SynCoGen: Synthesizable 3D Molecule Generation via Joint Reaction and Coordinate Modeling
Authors: Andrei Rekesh
Miruna Cretu
Dmytro Shevchuk
Pietro Lio
Robert A. Batey
Mike Tyers
Michał Koziarski
Cheng-Hao Liu
Venue: ICLR 2026 Poster (2026)
Keywords: molecule
generation
flowmatching
diffusion
chemistry
synthesizable
Primary area: generative models
TL;DR: multimodal model generates synthesizable molecules with their 3D coordinates, new SOTA across metrics and can perform conditional generation such as pharmacophore conditioning

Abstract: Ensuring synthesizability in generative small molecule design remains a major challenge. While recent developments in synthesizable molecule generation have demonstrated promising results, these efforts have been largely confined to 2D molecular graph representations, limiting the ability to perform geometry-based conditional generation. In this work, we present SYNCOGEN (Synthesizable Co-Generation), a single framework that combines simultaneous masked graph diffusion and flow matching for synthesizable 3D molecule generation. SYNCOGEN samples from the joint distribution of molecular building blocks, chemical reactions, and atomic coordinates. To train the model, we curated SYNSPACE, a dataset containing over 600K synthesis-aware building block graphs and 3.3M conformers. SYNCOGEN achieves state-of-the-art performance in unconditional small molecule graph and conformer generation, and the model delivers competitive performance in zero-shot molecular linker design and pharmacophore conditioning for protein ligand generation in drug discovery. Overall, this multimodal formulation represents a foundation for future applications enabled by non-autoregressive molecular generation, including analog expansion, lead optimization, and direct structure conditioning.

Published as a conference paper at ICLR 2026
SYNCOGEN: SYNTHESIZABLE 3D MOLECULE GENER- ATION VIA JOINT REACTION AND COORDINATE MOD- ELING
Andrei Rekesh 2: : Miruna Cretu", Dmytro Shevchuk 12, Vignesh Ram Somnath', Pietro Lid", Robert A. Batey', Mike Tyers' Michat Koziarski Cheng-Hao 8.7,.
University of Toronto, "The Hospital for Sick Children, UUnieerstty of Cambridge. 'ETH Zürich, Veecoo Institute, "Mila Quebec Al Institute, "McGill University, *Caltech
ABSTRACT
Synthesizability remains critical bottleneck in generative molecular design. While recent advances have addressed synthesizabilityy in 2D graphs, extending these constraints to 3D for geometry-based conditional generation remains largely un- explored. In this work, we present SYNCOGEN (Synthesizable Co-Generation), a single framework that combines simultaneous masked graph diffusion and flow matching for synthesizable 3D molecule generation. SYNCOGEN samples from the joint distribution of molecular building blocks, chemical reactions, and atomic coordinates. To train the model, we curated SYNSPACE, a dataset family containing over 1.2M synthesis aware building block graphs and 7.5M conformers. SYNCO- GEN achieves state-of-ther -art performance in unconditional small molecule graph and conformer co-generation. For protein ligand generation in drug discovery, the amortized model delivers superior performance in both molecular linker design and cearmacophore-conddiionn
generation across diverse targets without relying on any scoring functions. Overall, this multimodal non-autoregressive formulation represents a foundation for range of molecular design applications, including analog expansion, lead optimization, and direct de novo design.
INTRODUCTION
Generative models significantly enhance the efficiency of chemical space exploration in drug discovery by directly sampling molecules with desired properties. However, a key bottleneck their practical deployment is low synthetic accessibility; that is. generated molecules are often difficult or impossible to produce in the laboratory (Gao & Coley 2020). To address this limitation, recent work has turned to cemplate-based methods that emulate the chemical synthesis process by constructing synthesis trees that link molecular building blocks through known reaction templates (Koziarski et al. 2024] Cretu al. 2024 Seo al. 2024; Gaiñski et al., 2025 Gao et al. 2024 Jocys al. 2024 Swanson et al. 2024). ). These representations, while useful for downstream experimental validation, do not describe the underlying 3D geometry and thus cannot capitalize on the conformational information
that is often crucial for diverse chemical and biological properties.
Parallel advances in generative molecular design have explored spatial modeling at the atomic level. Inspired by advances in protein structure prediction (Yang et al.) 2025) Campbell al. 2024 Wang et al. (025) and the development of generative frameworks such as diffusion and flow matching, recent work has focused on directly sampling 3D atomic coordinates of small molecules
Hassan et al., 2024 Jing et al., 2022 Fan et al. 2024). These methods learn to generate spatially meaningful, property-alignee conformations along with molecular graphs. The ability to model atomic coordinates directly increases the expressivity of these approaches, enabling applications such
as nocket-conditionn generation (Lee & Cho 2024), scaffold hopping (Torge et al., 2023] Yoo et 2024), analog discovery (Sun et al., 2025), and molecular optimization (Morehead & Cheng 2024). However, without considering practical synthesis routes, integrating synthesizability constraints into these models remains major challenge, and most existing 3D generative approaches do not ensure that proposed molecules can be made in practice.
"oorreponndence rekesh@mai .utoronto.co ca and changhao. liu@mai mmgi

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Figure 1: SYNCOGEN is a simultancous masked graph diffusion and flow matching model that generates synthesizable molecules in 3D coordinate space. Each node corresponds to building block, and edges encode chemical reactions. Note that graphs are not necessarily path graphs, the leaving groups not displayed, and there is no order which nodes and edges are denoised.
This work introduces SYNCOGEN (Synthesizable Co-Generation), generative modeling framework aiming to bridge the gap between 3D molecular generation and practical synthetic accessibility (Figure D. Our main contributions as follows:
Generative Framework: We propose a novel generative framework that combines masked graph diffusion with flow matching in unified time to jointly sample from the distribution over building block reaction graphs and of 3D coordinates, tying structure- and synthesis-awar aware modeling.
dataset family SYNSPACE, comprising 1.2M synthesizable molecules represented as building block reaction graphs, along with 7.5M associated low low-energy conformations. Compared
Molecular Dataset: We curate
mathon-bbssed datasets, SYNSPACE enables models to generate more readily synthesizable molecules and directly suggest streamlined synthetic routes.
We demonstrate that SYNCOGEN achieves satte-of-th-az performance 3D molecule generation, producing physically realistic conformers while explicitly tracing reaction steps. Ablations show our modelling choices are crucial for the performance. Importantly, SyNCOGEN performs 3D conditional molecular generation tasks including linker design and pharmacophorr-cconitioneee generation, highlighting its applicability for drug discovery.
Empirical Validation:
Our code can be found at http://s//attt.oooooo/aaeeeeeees Our data can be found http:s/swuaggnnrreeee////eeessss
2 BACKGROUND AND RELATED WORK
Flow Matching. Given two distributions Po and P1, and interpolating probability path Pe such
that Pt=0 Po and P:=1 P), flow matching (Lipman et al. 2023 Albergo et al. 2023 Liu et al. 2023: Peluchetti 2023 Tong al. 2023) aims learn the underlying vector field 14 that generates Pr. Since un is not known in closed form, flow matching instead defines a conditional probability path Paj1 and its corresponding vector field uyj1 The marginal vector field u, can then be learnt with a parametric up by regressing against Zaj with the CFM objective:
(CFM(0) Ex,xxriix (- (x; 0) Uajz u (x|x:)|1
(I)
Masked Discrete Diffusion Models. Let Pdata be one-hot encoding over K categories.
