow
85.00 (:: 7.87)
69.33 ( 3.86)
80.00 (:: 4.24)
69.67 (1: 14.06)
60.00 (1: 15.64)
GBA
IDHI
KAT2A
MAPK1
MTORC1
Fragment
FragGFN
5.00 4.24)
4.50 (:: 1.66)
(#: 0.8)
(:: 0.83)
2.75 1.30)
FragGEN+SA
3.00 (:: 1.00)
4.50 (#: 4.97)
1.50 (+: 0.50)
3,25 (:: 1.48)
3.50 (#: 2.50)
SynNet
50.00 0.00)
50.00 (:: 0.00)
45.83 (:: 27.32)
50.00 (:: 0.00)
54.17 7.22)
BBAR
17.75 (:: 2.28)
19.50 (+: 1.50)
18.75 (:: 1.92)
16,25 (:t: 3.49)
18.75 (1: 3.90)
SynFlowNet
58.00 (d: 4.64)
59.00 (d: 4.06)
55.50 (:: 10.23)
47.25 (1: 6.61)
57.00 (1: 7.58)
Reaction
SynFlowNer
61.50 3.84)
60.50 c:: 3.91)
57.25 (:: 4.97)
44.50 (1: 9.29)
62.00 1.22)
RGFN
48.00 r::: 1.22)
43.00 (:: 2.74)
49,00 (1 1.22)
42,00 (:t: 3.00)
44.50 (:: 4.03)
RxnFlow
66.00 (# 1.58)
64.00 ( 5.05)
66,50 (# 2.06)
63.00 (# 4.64)
70.50 (# 2.87)
3D Reaction
3DSynthFlow
64.67 (d: 3.09)
65.67 (1L 13.91)
68.00 (1 19.51)
54.67 (1 10.50)
64.67 (1. 15.69)
OPRK1
РKM2
PPARG
TP53
VDR
Fragment
FragGFN
2.50
2.29)
8.75 3.10)
0.75 (+) 0.43)
4.25
1.64)
3.50
2.18)
FragGEN+SA
3.25
1.79)
9.75 (:: 2.28)
1,25 (:: 1.09)
2.25 (t: 1,92)
3.75
2.77)
SynNet
54.17
7.22)
50.00
0.00)
54.17 (1) 7.22)
29.17 18.16)
45,83
7.22)
BBAR
13.75 (1:: 3.11)
20.00 (1: 0.71)
15.50 (1: 2.29)
18.50 (1: 3.28)
12.25 (1: 3.34)
SynFlowNet
56.50 (::: 7.63)
50.75 (1: 1.09)
53.50 (1L 5.68)
55.50 (1L 9.94)
53.50 (1: 1.80)
Reaction
SynFlowNet
56.25
2.49)
58.00
7.00)
57.00 (1. 5.74)
66.50
6.80)
53.50
3.84)
RGFN
48.00 (1L. 2.55)
48.50 (1. 3.20)
47.00 (1. 5.83)
53.25 (1. 3.63)
46.50
2.69)
RxnFlow
72.25 (#: 2.05)
62,00 (#: 3.24)
65.50 (+: 4.03)
67.50 (+b 2.96)
66.75 (#: 2.28)
Reaction
3DSynthFlow
67.33 (d.: 20.37)
78.67 (.L. 8.73)
65.67 (1 8.18)
61.33 (1L 11.73)
74.00 (1. 17.15)
27

---

Compositional Flows for 3D Molecule and Synthesis Pathway Co-design
Table 20. Average synthesis steps estimated from AiZynthFinder for top-100 diverse modes generated against 15 LIT-PCBA targets. The hest results are bold.