Discrete diffusion models (Austin et al. 2021 Sahoo et al.) 2024 Shi et al.) 2024) map the complex
data distribution Pdata simpler distribution via Markov process, with absorbing (or masked) diffusion being the most common. In the masked diffusion framework, the forward interpolation process (Pt)xe(o.1) with the associated noise schedule (as)rejo.1) results in marginals q(z xx) Cat(z;; a,x (1 ox) m.) where 2, and denote intermediate latent variables and the one-hot
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encoding for the special [MASK] token, respectively. The posterior can be derived as:
Cat(zs; Zt);
24 o m
gzz, Zr, x) Cat(zs; (--a)mm(aaaaa
(2)
1-0+
The optimal reverse process po | 2t) takes the same form but with zp Zr, () in place of the true x.
We adopt the zero-masking and carry-over unmasking modifications of Sahoo al. (2024).
Multimodal Generative Models. Multimodal data generation (e.g. text-images, audio-vision, sequences/atomie types and 3D structures) represents a challenging frontier for generative models and has seen growing interest in recent times. Current approaches for this task typically either- 1) tokenize multimodal data into discrete tokens, followed by a autoregressive generation (Meta) [0044]
Xie et al., 2024 Lu al. ). 2) utilize diffusion / flow models for each modality in its native space (Lee et al.
2023 Zhang et al. 2024) Camphell et al. [024]] [rwin et al. (025). Diffusion and
flow models also offer flexibility in terms of coupled (Lee al. 2023] Irwin al. 2025) decoupled
(Campbell et al.
2024 Bao et al. 2023 Kim et al.) (024)) diffusion schedules across modalities.
SYNCOGEN uses coupled diffusion schedule but at two resolutions, with discrete diffusion for
graphs of building blocks and reactions, and a flow for atomic coordinates in building blocks.
3D Molecular Generation. Several recent works (Irwin et al. 2025 Le et al. 2024 Vignac et al. 2023; Huang et al.] 2023] Dunn & Koes, (024) have studied unconditional molecular structure generation by sampling from the joint distribution over atom types and coordinates. However, these models lack the ability constrain the design space synthetically accessible molecules. In concurrent work, (Shen et al.] (205)) uses generated 3D structures to guide GFlowNet policies in designing the graph of synthon-based linear molecules, but does not account for structural quality.
Synthesizable Molecule Generation. Beyond directly optimizing synthesizability scores (Liu et al. 2022; Guo & Schwaller 2023) which are often unreliable - the predominant approach to ensuring synthetic accessibility in generative models is to incorporate reaction templates. Early methods explored autoencoders (Bradshaw et al., 2019 2020), genetic algorithms (Gao et al., 2022). and reinforcement learning (Gottipati et al. [2020] Horwood & Noutahi, 2020). Recently, GFlowNet-
(Koziarski et al., 2024 Cretu et al. [024]] Seo et al. 2024 Gainski et al. and transformer-
(Gao et al. [0024] Jocys al., 2024) methods have gained prominence. Such generative models have already shown practical utility in biological discovery tasks (Swanson et al. (004).. However, most methods only generate molecular graphs and do not produce 3D structures. The recent CGFlow [Shen] it al. (2025) performs 3D generation via a GFlowNet policy augmented with flow matching; however, CGFlow optimizes reward and typically requires a full training for each target pocket.
3 DATASET
Training a synthesizability-awaaa model to co-generate both 2D structures and 3D positions requires a dataset of easily synthesizable molecules an appropriate format. In addition to atomic coordinates, this includes a graph-based representation from which plausible synthetic pathways can be inferred. common approach is to use synthons theoretical structural units that can be combined to form complete molecules(Baker et al. 2024) Grigg et al. 2025) Ledel-Lacruz et al. (025). Synthon- representations do not guarantee the existence
valid synthesis route, and they do not directly provide one even if it exists. Moreover, they lack the flexibility to constrain the reaction space, which often critical when prioritizing high-yield, high-reliability reactions or operating within the limits of automated synthesis platforms such as self-driving labs (Abolhasani & Kumacheva 2023).
Alternatively, many synthesis sytthesis-aware aware generators employ external reaction simulators, such as RDKit, to couple building blocks iteratively. While convenient, such black-bor steps offer no fine-graines control when a reagent has multiple reaction centers, distinct atoms or atom sets that can each serve as the site of bond formation or cleavage in a reaction. They also do not define atom mappings between reactants and products, making it impossible to trace product atoms back to their parent building blocks, which complicates edge assignment in building block graph generation. To overcome these limitations, we curate new family of datasets, SYNSPACE (Figure 2). comprising building block-level reaction graphs pairs with corresponding atom- and block-level graphs. We then calculate multiple 3D conformations for each graph using semi-empirical methods (Bannwarth al. 2019).
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Building selection
Reaction center
center
Buchwald- Harteei Coupling
Aua
coupling
the
Reductiva
Figure 2: Overview of SYNSPACE creation process. Highly synthesizable molecules are proce- durally constructed by iteratively sampling synthesis pathways from a set of building blocks and reactions. Starting from initial block, the procedure selects reaction center, compatible reaction, and a suitable reactant. After the final structure is assembled, multiple low-energy 3D conformations are generated. We provide two SYNSPACE datasets from two vocabularies, practically focused core set and an extended variant; each dataset contains 600k graphs with 3-4M conformers.
3.1 SYNSPACE: GRAPH GENERATION
We first construct two curated vocabularies adapted from the collection proposed by Koziarski et al. (2024). The first vocabulary pairs 93 low-cost, commercially available building blocks with 19 high-yield reaction templates, defining a virtual synthesis space of over billion molecules. The second vocabulary is superset with 378 building blocks with 26 reactions, expanding the synthesis space to over a trillion molecules. All building blocks were selected because they are known to undergo the chosen reactions, acknowledging that the presence of nominally compatible functional group alone does not guarantee participation in the corresponding transformation. We utilize reactions that (1) ensure all product atoms originate from the two input reagents, and (2) involve most one leaving group per reagent. We emphasize that these constraints yield simple, robust chemistries that are routinely executed and support rapid multi-step synthesis from inexpensive, in-stock reagents.
We procedurally generate SYNSPACE from the smaller vocabulary, SYNSPACE-L from the larger superset, by iteratively coupling building block graphs at their reaction centers with compatible reaction templates (Appendix(A.2)
For SYNSPACE, obtained 622,766 building block reaction graphs, each constructed from 2 to 4 sequential reactions. For each molecule, we generate multiple 3D conformations (Section 3.2 yielding 3,360,908 conformers. Similarly, SYNSPACE-L. contains 600,000 graphs and 267 conformations. Unless otherwise noted, all models are trained on SYNSPACE, which emphasizes practicality as its fewer building blocks are more readily stocked, whereas SYNSPACE-L is reserved for when a larger, more exploratory search space is required.
SYNSPACE contains diverse molecules that are drug-like (e.g., LogP ~ 2.5: broad range of topological polar surface areas; large fraction of sp² carbons). Importantly, compared to Geom-Drugs (Axelrod & Gomez-Bombarelln 2022), SYNSPACE contains substantially more unique Murcko scaffolds, indicating breadth despite the building block space. With a larger accessible space, SYNSPACE- L preserves similar physicochemical profiles and scaffold diversity. See Appendix A.3 for details.
Note: Injectivity. Many commercial building blocks contain multiple reaction centers, each compatible with different set of corresponding reaction centers other blocks. Thus, a building block-level reaction graph G. = (X, E) is not fully specified when edges are parametrized by the reaction alone. To achieve injective correspondence, we label edges from node i j > i by the triple ej = (r, v; 2;), where r is the coupling reaction and (1) U2) are the participating reaction centers on the source and destination blocks, respectively. Stereoisomers that form during reactions collapse to the same (X, E)) representation, but this granularity suffices for our current scope.
3.2 SYNSPACE: CONFORMATION GENERATION
For each molecular graph, 50 initial conformers were generated using the ETKDG (Riniker & energy-minimized minimized using the MMFF94 force field, and all conformers within 10 kcal/mol of the global minimum were retained.
Landrum 2013) algorithm (RDKit implementation). These structures were energy
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The resulting geometries were then re-optimized with the semi-empirical GFN2-xTB (Bannwarth et al.] 2019) method, after which the same 10 kcal/mol energy threshold was applied. At every stage, redundant structures were removed by gcometry-basee clustering (RMSD < 1.5A). This workflow yields, average. 5.4 distinct conformers per graph. Relative to exhaustive approaches such as CREST (Pracht et al. 2024), the workflow is several orders of magnitude faster; despite occasionally omitting some conformations, the retained structures are diverse and reproduce the bond-length, bond-angle, and anggle distributions observed in CREST-deriver datasets (see Section 5.1
3.3 SYNSPACE: PIARRAACPPHORT GENERATION
For each conformer of a molecule SYNSPACE and SYNSPACE-L, we generate a pharmacophore profile consisting of one-hot pharmacophore types X pharm E {0, 1) 1 NNtamx Mope and positions Cphum E RR-Nam x3 using ShePhERD Adams et al. (2025). Here, Npharm and Nyyes correspond to the number of pharmacophore features and the number of pharmacophore types, respectively.
4 METHODS
Notation. Let B be the building-block vocabulary and R the set of reaction templates, with cardinalities B := [B] and R == (R]. Let N denote the maximum number of building blocks per molecule and M the maximum number of atoms per building block. For each block b E B we denote its set of reaction-center atoms by V(b); the global maximum of these counts is Vimax := m [b)]. Hence, tensor shapes contain factors such B 1 (to accommodate the masked max + 2 (to accommodate the no-edge and masked tokens 2g and Tg), together with the bounds N and M introduced above.
token x in X), R V2
SYNCOGEN. SYNCOGEN generates building block-level reaction graphs and coordinates. Each molecule is represented by a triple (X, E, C) where X E {0, 1 >x encodes the sequence of building-block identities, E' {0, 1e..x - +2 labels the coupling reaction (and centers) between every building block pair, and E NxM33 stores all atomic coordinates. We detail the parameterization of graphs (X, E) in Appendix B.4 Training combines two diffusion schemes: 1) discrete absorbing process on (X, E) using the categorical forward kernel of Sahoo et al. (2024), and 2) continuous, visibility-awarr process C whose endpoints are (i) potoorrannlationlllllliig isotropic Gaussian and (ii) a re-centered ground truth, considering all "visible" atoms in the prior (see Section 4.2p. For intuitive schematic and description of the training procedure, Appendix B.
4.1 MODEL ARCHITECTURE
We adapt SE(3) architecture originally designed for all-atom molecular design (SEMLAFLLOW (Irwin et al., 2025)) as the prineipal backbone to generate both coordinates and graphs. At each timestep t, SYNCOGEN predicts building block logits LØ LE and shifted co- ordinate estimate Čt. The loss is the weighted sum of the cross-entropy term Lgraph on (X, F.), the masked coordinate MSE term LMSE, and the short-range pairwise distance term Epair (see Appendices B.7 and B. for details). We define additional building-blowd block-too-atom featurization in Appendix B.5 and atom-to- hitn-to-buiddig-bblee block output layers in Appendix B.10
Pharmacophore Conditioning Backbone. To accommodate pharmacophores conditioning information, we design a modified backbone to represent each as an "atom" with no weight during centering operations. After atom featurization, pharmacophore types are fed through a separate featurization head and concatenated to invariant atom type features, i.e. Xmodel [MLPacmm (a MLPphamm (X (Xphum)) E (NN+N Pharmacophore coordinates are concate- nated directly to atomic coordinates, Cmodel [C, Cpham] E (N and therefore undergo identical data augmentation beforehand (including that induced by data pairing, see Section 4.2). Cmodel and Xmodel are then passed to the sndivariant-nvvrrin dynamics module. Prior to final output layers, expanded atve- hidden-layer outputs are truncated the total number of atoms N M.
4.2 NOISING SCHEMES
Graph Noising. We noise true graphs (Xu, Eo) to obtain (Xe, Ex) using the procedure described in Section [ In practice, as all true edge matrices Eg are symmetric, we symmetrize the sampled probabilities for the noising and denoising of F,, correspondingly (see Appendix B.11).
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Coordinate Noising During sampling, for any time t where some X, contains masked building block, we do not know the block's 's identity or atom count and thus represent its coordinates by a vector containing M atoms of unknown type, where M is chosen upper bound on the number of atoms in a building block. To match this lack of information at training time, we perform the following: (i) First, we generate a noised graph (X,, Ex) and draw C ~ NN ())x(MM)) (ii) We then design visibility mask St that considers all M atoms for each noised building block containing m S M atoms in X2 as valid. (iii) To keep atom counts identical within individual data pairs, St is applied to both Co and Ct. (iv) The additional M m "padding" atoms in C1 are copied to Co to create modified ground-truth Co- (v) With consistent number of atoms in place, both are centered. For a visual diagram describing this procedure, see Appendix [
Thus, we construct centered, tisibliity-maser data-noise coordinate pairs (Ci, Co) that both contain [St] "visible" atoms to match the information available to the model during sampling. Input to the model C₁ is then obtained by linearly interpolating C = (1 - -) + t(C1). Essentially, we task the model with rearranging the true atoms while disregarding padding by learning to fix padding atoms in place. See Algorithm 2 for formalization. We note a caveat in equivariance in Appendix [..6
Flexible Atom Count. Most 3D molecule generation methods require specifying the number of atoms during inference. Because the prior of SYNCOGEN is over building blocks, we naturally handle flexible number of atoms during generation and model any excessive atoms as padding.
4.3 TRAINING-TIME CONSTRAINTS
For discrete diffusion, SYNCOGEN inherits training-time simplifications from MDLM (Sahoo et al., 2024). including zero masked logit probabilities and carry-over logit unmasking during sampling. In addition, we implement the following:
1. No-Edge Diagonals. We set the diagonals of all edge logit predictions 1.g to no-edge, as no building block has coupling reaction- -ndducedd bond to itself.