Average Number of Synthesis Steps ())
Category
Method
ADRB2
ALDHI
_aR_ago
ESR _an_aoo
FEN1
FragGFN
3.60 (#: 0.10)
3.83 (#: 0.88)
3.76 (#: 0.20)
3,76 (# 0.16)
3.34 (#: 0.18)
Fragment
FragGFN+SA
3.73 (# 0.09)
3,66 (#: 0.04)
3.66 (#: 0.07)
3.67 (# 0.21)
3.79 (#: 0.19)
SynNet
3.29 (#: 0.36)
3.50 (#: 0.00)
3.00 (:: 0.00)
4.13 (#: 0.89)
3,50 (:: 0.00)
BBAR
3.60 (#: 0.17)
3.62 (#: 0.19)
3,76 c:: 0.04)
3,72 0.11)
3.59 (#: 0.14)
SynFlowNet
2.64 (#:
2.48 (+: 0.07)
2.60 (:: 0.25)
2.45 0.09)
2.56 0.29)
Reaction
SynFlowNet
2.42 (#: 0.10)
2.48 0.10
2.38 0.10)
2.34 (# 0.30)
2,41 (#:
RGFN
2.88 (#: 0.21)
2,65 (#: 0.08)
2.78 (# 0.19)
2.91 (# 0.23)
2.76 (.177
RxnFlow
2.42 (#: 0.23)
2.19 0.12)
1.95 0.20)
2.15 0.18)
2.23 (2 0.18)
3D Reaction
3DSynthFlow
1.77 (#: 0.37)
2.23 (4: 0.16)
2.02 (#: 0.20)
2.43 (1: 0.61)
2.73 (1: 0.50)
GBA
IDH1
KAT2A
MAPK1
MTORCI
Fragment
FragGFN
3,94 (#: 0.11)
(#: 0.10)
3.78 (#: 0.09)
3.72 0.18)
3.84 ( 0.18)
FragGEN+SA
(. (#: 0.15)
3.84 (#: 0.23)
3.66 (: 0.18)
3.69 (# 0.21)
3,94 (# 0.08)
SynNet
3.38 (d: 0.22)
3.38 (d: 0.22)
3.46 (:: 0.95)
3.50 0.00)
( 0.36)
BBAR
3.71 (d: 0.12)
3.68 (+: 0.02)
3.63 (: 0.05)
3.73 (1: 0.05)
3.77 (1: 0.09)
SynFlowNet
2.48 (d: 0.18)
2.61 (1: 0.13)
2.45 ( 0.37)
2.81 (1: 0.24)
2.44 (1: 0.27)
Reaction
SynFlowNet
2.45 (:: 0.08)
2.46 (d: 0.12)
2.45 (1: 0.12)
2,83 0.27)
2.39 (1: 0.17)
RGFN
2.77 (1: 0.20)
2.97 (1: 0.15)
2.78 (:: 0.10)
2.86 (1 0.19)
2.92 (1: 0.06)
RxnFlow
2.10 (# 0.08)
2.16 0.11
2.29 (# 0.05)
2.29 (# 0.11)
2.05 (# 0.09)
3D Reaction
3DSynthFlow
2.47 (1: 0.24)
2.49 0.42)
2.47 (1 0.61)
2.70 (1 0.33)
2.42 (L 0.61)
OPRK1
PKM2
PPARG
TP53
VDR
FragGFN
3.82
3.71 (t 0.12)
3.73 0.24)
3.73 0.23)
3.75
Fragment
FragGEN+SA
3.62 (d: 0.12)
3.84 (d: 0.21)
3.71 (:: 0.04)
3.66 0.05)
3.67 (1: 0.25)
SynNet
3.29 (1:
3.50 (1 0.00)
3,29 0.36)
3.67
3.63 (L 0.22)
BBAR
3.70 (1: 0.17)
3.61 (1 0.05)
3.72 (1. 0.13)
3.65 (1 0.05)
3.77 (L 0.16)
SynFlowNer
2.49 (1: 0.33)
2.62 (1 0.10)
2.56 (:L: 0.12)
2.51 (1 0.27)
2.55 (1 0.09)
Reaction
SynFlowNet
2.50 0.11)
2.52 (1: 0.20)
2.53 0.06)
2.34 0.10)
2.51 0.17)
RGFN
2.81 (1: 0.12)
2.82 0.10
2,82 (1. 0.18)
2.64 (1 0.10)
2.84 (L 0.18)
RxnFlow
2.00 (#: 0.09)
2,34 (.1
2.21 (# 0.06)
2.12 (# 0.12)
2.12 (#: 0.12)
3D Reaction
3DSynthFlow
2.34 (1: 0.53)
2,20 (1 0.41)
2.61 (d: 0.39)
2.73 (1L 0.47)
2.25 (1L 0.78)
28

---

Compasitional Flows for 3D Molecule and Synthesis Pathway Co-design
F.8. Example generation trajectories
0=
t 0.3
t 0.6
t t=1
Amide Condensation
Amidization
Amidization
Amidization
1,2, 4-Oxadiazole Formation
Figure The example generation trajectory against ALDHI target. The top row shows the molecule æ; (green), The mid row shows the predicted final pose at each time step (cyan). The bottom row shows the synthesis pathway.
29


Reviews:
[{"review_id": "2wmAfWuWKh", "reviewer": "Reviewer_Z8PT", "summary": "This paper introduces Compositional Generative Flows (CGFlow), a framework that extends flow matching to generate objects with compositional structures and continuous features simultaneously. CGFlow combines two interleaved processes: Compositional Flow for modeling the probability path of compositional structures and State Flow for managing continuous states associated with these structures. The authors apply CGFlow to drug design through 3DSynthFlow, which jointly designs molecules' 3D binding poses and their synthetic pathways. By co-designing the 3D molecular structure and synthesis pathway, 3DSynthFlow achieves state-of-the-art binding affinity across all 15 targets in the LIT-PCBA benchmark compared to synthesis-based baselines. Evaluation using PoseCheck shows that molecules designed by 3DSynthFlow exhibit more protein-ligand interactions, demonstrating the value of 3D structure and synthesis pathway co-design. This approach addresses key challenges in drug discovery by ensuring both strong binding affinity and synthesizability.", "questions": "", "limitations": "", "rating": 5, "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": "We sincerely thank the reviewer for their thoughtful and detailed evaluation, and for recognizing the significance of our framework contribution and its application to 3D molecule and synthesis pathway co-design.\n\n> W1. More analysis of cases where the method performs poorly or limitations in certain chemical spaces.\n\nOur synthesis-based action space based on brick & linker synthons does not yet explore certain synthetic pathways such as ring-forming reactions, and nonlinear synthetic pathways, as pointed out by Reviewer ScwC. Our method predicts the 3D binding poses of intermediate states. This synthon-based generation is chosen to prevent the atoms from intermediate states being lost from reactions or forming new rings - which would degrade the accuracy of pose prediction for intermediate states.\n\nMoreover, our pose prediction module is trained on the CrossDocked2020 dataset, in which binding pockets are extracted with a distance cutoff based on the reference ligand structure, resulting in an inherently biased pocket to its reference ligand. This can negatively impact pose prediction accuracy if generated molecules optimally bind to a different subpocket from the reference ligand or are larger than the reference ligand. This issue arises during reinforcement learning-driven exploration of diverse chemical spaces. Addressing this limitation would require employing an unbiased pocket structure (e.g., using a center-based cutoff) or a full-protein structure, and we highlight this as a consideration for real-world application of our method.\n\nFinally, our training of poses is currently biased towards Vina docking poses from the CrossDocked2020 dataset. A promising direction to remove this bias is training the model on an experimental structure dataset.\n\n> W2. A more explicit discussion of the implementation challenges and computational overhead.\n\nThank you for this suggestion! We will incorporate the following details in our final manuscript. The state-flow model (i.e., the pocket-conditional pose predictor) was trained for 100 epochs using a batch size of 32 on 4 L40 GPUs (48GB), taking a total of 18.4 hours. Importantly, as the state-flow model is trained on the CrossDocked dataset and can be reused across different test pockets, it incurs only a one-time computational cost. We also plan to release the model weights, so users will only need to train the composition-flow model tailored to their custom reward function and target.\n\nThe composition-flow model is trained individually for each pocket for 1,000 steps with batch size of 64 and 80 flow matching steps. The training with GPU-accelerated docking takes 12-20 hours (depending on targets) on a single A4000 GPU (16GB). We find this computational requirement accessible for most practical drug discovery campaigns. Furthermore, the composition-flow model can also be trained in a pocket-conditioned manner (Please see SBDD benchmark in our response to Reviewer eDTU) to sample molecules for any target pocket in a zero-shot manner, making model training a one-time cost in this setting.\n|Flow matching steps|Avg Vina (↓)|Top 100 Vina (↓)|Training time (sec/iter)|Sampling time (sec/mol)|\n|-|-|-|-|-|\n|10|$-10.28\\pm0.32$|$-14.27\\pm0.59$|33|0.053|\n|20|$-10.24\\pm0.18$|$-14.38\\pm0.22$|34|0.080|\n|40|$-10.40\\pm0.13$|$-14.51\\pm0.27$|39|0.123|\n|60|$-10.50\\pm0.14$|$-14.57\\pm0.24$|44|0.160|\n|80|$-10.44\\pm0.18$|$-14.53\\pm0.16$|49|0.199|\n\nThe sampling time of our model is 0.05~0.20 seconds/molecule depending on the choice of number of flow matching steps. We further analyzed how the number of flow matching steps impacts performance using the ALDH1 target with the Vina reward. Performance slightly improves with increased flow matching steps and saturates around 40-60 steps. We attribute this marginal improvement to the fact that the pose prediction module’s primary role is providing a spatial context between intermediate molecules and the pocket; thus, extremely precise pose predictions have limited additional impact on model decisions.