2. Edge Count Limit. Let kg := I= [E, & {TEAAE} be the number of unmasked true edges in the upper triangle of E,. If k2 = n 1, we have the correct number of edges for molecule containing n building blocks and therefore set remaining edge logits to Ag-
3. Compatibility Masking, Assume that for some Fr an edge entry is already denoised, [t =
(r, o 22), meaning that building block reacts with building block via reaction r and centers
E V V(Xi), ey E V(X)). Define the sets of center-matched reagents
BA = { E B (b, u) matches reagent A in r},
(3)
B b B (b, v) matches reagent B in r).
For every node slot (resp. j) we construct a dB)-dimensoonal binary mask
Xr, = [bb E B,A, X,,k = [b, E B, 1. = 1,..,,,,,,,, [B..
(4)
so that the soft-max for Xzli,-] (resp. Xe -D) is evaluated only over the 1-entries of X, (resp. X2). Analogously, once node identity X.D] = b is denoised, incoming edge channels (i, j)
with > i are masked to reactions (r, Us, v2y) such that b E BB
For visual diagram of the above, see Appendix B.2
Put simply. we restrict logits to disallow loops (e.g. macrocycles. which are often synthetically challenging), to impose a limit on the number of edges, and to better ensure the selection of chemically compatible building blocks and reactions.
4.4 SAMPLING
Sampling begins by drawing a building block count n. ~ Cat (aiinn)))) ), setting the node and edge tensors to the masked tokens, X [ = xx, E Ei j.] = Tg for every S i,j < N, and padding all (i (i n) rows/columns with the no-edge token Ag. The initial coordinates are an isotropic Gaussian C ~ NO, NX From this state, each step (i) recenters the current coordinates by the visibility mask S, derived from X,, (ii) generates node and edge logits and coordinate predictions with the trained model, (iii) draws the next discrete state from (ii), and (iv) updates coordinates via an Euler step. After a final, deterministic pass, we calculate (Xo, Ea) = arg max, I [ .... .|] and center the coordinates to yield the molecule (Xo; Bo, Co). Complete pseudocode is provided in Appendix B.8

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We note discrete and continuous schemes share unified time. Lastly, find inference annealing on the coordinates (see Appendix (.2) yields small performance gains at sampling time.
Note: Inference-Tinee Edge Constraints. By construction, a molecule containing n connected building blocks contains exactly
edges, and building block j 0 has single unique parent i < j. Consequently, sampling of redundant or impossible edges can be eliminated at inference time as described in Appendix B.9 and visualized in Appendix [3.
EXPERIMENTS
5.1 De Novo 3D MOLECULE GENERATION
We first study SYNCOGEN in unconditional molecule generation jointly with 3D coordinates and reaction graphs. We evaluate SYNCOGEN against several recently published all-atom generation frameworks which produce 3D coordinates, including SemlaFlow (Irwin et al. 2025), EQGAT-Diff (Le et al. 2024), MiDi VVignac et al. (023), JODO (Huang et al., 2023). and FlowMol (Dunn & Koes 2024). To isolate modeling effects from data, we retrain SemlaFlow on atomic types/coordinates in SYNSPACE for the same number of epochs as SYNCOGEN.
For each model, we sample 1000 molecules and compute stringent metrics capturing chemical soundness, synthetic accessibility, conformer quality, and distributional fidelity. Regarding the molecular graphs, we report the RDKit sanitization validity (Valid.) and retrosynthetic solve rate (AiZynthFinder (Genheden et al.) 2020) (AiZyn.) and Syntheseus (Maziarz et al.) (025)) (Synth.)). For conformers, introduce two chysics-based metries: the median non-bonded interaction energies per atom via the forcefield method GFN-FF and via the semiempirical quantum chemistry method GFN2- xTB Bannwarth et al. (2199) Spicher & Grimme (2020); also check PoseBusters (Buttenschoen et al. (024) validity rate (PB). We evaluate the diversity (Div.) as the average pairwise Tanimoto dissimilarity of the Morgan2 fingerprints, novelty (Nov.) as the percentage of candidates not appearing in the training set, and the Fréchet ChemNet Distance (Preuer et al. 2018) (FCD) between generated samples and the training distribution. See Appendix for details.
Table I: Comparison of generative methods for de novo 3D molecule generation.
Primary metrics
Secondary metrics
Group
Method
Valid. AiZyn. f Synth. GENN-FF XTB
PB1
FCD Div. Nov. 1
Rans & coords
SYNCOGEN
96.7
50
72
3.01
-0.91
87.2
2.91
0.78
93.9
SEMLAFLOOW
93.3
38
36
5.96
-0.72
87.2
7.21
0.85
99.6
SEMLAFLOW SYNSPACE
72.0
3.27
-0.80
60.3
2.95
0.80
93.0
EQGAT-diff
85.9
37
24
4.89
-0.73
78.9
6.75
0.86
99.5
Atoms coords MiDi
74.4
33
31
4.90
-0.74
63.0
6.00
0.85
99.6
JODO
91.1
4.72
-0.74
84.1
4.22
0.85
99.4
FlowMol-CTMC
89.5
24
25
5.91
-0.68
69.3
13.0
0.86
99.8
NlowMol-Gusssan
48.3
6
8
4.24
-0.71
30.7
21.0
0.86 99.7
See Table for results, and Figures 15 and 18 for examples. For chemical reasonableness, SYnCo- GEN generates almost entirely valid molecules. Our generation details the reaction and building blocks in multi-step reaction pathway, and as result, our molecules are significantly more synthesiz- able compared to baseline methods. Because AiZyyntFFinder and Syntheseus solve only 50-70 of known like molecules, our 50-72 % scores likely underestimate true synthesizability. A rigorous conformer geometry and energy comparison between all methods is provided in Appendix [.5]
Structurally, the generated conformers reproduce the data energy distributions and have very favor- able non-covalent interaction energies as evaluated by semi-empirical quantum-chemine especially when compared to the baseline methods (Table [ and Figure 3). This is evident from the lack of structural changes upon further geometric relaxation (Figure 16). The Wasserstein-1 distances and Jensen-Shaen Shannon divergence can found in Appendix [.5 and Figure [4] The low non- bonded energies indicate SyNCOGEN learns to sample many intramolecular interactions (Figure [5). Quantitatively. 87% of these conformers pass PoseBusters pose plausibility checks. Furthermore, SYNCOGEN reproduces the delicate data distribution of bond lengths, angles, and dihedrals (Figures
methods,
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Figure 3: Conformer geometry and energy distribution. Distributions of a) bond lengths, b-c) dihedral angles, d) average per-atom GFN-FF non-bonded interaction energies. Solid curves denote training data densities; lower subpanels in (a-c) show deviations between generated samples and data.
and 14). For example, SYNCOGEN generates fewer sp Spp bonds that too short, captures sharp bond angle distributions (e.g., SpppCCpssppp N), and replicates both flexible dihedral angle distribution (e.g. sp"CCsp""Csppp C-pp""ss" and rigid dihedral angles (e.g. C-ssCssssssp"C--ee
Beyond sample quality, SyNCOGEN also captures the training distribution as indicated by the low FCD, while generally producing novel molecules. In exchange for synthesizability, the generated samples have slightly lower diversity due to using a (limited) set of reaction building blocks. All generated samples are unique. Furthermore, the multi-modal model can perform zero-shot conformer generation at quality similar to ETKDG(RDKit) when given random reaction-graphs (Table (7).