\n\n> Theoretical Claim & Question\n\nWe thank the reviewer for this insightful observation. Indeed, our current theoretical analysis leverages determinism through fixing the random seed primarily for analytical clarity. However, this leads to deterministic noise sampling for the initial synthon states; for example, when `C(=O)[*]` and `[*]NC` are sequentially added, their initial coordinates are identical. To maintain determinism while preventing synthons from receiving the same initial states, we can use the molecule size or a hash of the molecule to set distinct random seeds across the generation process.\n\nWe acknowledge this limitation explicitly and highlight extending our theoretical framework to handle fully stochastic environments, using Expected Flow Networks [1] as a promising direction for future research.\n\nReference:\n1. Jiralerspong, Marco, et al. \"Expected flow networks in stochastic environments and two-player zero-sum games.\" ICLR 2024.", "claims_and_evidence": "The claims in the paper are generally well-supported by clear and convincing evidence\n\nThe evidence is presented in a transparent manner with multiple evaluation metrics, statistical significance indicated by standard deviations across multiple runs, and comprehensive comparisons against relevant baseline methods.", "methods_and_evaluation_criteria": "The CGFlow framework logically extends flow matching to handle compositional objects with continuous features, which is precisely what's needed for molecular design where both structure and 3D conformation matter. The theoretical foundation connecting compositional flow with GFlowNets for discrete structure generation and state flow for continuous features is sound.\n\nFor evaluation, their choice of the LIT-PCBA benchmark is appropriate as it's a standard dataset for structure-based drug design.\n\nThe authors also conduct ablation studies on reward computation approaches and compare against multiple baselines including both fragment-based and reaction-based methods. Their experimental setup effectively demonstrates the value of jointly modeling 3D structure and synthesis pathways, which directly addresses limitations in prior work that focused on only one aspect or the other.\n\nHowever, the authors claim their approach handles \"compositional objects with continuous features\" broadly, but their evaluation is restricted only to molecular design. This raises questions about the true generalizability of CGFlow to other domains.", "theoretical_claims": "The main theoretical component appears in Appendix B (pages 14-15) where the authors develop the trajectory balance objective for their compositional flow model. The proof relies heavily on determinism introduced by fixing the random seed, which feels like a theoretical workaround rather than a principled approach. Please correct me if I'm wrong.", "experimental_designs_or_analyses": "The use of the LIT-PCBA benchmark with 15 diverse protein targets is appropriate and comprehensive. \n\nThe authors compare against a broad range of relevant baselines including fragment-based methods and reaction-based methods. This is thorough and appropriate.\n\nHowever, the paper lacks details about computational requirements and training time comparisons, which is important for assessing practical applicability.", "relation_to_broader_scientific_literature": "- The authors build upon prior flow matching work by Lipman et al. (2023) and extend it to handle compositional structures\n- The paper incorporates the GFlowNet framework introduced by Bengio et al. (2021) for exploring discrete compositional spaces. \n- The authors connect their work to recent advances in sequential diffusion models.\n- The authors address the synthesizability challenge highlighted by Gao & Coley (2020)", "essential_references_not_discussed": "not to my knowledge.", "other_strengths_and_weaknesses": "- Strengths:\n* The work addresses a significant real-world challenge in drug discovery by simultaneously optimizing for binding affinity and synthesizability. The practical utility is clear and valuable.\n* The figures (especially Figure 1) effectively illustrate the concept of interleaving compositional structure and continuous state generation, helping readers understand a complex methodology.\n\n- Weaknesses (just because I have to):\n* The paper would be stronger with more analysis of cases where the method performs poorly or limitations in certain chemical spaces.\n* The method introduces additional complexity compared to existing approaches. A more explicit discussion of the implementation challenges and computational overhead would provide a more balanced assessment of practical applicability.\n\nOverall, the paper presents a significant contribution by addressing the important challenge of jointly modeling 3D structure and synthesizability in molecular design, with a methodologically sound approach that could inspire future work in compositional generative modeling.", "other_comments_or_suggestions": "NA", "questions_for_authors": "Could you explain the rationale behind the footnote of page 14?", "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": "vMHtLKDMrJ", "reviewer": "Reviewer_eDTU", "summary": "The paper introduces Compositional Generative Flows (CGFlow), a novel framework designed for the generation of compositional objects with continuous features in generative applications, such as synthesis-based 3D molecular design. CGFlow extends flow matching by enabling the generation of objects in compositional steps while modeling continuous states. This is accomplished through a straightforward expansion of the flow matching interpolation process to model compositional state transitions. Additionally, CGFlow builds upon the theoretical foundations of generative flow networks (GFlowNets), allowing for reward-guided sampling of compositional structures.\n\nThe framework is applied to synthesizable drug design by simultaneously designing both the molecule's synthetic pathway and its 3D binding pose. CGFlow achieves state-of-the-art binding affinity compared to synthesis-based baselines, demonstrated across all 15 targets of the LIT-PCBA benchmark. Further evaluation with PoseCheck indicates that molecules designed using CGFlow exhibit a higher number of key protein-ligand interactions, underscoring the benefits of co-designing 3D molecular structures alongside their synthetic pathways.\n\n## update after rebuttal\n\nI keep my original rating. The authors have provided more evaluations in their rebuttal. My main concern is that the improvement of the proposed method over RxnFlow is too marginal while it introduces much more latency.", "questions": "", "limitations": "", "rating": 1, "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": "We highly appreciate this reviewer’s constructive feedback and insightful suggestions. We would like to clarify and address all of these points to the best of our ability in the response below. \n\n> W1: Lack of ablation studies about time scheduling of state flow model\n\nThank you for the valuable suggestion. We conducted an ablation study to assess the effect of time scheduling in state flow training, comparing three settings: partial (partial overlap of synthon denoising), no overlap (strictly autoregressive), and till end (all synthons denoised until $t=1$).\n\nWe compared the average local-optimized Vina docking scores across different training iterations for the ALDH1 target below:\n\n| \\# of mol explored | 10,000 | 20,000 | 30,000 |\n|-|-|-|-|\n| no overlap | $-5.68 \\pm 0.29$ | $-6.33 \\pm 0.26$ | $-7.02 \\pm 0.34$ |\n| partial | $-6.28 \\pm 0.22$ | $-7.28 \\pm 0.21$ | $-7.22 \\pm 0.12$ |\n| till end | $-7.15 \\pm 0.40$ | $-7.60 \\pm 0.29$ |$ -7.79 \\pm 0.12$ |\n\nCGFlow’s overlapping noise scheduling, where positions are refined as synthons are added, clearly outperforms conventional autoregressive approaches (no overlap). \n\n> W2 & W3: Lack of comprehensive evaluation (e.g., CrossDocked2020) and SBDD baselines.\n\nFollowing your suggestions, we evaluated CGFlow on CrossDocked2020 against established SBDD baselines. Using the same conditional objective and proxy setup as TacoGFN and RxnFlow, we generated 100 molecules per pocket in a zero-shot manner without an additional optimizing process for test targets. We varied the reward exponentiation parameter β (Low: U(1,64), Medium: U(32,64), High: U(48,64)) to balance exploitation and exploration for sampling.\n\n|   |Validity(↑)|Vina(↓)|QED(↑)|AiZyn. Succ Rate(↑)|Div(↑)|Time(↓)|\n|---|---|---|---|---|---|---|\n|Reference| - | -7.71|0.48|36.1| - | - |\n|FLAG|99.7|-7.07|0.49|21.9|0.82|1047|\n|DecompDiff|66.0|-8.35|0.37|0.9|0.84|6189|\n|MolCRAFT|96.7|-8.05|0.50|16.5|0.84|141|\n|MolCRAFT-large|70.8|-9.25|0.45|3.9|0.82 | >141|\n|TacoGFN|100.0|-8.24|0.67|1.3|0.67|4|\n|RxnFlow|100.0|-8.85|0.67|34.8|0.81|4|\n|CGFlow (low β)|100.0|-9.00|0.72|55.0|0.79|24|\n|CGFlow (med β)|100.0|-9.16|0.73|56.6|0.76|24|\n|CGFlow (high β)|100.0|-9.38|0.74|62.2|0.66|24|\n\nCGFlow reduces Vina from -8.85 (RxnFlow) to -9.38 (CGFlow-high beta), outperforming all baselines. It also yields the highest QED scores (0.72–0.74) and highest AiZynthFinder success rate (62.2%) compared to all baselines, underscoring the practical benefits of synthesis-aware generation. CGFlow shows consistent synthesis success rate across both CrossDock (55.0%–62.2%) and LIT-PCBA (53.1%) benchmarks.\n\n> W4. Concerns about reward hacking by generating larger molecules. \n\nTo address this concern, we conducted additional experiments on the first five targets, restricting heavy atom count (HAC) to 40. CGFlow still outperforms RxnFlow in Vina score (-10.94 vs -10.46) with comparable HAC (29.63 vs 29.37). Moreover, CGFlow achieves the highest ligand efficiency (0.375) - computed by Vina / HAC, confirming that our binding affinity gains stem from the 3D co-design strategy rather than molecule size.