Our various training time ablations (Table B) show that the largest performance gains originate from our chemistry-sensitiee graph constraints and self-conditioningg with small contributions from other training/sampling details. A large performance gap between SYNCOGEN and SemlaFlow retrained on SYNSPACE further shows that our training procedure, rather than the architecture or dataset, is the primary driver of performance. Appendix D.2 sampling-tine ablations schedules, annealing, and edge sampling strategies, which show the joint schedule is beneficial for stable co-generatio.
Finally, we demonstrate that SYNCOGEN is not limited by vocabulary size. When trained on SYNSPACE-L, whose search space is larger by several orders of magnitude (Appendix D.3), the model retains high RDKit validity, realistic conformer energies, and strong retrosynthesis solve rates. This indicates that SYNCOGEN can be readily scaled broader chemical spaces with little sacrifice on generation quality or synthesizability.
5.2 MOLECULAR INPAINTING FOR FRAGMENT LINKING
To demonstrate SYNCOGEN in drug discovery, we study fragment linking (Bancet et al., 2020) to design easily synthesizable analogs of hard-to-make drugs. Fragment linking can create potent molecules by connecting smaller fragments known to bind distinct regions of target site. We formulate this as molecular inpainting task: given a known ligand, we fix the identity and coordinates of two fragments and sample its missing parts consistent with both geometry and reaction grammar.
As case studies, we select several FDA-approved, hardtti-syathesizee small molecules with experi- mental crystal structures bound to different target proteins: human plasma kallikrein (PDB: 7N7X), caltidruu-resiistan HIV protease (PDB: 4EYR), and human syclin-dependent kinase (PDB: 5L2S). Each ligand contains at least two of our building blocks. At sampling time, we condition on the substructure match by keeping fixed fragments denoised and interpolating the remaining coordinates (Appendix B.18).
Generated molecules are evaluated with AutoDock Vina (Figure 4 (Eberhardt et al. 2021). SYNCO- GEN consistently produces molecules with docking scores on par with or better than the native ligand while satisfying constraints on the presence of specific building blocks. AlphaFold3 (Abramson et al. 2024b) predictions on selected protein-ligand pairs show similar binding positions in the selected pockets well (Figures 4 and 177. Crucially, unlike existing approaches (Schneuing et al.)
2024: Igashov et al. 2024), the model links fragments using building blocks and reactions to ensure streamlined synthetic routes of the designs (Table 8 and Figure 18).
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Figure 4: Molecular inpainting, a) Fragment linking with three ligands in the PDB that contain substructure matches with our building blocks. For each structure, we show three examples of linkers generated by SyNCOGEN and the distribution of Vina docking scores (lower is better). b) Proposed synthesis pathway for molecule (1) sampled from our model and c) structure of (1) (blue) docked onto PDB 7N7X using AlphaFold3 compared against the PDB ligand (beige).
Using SYNCOGEN for tragment-linkingg does not require retraining. although validities and energies can be improved with motif-scaffolding fine-tuning (Table 8) We benchmarked SYnCoGEN against the state-of-N the-art, purpose- buill Tragment-linking model DiffLinker (Igashov et al. 2024).
SYNCOGEN is the only method that produces synthesizable molecules with 58-79% retrosynthesis solve rate (0% for DiffLinker, T8ble(8). Compared DiffLinker, our molecules have lower interaction energies, no disconnected fragments, reduced hard-to-synthesize features (Table 99) and similar PoseBuster validity rate. The synthesizable inpainted molecules now enables wet-lab tasks such as scaffold hopping, analog generation, or PROTAC design (Békés et al., 2022 Chirnomas et al. (023).
5.3 AMORTIZED PHARMACOPHORE CONDITIONING
We evaluate SYNCOGEN on amortized design of de novo small-molecule binders conditioned solely on pharmacophore profiles (Sections 3.3 and 4.I). This setting avoids any external reward models (which can encourage reward hacking) and instead asks the generator to directly realize 3D arrangements of interaction features that are compatible with target pocket or reference ligand. Pharmacophore types and positions are visible to the model during training. To aid generalization, we randomly sample a maximum of pharmacophore features during data loading.
We evaluate on three hard-to- to-synthesize reference ligands with disease-relevant targets: ozanimod, scopolamine, and 1R-107 (PDB: 7EW0, 8CVD, 7UVU), and seven targets from the LIT-PCBA benchmark (Tran-Nguyen et al., 2020): 21OK, 2P15, 2V3D, 3ZME, 47ZN, SFV7, and 51.2M. We compare SYNCOGEN against three baselines. ShEPhERD (Adams et al. (025)) is state-of-the-ar 3D generator conditioned on pharmacophore interaction profiles but does not enforce synthesizability. SynFormer (Gao al. 2024) generates synthesizable 2D molecules; condition it native ligands for analogue generation. CGFlow (Shen et al,) (025)) generates synthesis pathways with 3D poses. For the pocket-conditioned reward from Shen et al. (024) align with amortized sampling setup (CGFlow-ZS) For each target, we generate 100 molecules per method based on the cognate ligand pharmacophore profile and dock valid samples with Autodock Vina.
CGFlow,
On average, SYNCOGEN produces de novo molecules with better or competitive docking scores compared to ShEPhERD, CGFlow-Z ZS. SynFormer, and the native ligand (Figure Our top samples surpass all baselines in 8 out 10 targets. Qualitatively, SyNCOGEN molecules dock to the same pocket and replicate key pharmacophoric contacts the known ligand with a high degree of shape overlap (Figure 20 Compared the 3D method ShEPhERD, SYNCOGEN -generated molecules

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Wins Across Targets
8/10 Best
7/10 Median
Vina Score (kcollmml)
-00
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Synformer
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SynCoGen
Redocked FDB
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Model
Val. f AiZyn. f Synth. f PB f Div. f
SynFormer 100.0
42
0.82
ShEPhERD 38.5
12
0.34
0.86
CGFlow-ZS
100.0
45
16
0.75
SYNCOGEN
86.3
61
78
0.59
0.80
generation. Top: Docking comparison 10 targets from the PDB/LIT-PCB. benchmark (lower is better). Inset: target wins by method, where SYNCO- GEN achieves the best docking score 8/10 targets (best sample) and 7/10 (median). Bottom left: Aggregated conditional generation metrics for all 10 targets. Bottom right: Docked SYNCOGEN- generated molecules (green) overlaid with PDB ligand (magenta) for 5L2M, 5FV7 and 3ZME.
Figure 5: Pharmacophore--onditoo
have markedly higher RDKit validity and PoseBusters validity rate (by 45% and 25%, respectively), indicating more chemically and geometrically plausible structures. Most importantly, across all baselines, including synthesis-constraine ones, SYNCOGEN achieves significantly better retrosyn- thesis solve rates (by 15-65%) and reduces hard-to-synthesize features (Table (O), while maintaining comparable diversity. These results suggest that the added complexity of generating synthesizable molecules and their 3D poses within our mothesis-coostraiine search space (see Figure 19) offers an amortized way to design high-affinity, readily synthesizable molecules de novo.
CONCLUSION
In this work, introduced SYNCOGEN, multimodal generative model that jointly samples sollding-block reaction graphs and atomic coordinates. Our chemistry-aware training procedures enable this model to learn design synthesizable molecules directly in Cartesian space. To support this framework, we curated SYNSPACE, a new dataset family comprising 1 1.2M readily synthesizable molecules paired with 7.5M low-energy 3D conformations.
SynCoGEN achieves state-of -ft-----thhttteee- art performance across 3D molecular generation benchmarks, while natively returning a tractable synthetic route for each structure. Crucially, SyNCoGEN establishes a standard for zero-shol farget-conditional design: without target-specific retraining external rewards, the model generates strong predicted binders 3D and ensures synthesizable chemistry demonstrated here through both fragment-linking and pharmacophore-condiiee con.itrooeooiiiooeedde generation.
The design space of SyNCOGEN is not limited to SYNSPACE. Our code base supports custom building blocks and reactions and finetuningretrraningg our models. Looking forward, future works should experimentally validate the synthesis and binding of these de novo designs to establish the practical impact of 3D-conditioned synthesizable molecular generation for drug discovery.
ACKNOWLEDGMENNS
The authors thank Joey Bose (University of Oxford), Stephen Lu (MeGill University), and Francesca- Zhoufan (Caltech) for helpful discussions. This work is enabled by high- high-performace computing the Digital Research Alliance of Canada and Mila.
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ETHICS STATEMENT
While intended for research in drug discovery, any generative chemistry system has dual-use risk (e.g., suggesting toxic or hazardous compounds), We mitigate this by constraining generation to commercially available building blocks and limited set of high-yield reaction templates, representing products as explicit reaction graphs, which enables expert review of routes.
REPRODUCIBILITY STATEMENT
We provide code for this study, including end-to-end training and sampling scripts for the joint multi-modal model, configuration files, evaluation pipelines that reproduce the metrics, and data preparation code to regenerate the conformer sets and pharmacophore features. We also release pretrained checkpoints and commands to reproduce: unconditional generation, tragment-linkinn inpainting, and caarmacophhre-condiiie generate a new training dataset given custom reactions and building blocks.
sampling. Our repository contains simple commands to
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A CHEMISTRY AND DATASET DETAILS
A.1 BUILDING BLOCKS AND REACTIONS
For the small vocabulary, the 93 selected commercial building blocks and their respective reaction centers are shown in Figure 6 For chemical reactions, we focused on cross-coupling reactions to link fragments together. We chose 8 classes of robust reactions, which can be subdivided into 19 types of reaction templates, see Figure 7 The remaining building blocks and reactions that define the large vocabulary are shown in Figure 8 and Figure respectively. We that our reaction modeling simplified. For example, boronic acids in building blocks (B(OH);) are replaced with boranes (BH2); we not consider the need for chemical protection on certain functional groups (e.g. N-Boc); we do not consider directing group effects or stoichiometry when multiple reaction centers are available; we do not consider macrocycles. These edge cases are limitations of the current method, but they are comparably minimal through the careful curation of building blocks to avoid such infeasible chemical reactions.
A.2 GRAPH GENERATION
Helper definitions. We annotate each building block with its reaction center atom indices V(6) S
(b)) and its and each intrinsic atom-level graph by H(b) == (V(b), L(b)). where ((b) is the of atoms in b and L(b) S V(b) (bb) is the set of covalent bonds internal to the block. Each reaction template is annotated with Boolean tuple ([La(r), (r(r) {0, 1]2 describing whether reagent A or reagent B in r, respectively, contains a leaving atom.
Given the current atom graph G. (Va, I.a) and an atom " E Va of degree 1, the routine Vo such that (u,v) E La. Throughout the
UNIQUENEIGHBOR( returns the single atom vocabulary, every leaving-grove group center has exactly one neighbour.
A reaction template r is considered compatible with (b;, v) and (6, 8) if it queries for first and second reagent substructures that match (bi, v) and (6, 7), respectively.
Lastly, while the model is compatible with reactions containing more leaving groups, we do not consider them as the dataset construction requires custom atom attribution between reactants and products.
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CHONOO
DE006O
ATTIOO
O
O
I8 Biditnkkddt//aaal (ocal
17 OCCOCETUOO
CHOO0
COKOO
MOrer220 to
DHOKCOOOI
DHGOOCSC
CO
30 POTECC
OXCE:
X: DO0O
I1 SCKOOOO
23 NOXOOC
50 BOOCK
30
DELUCNEE
ESCLKCCOCL
COCUCEL
CIEEOOCEI o Mccosfffommmc
ledenitedd
Figure 6: List of building blocks for the small vocabulary, their respective reaction centers (in red), and their canonical SMILES representation.
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Buchwakd anyl bromide, secondary
Suzuki anyl bromide (=11eer1/s-2/Hpp-1cc11----e
Ra
HD
R4
Suzukii aryl iodide ((::)))0,[e=2]] (e)p::=:-aa))---:)))) HO
Buchwaldd bromide, amine
[e:1]|Br) |//// 20 sofe: ())
A1
Amide coupling, primary amine
[C: [[]-((O22)HOO] 3HP6 (/C [hn
Estentiiation reaction
[c:1]- (1681
==(C:1][[002)) (0:3) (OAAA//AAONO.AAA
H&N
[C:1] coupling, secondary
OH
Co BBA.:///
Primary amine sultonyl chiorde subssatution
[*GAISIC=(O.M CC (TX p48R15IC-1O M0J=100NN:11110 7]x-
HN
R,
H&N
Willimsonn ether synthesis bromide [M6:4 (Br) (Brri/rrriis//COOOO N):
Secondary amine sufforyl chloride substiutton
[N68/S/C-ID
BICCCC---DNNNN111PO NI): N0T::11|NN:1111 10099111C-00 Mj::00) (tt.::)-CC---111111:0: 10- (: OJNN 111668 -1000------11100000--0000----100 (00-
R2
Willimssnn ether synthesis chioride (484) (H (#8815|C-|0 2--n3 p:gee:cchh...221.000s//////aaa00
HN
Reductive amination, primary amine aldehyde
(V-1:)/--1O.NI:: 10:00N122:111 (Ch:2)00000: (pppAl/(CC(ON)-1100 () ((6:3)
Williameon ether synthesis iodide [#0 (0l.::::10.).aaaSCC--- (Ch:3] xx(M8:4) 1.W.:4/H0022110000000000500000
H&N
Reductive amination. secondary amine and aldehyde
|ecks//C= Ni)-1o)-(Nhtt (reN::::://sssscCCcCas (io.ss/C=-..))222000 (Ch2))(43)))00 >>(#88151C- NJ: 10: (E-HNNNT----aaa T3--48//5(C- 20)o::o---......0-cc22222222 23226)22222223
Alkyl bromide aromatic N-Ht alkylation 46-4-C22 (HB1 / NDI 10j- - Ng:20)
sof86 Nh:2), (N8811/CC1O0O (0NN))200)--880000000000
HN-X
HN
Br
Reductive amination, primary amine and kelone
Alkyl lodide aromatic NHH akylation
[N NI:::-- 110: +* Nh ([
gal 4ijcc22 1)-1 (46 (SC-AISSC:-O.AA (0)-
ghlee 4) [Ch2:1] (Nhh:))) (CCC:s//SCCCCCCCCC -
H&N
HN-X
[Ch2: 1/I ( (Nh:l) C-10
aromatic
akylation
|068/5/C- (O 10JIO (t////////--OO.N01111--. (e8:3 ( 2212))888441-0000
Reductive aminnttion, secondary amine and ketone
R'
N
Figure 7: List of chemical reactions for the small vocabulary used to connect building blocks and their SMARTS representation. Newly formed bonds are highlighted in pink.