\n\n| |Vina (↓)|Ligand Efficiency (↑)|Avg Heavy atom count|\n|-|-|-|-|\n|SynFlownet|-8.644|0.335|26.44|\n|RGFN|-9.085|0.329|28.02|\n|RxnFlow|-10.457|0.362|29.37|\n|CGFlow (rebuttal)|-10.940|0.375|29.63|\n\n> W2 / W4: Measurement of training efficiency / The vina improvement over RxnFlow is marginal \n\nWe kindly refer the reviewer to our response to Reviewer ScwC (Weakness 1) for experimental results on training efficiency - where we show CGFlow discovers 4.7× more diverse modes than RxnFlow. We note that optimization of docking scores is restricted by the saturation of the pocket's binding interactions. At that point, discovering more diverse binding modes becomes more important to maximize the success rate of practical applications.\n\n> W4. Degeneration in Success Rate (synthesizability) and synthesize steps \n\nThe small drop in AiZynthFinder synthesizability arises from our transition from reaction-based generation (RxnFlow) to a synthon-based (brick-and-linker) approach. Reaction-based generation often halts prematurely if a state molecule lacks any reactive functional groups, while the synthon-based method can easily construct molecules with longer synthetic trajectories. We emphasize that our approach use the building block and synthesis reactions from Enamine REAL and xREAL, known for a wet-lab synthetic success rate of 80%.\n\n> W2/Q1. Lack of evaluation in geometrical properties and questions regarding generated poses.\n\nWe evaluated various geometrical properties and Vina score of the generated poses of the top 100 molecules of local-optimized Vina optimization across 3 seeds.\n\n|Metric|Validity|Med. Energy|Med. Strain Energy|Score|Minimize|Dock|Redock RMSD<1Å|Redock RMSD<2Å|\n|-|-|-|-|-|-|-|-|-|\n|Value|$1.0\\pm0.0$|$226.89\\pm18.83$|$147.82\\pm17.95$|$-8.749\\pm0.438$|$-12.240\\pm0.127$|$-12.915\\pm0.104$|$13.3 \\pm2.1$%|$57.3\\pm10.6$%|", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "I have checked all theoretical claims and found that they are correct.", "experimental_designs_or_analyses": "Yes. I also recommend to conduct experiments on CrossDocked2020 or BindingMOAD.", "relation_to_broader_scientific_literature": "The key contributions of the paper mainly relate to RxnFlow and Diffusion forcing. The work combines the ideas from both. The related works have been discussed in the paper. Additionally, I recommend the authors to cite and compare with other references which resemble this work somewhat [1].\n\n[1] Ghorbani, Mahdi, et al. \"Autoregressive fragment-based diffusion for pocket-aware ligand design.\" arXiv preprint arXiv:2401.05370 (2023).", "essential_references_not_discussed": "See above.\n\nFor a more comprehensive evaluation, the authors could consider comparing their CGFlow framework against structure-based drug design (SBDD) baselines, including references [1,2,3] among others. This would provide a more thorough assessment of CGFlow's performance and robustness in the context of established SBDD methodologies, enabling a clearer understanding of its strengths and potential areas of improvement.\n\n[1] Zhang, Z. and Liu, Q., 2023, July. Learning subpocket prototypes for generalizable structure-based drug design. In International Conference on Machine Learning (pp. 41382-41398). PMLR.\n\n[2] Zhou, X., Cheng, X., Yang, Y., Bao, Y., Wang, L. and Gu, Q., 2024. Decompopt: Controllable and decomposed diffusion models for structure-based molecular optimization. arXiv preprint arXiv:2403.13829.\n\n[3] Qu, Y., Qiu, K., Song, Y., Gong, J., Han, J., Zheng, M., Zhou, H. and Ma, W.Y., 2024. Molcraft: Structure-based drug design in continuous parameter space. arXiv preprint arXiv:2404.12141.", "other_strengths_and_weaknesses": "Strengths:\n1. This work introduces 3D information of ligands into RxnFlow-like frameworks, which enable modeling protein-ligand interactions.\n\nWeaknesses:\n1. Lack of ablation studies: since the time scheduler plays an important role in the proposed compositional flow matching, the related ablation studies are required. Currently, no related ablation studies are provided. What if the denoising process of coordinates have no overlap across different synthons?\n\n2. Lack of comprehensive evaluation: test on more datasets, such as CrossDocked2020 and BindingMOAD; measurement of training efficiency; lack of evaluation in geometrical properties since this paper is related to 3D molecule generation.\n\n3. Lack of baselines: SBDD baselines. \n\n4. The performance is not good: The vina improvement over RxnFlow is marginal, but the degeneration in Success Rate (synthesizability) and synthesize steps is obvious. It is well-known that the ligands with larger molecular weights tend to have better Vina scores. So it is suspectable that the slight improvement in Vina score comes from more synthesis steps.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "I noticed that the evaluation results in local optimized posed and rocked. Have you evaluated the Vina score directly on the generated poses? Have you checked the RMSD between the generated poses and redocked poses.", "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": "5TRy3LL80M", "reviewer": "Reviewer_ScwC", "summary": "The paper introduces a novel flow matching framework, 3DSynthFlow, for generating synthesizable molecules within protein pockets by sequentially selecting discrete building blocks and simultaneously modeling their coordinates. The authors evaluate 3DSynthFlow against all 15 protein targets in the LIT-PCBA virtual screening benchmark.", "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": "We appreciate the reviewer for volunteering their valuable time and providing insightful feedback to our paper. We are addressing their questions one by one in our response below.\n\n> W1. Evaluation of the diversity and chemical properties. \n\nTo further address the reviewer’s suggestion, we now compare sampling efficiency, diversity and other chemical properties of our method (CGFlow) against the 2D baseline (RxnFlow) on the first 5 LIT-PCBA targets. We define high-scoring modes as those with QED > 0.5, Vina < -10 kcal/mol for all pockets except FEN1, which we use -7 kcal/mol, and mode similarity < 0.5.\n\nThe table below shows the number of unique high-scoring modes identified after sampling 10k molecules: \n\n| |ADRB2|ALDH1|ESR_ago|ESR_antago|FEN1|Avg|\n| - | - | - | - | - | - | - |\n|RxnFlow|69|97|38|28|116|69.6|\n|CGFlow|276|417|358|213|358|324.4|\n\nCGFlow consistently outperforms RxnFlow in sampling efficiency, discovering 4.7x more diverse modes. Since mode diversity increases experimental success, this improvement highlights the practical advantage of our approach.\n\nWe further report the full sampling trend for ADRB2 and the average properties of the top 100 diverse modes. Diversity here is computed without similarity-based filtering to avoid artificial inflation. Our results confirm CGFlow's superior efficiency in discovering diverse modes with good QED and Vina scores.\n\n|\\# of mol explored|1000|10000|64000|Vina|QED|MW|HAC|LogP|Diversity|\n|-|-|-|-|-|-|-|-|-|-|\n|RxnFlow|2|69|1448| -11.57|0.67|388.5|28.2|4.25|0.88|\n|CGFlow|20|276|4323| -12.34|0.69|386.1|27.9|4.38|0.85|\n\nWe thank the reviewer for their comment, which motivated us to further highlight the strengths of our approach.\n\n> W2. Concern about computational cost.\n\nWe kindly refer the reviewer to our response to Reviewer Z8PT (Weakness 2) for further clarification on computational cost.\n\n> W3. Concern about limited search space due to the brick-and-linker formulation.\n\nWe appreciate the reviewer highlighting this important limitation regarding our synthesis approach. Indeed, as the reviewer pointed out, our current brick-and-linker formulation restricts the explored chemical space to linear molecules by excluding nonlinear reactions, such as ring formation. However, this constraint can be substantially mitigated by expanding the chemical search space through incorporating a larger building block library. For example, V-SYNTHES [1], a pioneering work in exploring Enamine REAL Space using a brick-and-linker strategy, successfully achieved a notable hit rate of 33%.\n\n> Q1. Question about the size of state space and unique building blocks explored during training.\n\nWe estimate the sample space according to the number of synthetic steps: $10^{11}$ molecules with a single reaction step, $10^{17}$ molecules with two reaction steps, and $10^{23}$ molecules with three reaction steps. In our experiments, we employed up to two reaction steps according to Enamine REAL, and the state space size is similar to RGFN (up to 4 steps with 8,350 blocks) and SynFlowNet (up to 3 steps with 200k blocks).\n\nAdditionally, we analyzed the number of unique building blocks (BBs) explored during training across the first 5 LIT-PCBA targets. Our model explored an average of ~55,000 unique BBs within 1,000 training iterations with a batch size of 64. This demonstrates a significantly broader exploration compared to SynFlowNet, which reported exploring ~15,000 unique BBs during 8,000 training iterations with a batch size of 8.\n\n|Target|ADRB2|ALDH1|ESR_ago|ESR_antago|FEN1|\n|-|-|-|-|-|-|\n|Number of Unique blocks|$45520\\pm7876$|$48644\\pm1983$|$55211\\pm5611$|$58097\\pm8529$|$69400\\pm5259$|\n\n> Q2. clarification as to the training details of the state flow model. \n\nYes, you are absolutely correct that during training, the state flow model encounters \"partial\" CrossDocked molecules. Specifically, we decompose each molecule into up to three fragments using 38 bimolecular Enamine synthesis protocols defined by reaction SMARTS. We then randomly sample a fragment ordering, matching the fragment introduction schedule used in the Compositional Flow model (e.g., fragment A at $t=0$, B at $t=0.3$, etc.). A random time step is sampled so that at earlier steps, the model sees \"partial\" structures. This design enables the state flow model to learn realistic fragment docking conformations aligned with the fragment selection process of compositional flow.\n\nImportantly, the decomposition is not intended to recover purchasable Enamine synthons but to expose the model to chemically meaningful substructures for learning protein-pocket conformations. While guided by Enamine protocols, exact synthon matching is unnecessary, allowing us to use any molecules for pose prediction training. We will clarify these points in the revised appendix.