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AQ
Y
O
D
D
g
X
+
O
A
vp
Apm
X
m
ANCONCEOS
Yr
X0
XD-
X-
You
A
7-0
A
Ank
X
x-Q
Yinr Aprd
d<
June
X
x
M
X
C
U
C
suves
C
D
X
+
A
X
D
AA
X
A
8
+
X
P
A
D-
XX
7
+
O
3-
X
1X
10
10
KCH
AA
Q4
14
0
XX
C
M0000000
99
4
3
9
10
0
0
P
O
C
X
>
moppom
2006
0
x
L
70
70
70-
70+
5
X
70-
20
Figure 8: The additional building blocks for the large vocabulary, their respective reaction centers (in red), and their canonical SMILES representation. The large vocabulary also includes all building blocks from the small vocabulary.
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Suzuki alkeny halide http:CCChSScacemo.oocc///////aa1
HO
HO
X: CI. Br,
Sonogashira aryl halide
X: CI,
Thiol alkylation
[48:1) (4, (
R
SH
S R
CI Br,
Figure 9: The additional of chemical reactions (from 3 classes) for the large vocabulary used to connect building blocks and their SMARTS representation. Newly formed bonds highlighted in pink. The large vocabulary also includes all reactions from the small vocabulary.
Algorithm Fragment-by- by-frgmentt assembly with COUPLE
Inputs: vocab B, reactions R, depth limit T
Output: atom graph Ga. building block graph Gy = E)
function COUPL.H(Ga, bi, b, r: (wa, 8))
2: append all atoms and bonds of Hbb) to Ga
1. Handle leaving groups
3: if (r) then
leaves in reagent A
4:
Uj < UNIQUENEIGHBOR
5:
delete atom U; (and its bond) from Ga
6:
U. +-
reroute to neighbour
7:
end if
8:
if (B(rr = 1 then
T leaves in reagent B
9:
Ut < (NIQUENEIGHBOR(
10:
delete atom ë (and its bond) from G2
i 6-4 44
reroute to neighbour
12:
end if
13: add covalent bond between v; and
Add cross-bond
14: return G.
15: end function
16: by <- UniformPick(B)); G, + (1bb):: Gj (bo)
17: for = 1 to T do
18: L enumerate compatible 5-tuples (bi, v. 6,
19:
if = Ø then break
20:
end if
21:
b, b,r,b, (b,, v,r,
+ UniformPick(L)
et 6,
G. COUPLE(G,, by b, r. (v, 8)) G 8)
24:
25: end for
26: return (Ga, Gş)
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A.3 SYNSPACE STATISTICS
Table 2: Average molecular properties of SYNSPACE and SYNSPACE-L. datasets, in comparison with
GEOM-Drugs (Axelrod & Gomez-Bombarelii 2022)
Property
SYNCOGEN SYNSPACE-L.
GEOM Drugs
Molecular Weight
492.16
476.40
355.83
Number of Heavy Atoms
33.74
32.99
24.86
Octanol-Water Partition Coefficient (Log P)
2.44
3.01
2.91
Number of Hydrogen Bond Donors
2.75
3.30
1.19
Number of Hydrogen Bond Acceptors
6.74
6.25
4.83
Quantitative Estimate of Drug likeeesseness
0.43
0.36
0.65
Fraction of sp Carbons
0.41
0.37
0.30
Topological Polar Surface Area
111.32
110.08
73.73
Number of Rotatable Bonds
6.95
8.92
4.90
SAScore
3.34
3.28
2.51
Murcko Scaffold Number
443458
333180
92955
12
0.7-
6-122
0.22
Topological Polar Sur loc Ario
Par Calboss
Sydteeet
Sydeems
6.74
6:50
0:000
0.11
6.0
-1
3.50
Syauee
007
000
Derraty
0:00
0.0
Molcouuo (hoght)
QED
Figure 10: Distribution of SYNSPACE and SYNSPACE-L molecular property statisties, compared to GEOM Drugs
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B METHOD DETAILS
B. SIMPLIFIED TRAINING WORKFLOW
Below provide simplified illustration of the SYNCOGEN training process. For visual clarity, describe the procedure for a single building block.
Data Somple
BEBE
Forward Noising
0.25
0.50
0.25
Masked
Padding
Carton
Dromie
CE CO
Dota Pairing Module
Notsed
Ground Truth
SynCoGen
Coordinates
Building Black Logits
Reaction Logits
0:87
6.83
6:90
8.49
6.87
6.07
8.8:
SUBS Compatib Logit Masking
6:38
Figure 11: Simplified training workflow for SYNCOGEN using a single bromobenzene as an example.
Data are passed through the model during training according to the following process:
1. Noise injection. Coordinate positions and building block identities are noised/masked. If building block becomes masked, padding atoms are added its coordinates match the maximum number of atoms in any building block within the vocabulary M. In this example, M 10.
2. Ground-truth preparation. To keep the number of atoms consistent, the data pairing module (Appendix [B6) generates ground-truie truths with or without padding atoms and re- centers them accordingly. Note that padding atom positions identical in the noisy
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coordinates (sampled from the Gaussian prior) and the ground truth. Here, encourage the model to disregard atoms that are unlikely to assemble into the true molecule when the building block is unknown.
3. Backbone processing. The noised building blocks are passed through the backbone, which outputs building block logits, reaction logits and coordinates; we exemplify this for building blocks the diagram above. The correct index highlighted in green.
4. Index masking. The logits processed by the SUBS parameterization module introduced by Sahoo et al. (2024) and the compatibility logit masking module described in Appendix B.2 eliminate probability mass allocated to incompatible or impossible indices.
5. Loss computation. Negative log-likelihoods are computed over the modified logits.
Remark. Steps and 2, in particular, ensure that model inputs containing masked building blocks during training remain consistent with the information available for a corresponding example at sampling time. When building block is not known, neither is the number of atoms it contains. The absence of padding atoms during training would require direct selection atom counts per building block at sampling time, which constitutes strong constraint the building block identities and severely limits design flexibility.
B.2 COMPATIBILITY LOGIT MASKING
Below we provide simplitied illustration of the SYNCOGEN compatibility masking procedure for building blocks. For visual clarity, selection of building block attachment points is implicit and reactions are denoted by single one-hot item r, rather than a triple (r, U2 Uy).
Reagent
b)
B81
DD3
880
BB1
BB2
BB3
BB4
C-4
N3
8B0
M
BB1
rxn
Sububrustare Match
Reagent
8B3
BB4
Reagent
Reagent
C4 0.2
N3
BB
BB
Figure 12: Compatibility masking regime for building blocks. Gray and white squares indicate "masked" and "no edge", respectively. a) A denoised item at position (1,3) in E denotes that a reaction ri has been selected between building block and 3 in X. b) In X, the vocabulary is queried for substructure matches to reagents and 2 of at building block indices and respectively, and logits corresponding to incompatible building blocks are set 0.