\n\nReference:\n1. Sadybekov, Arman A., et al. \"Synthon-based ligand discovery in virtual libraries of over 11 billion compounds.\" Nature 601.7893 (2022): 452-459.", "claims_and_evidence": "The claims are adequately supported by the evidence presented in the paper.", "methods_and_evaluation_criteria": "The authors evaluate 3DSynthFlow on targets in the LIT-PCBA dataset using docking as an oracle. The exhaustive validation of the model on several protein targets and its consistent strong performance strengthens the results of the paper. However, the evaluation of the generated molecules for diversity and respective properties is somewhat lacking, discussed below in the Weaknesses section.", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "Discussed below.", "relation_to_broader_scientific_literature": "The paper builds on previous literature on synthesizable molecule generation with GFlowNets, and represents a step forward in template-based molecular synthesis with a new 3-dimensional flow matching component for atomic coordinates of selected building blocks.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Strengths:\n- This reviewer notes that the 3D information provided by the state flow model allows for better-informed building block selections with the GFlowNet at intermediate steps during molecule generation compared to 2D methods.\n- This reviewer agrees that reaction template-based generation constraints are important for practical molecular generation in 3D, and finds the sequential design apt for ensuring synthesizability while retaining the ability to denoise building block coordinates according to their respective local time steps.\n\nWeaknesses:\n- The evaluation of the diversity and chemical properties of generated molecules is insufficient. The authors do not report the diversity of molecules of the 3D co-design model (as measured by average Tanimoto similarity or number of high-scoring modes, etc.) compared to the 2D models or compare these metrics between molecules generated for different protein targets.\n- The approach seems to require training two separate models, the GFlowNet and the state flow (flow matching) model, which may prove somewhat computationally expensive. \n- The approach uses synthons rather than template-based molecular synthesis, which aids in the simplicity of combining building blocks. However, they restrict their synthesis process to a brick-and-linker formulation with up to 3 blocks, which limits the explored chemical space to linear molecules.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "- This reviewer is curious about the exploration space of the enamine synthons and requests that the authors provide an estimation of the state space size similar to that of Fig. 2 of SynFlowNet or Fig. 2 of RGFN. Additionally, the reviewer would like to see the number of unique building blocks explored for experiments, similar to Fig. 7 of SynFlowNet.\n- This reviewer would like more clarification as to the training details of the state flow model. In the appendix, there is mention of \"decomposing CrossDocked molecules\" to train the state flow model. However, it is unclear whether the training dataset for the state flow model contains \"partial\" CrossDocked molecules, which would aid in learning to dock the initial, individual fragments selected by the GFlowNet. This reviewer is also curious as to the success rate in decomposing molecules from CrossDocked into Enamine synthons, and what proportion of molecules succeed or fail to be decomposed.", "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 on Compositional Generative Flows presents a novel and methodologically sound approach for jointly modeling 3D structure and synthesizability in molecular design, addressing a significant real-world challenge in drug discovery. Reviewers identified various strengths, such as well-supported claims, a logical extension of flow matching, and appropriate benchmarks, but also raised concerns like limited generalizability, theoretical issues, lack of certain evaluations, and performance compared to baselines. The authors made substantial efforts in their rebuttals to address these concerns, providing more details on limitations, computational aspects, conducting additional experiments, and clarifying training details.  However, after discussion, reviewers still have concerns about the effectiveness of the proposed method from the empirical perspective. 
"The evaluation on CrossDock strengthens the results. However, the Vina scores of RxnFlow and CGFlow are quite similar (-8.85 versus -9.00), with RxnFlow showing a significantly faster inference time (4 versus 24). While the binding affinities are alike, CGFlow's slower generation is noteworthy. Moreover, increasing beta improves binding affinity but severely impacts diversity." After careful proof, the are chair regards this as valid, and authors should clarify this in the next version to make your manuscript stronger.
Decision: Accept (poster)