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B.3 SAMPLING EDGE LOGIT MASKING
rXsg
rXn
rxng
rxn,
rXN,
"No Edge"
rXN
BB1
6B3
BB3
BBD
330
BB4
BB2
Sampling constraints for edge denoising. When a reaction is denoised at position (2, 4) in F, all other incoming edges to building block index are set "no-edge"- this valid assumption as SynSpace does not contain macrocycles.
Figure 13:
B.4 BUILDING BLOCK-LEVEL REPRESENTATIONS
Let X E {0, 10.1)Nx181+1 be one-hot matrix where the 7th row encodes the identity of the 7th building block, and let E E {0, N) V2.. where Viaer max; [V(b]] A non-zero entry Bijr(w,,5) = 1 signals that block (center ey) couples to block j (center uy) via reaction r. Graphs (X, E) belonging to molecules containing < N building blocks are padded to N.
Reserved Channels.
We reserve dedicated masked (absorbing) token in both vocabularies:
x {0, 18,
mE {0, 1) |R| VMa
(5)
where x (resp. Tg) the one-hot vector whose single 1-entry corresponds to the masked node (resp. edge) channel. Besides the masked channel, we keep a dedicated no-edge channel, encoded by the one-hot vector
Ag E {0, 1 V
(6)
every edge slot may take one of three mutually exclusive states: concrete coupling label, the no-edge token Åg, or the masked token me.
B.5 ATOM-LEVEL REPRESENTATIONS
The SEMLAFLLOW Irwin et al. 2025) architecture propagates and updates invariant and equivariant features at the atom level. To ensure consistency with this framework, we calculate for each input graph (X,, E,) atom-level one-hot atom and bond features. Crucially, these features must be flexible to arbitrary masking present in X, and E,. With this in mind we set each atom feature Xatom (i, a) to concatenation of one-hot encodings
Xatom [ a]
5aym((aa)
[ring(i, a)), [a E v(X.)) E 1),1)
(7)
9-way one
where S.ym (i, a) is the one-hot vector over possible atom types (C, O. B, CI, Br, S, [MASK]) and ring(i, a) denotes whether not the atom is member of ring. Similarly, calculate bond
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feature matrix
Gorder (a,, az); bond is present,
Eslom ass ayl
(8)
05:
otherwise.
where dorder (as; (z) is the one-hot tensor over possible bond orders (single, double, triple, aromatic, [MASK]) between a; and aj. Extom is populated by loading the known bonds and respective bond orders within denoised building blocks. If some building block X; is noised, all edges between its M, i i + M) are set to the masked one-hot index. For graphs (X,, E2) corresponding to valid molecules in which all nodes and edges are denoised, we simply obtain the full bond feature matrix from the molecule described by (X,; E.).
constituent atoms Estom
B.6 DATA PAIRING
Algorithm 2 PAIRDATA (Co, So, t1,
Input: Co (clean coordinates), So (atom mask), C1 (prior sample), & [0, 1], Xx (partially masked
nodes)
Output: Co (re-centered ground truth), Ct (interpolated noisy coords)
1: D, < {il Xi[i] # f
>> denoised blocks visibility
2: S,
1l 4 V. A.
3: Ci + Cis.
4: Co + ZEROTANSOR()
5: for all (i, do
6: if' Volli, a] = then
7:
Coli, a) + Coli, a| - Cis.
8:
else if S a| then
dummy atom
9: Coli,a a + Ci [ d]
10: end if
11: end for
12: C. (1 t) C +t
13: return (Co, Ct)
Here, A; is the of all atom indices that constitute true atoms in Xo. Note that So for all where X, contains no masked building blocks.
Our data pairings result in both Co and C. that properly centered according to atoms that are possibly valid at time t. It is important to note that under this scheme, while the model is -qquiiaanaa with respect to the system defined by the partial mask S, it is not equivariant with respect to the orientation of the molecule itself unless Dj Ø, as the presence and temporary validity of masked dummy atoms offsets the true centering and thus breaks both translational and rotational equivariance.
Note: Non-Equivant Non-Equivariance
B.7 TRAINING ALGORITHM
Algorithm 3 Training step for SYNCOGEN
1: ~ 1)),1)
2: (X,, Fx) +- qe(Xo Fo)
3: C N0,
4: (Co, C.) PAIR(Ca. So, Xi)
center and interpolate coordinates (Algorithm) 2
5: (LX, ,,,,F,CC LF,,,))) + (X(,,, E,, Õo n,,
6: C + Lgaph + LMSE + Equir
> total loss (Appendix B.16
7: 8 0 17 -bla
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B.8 SAMPLING ALGORITHM
Algorithm 4 Sampling procedure for SYNCOGEN
1: n Cat(: (X1, Ei) +- (T); SiLi. + 1 n
draw n, initialize masks
2: C1 (0, O +- - Ci,s
b center Gaussian prior by initial mask
3:
for t= down to do
4:
C++C, - Cr...i
(L, L.F, Cf), + fo(X,, Es, Cr, n,
5:
6: T.F + SS-SAMMLEEDDESST.. n)
enforce one parent per building block (Algorithm 5
7: XI-Ait CATSAMPLE(LA EL- CATSAMLLC)TS))
take reverse step
(Appendix B.11)
CI-A++ C, + At(C; -C)
8:
9:
(Xe, Ei, Ct, St) (Xt-st, S..Etr Dr, Ct Se, St-
end for
LE 12: & arg max; [..., ki]; Egg arg max LØ k]: Co Co Co,so
11: LI, Co) + fo(Xo, Eu, n)
b final deterministic denoise (t = 0)
3
return (Xo, Eo, Co)
B.9 INFERENCE-TIMG EDGE CONSTRAINTS
Let EY E [0, ||=xnx|R[VVa be the soft-max edge probabilities produced at step The routine below resolves the unique parent for every building block column and returns probability tensor Eg with exactly one non-zero entry per column.
Algorithm SAMPLEEDGES! E2
Input: edge probabilities E Output: pruned probabilities E
1: F <
2: for j == 1
do (i) ~ Cat( ( (0si<)) [
3:
4: File,,iee 1
5: end for
return E
Eg is then symmetrized and fed discrete reverse sampler described Appendix B.11
B.10 BUILDING BLOCK LOGIT PREDICTIONS
The SEMLAFLOW Irwin
2025) backbone outputs atom-atom edge features E Entom R (NM) xeeus, To obtain building block-level tensors, we apply two parallel 2-D con- volutions (one for nodes, one for edges) with stride M, followed by MLP classifiers that map the pooled features back to their original one-hot vocabularies. Note that the presented model trained to predict maximum of building blocks, where the sizes of the molecules (average 566 Da) are near upper limits molecular weights for typical drug like molecules.
Stride-pooled convolution. Let dedge be the latent edge feature dimension. Each stream uses the block
Conv2d(dedte- > dedge: h = M, s= M) Conv2d(dedee - dedge. h = 1, = 1), (9) so every M M atom patch collapses single building block entry. This produces
X poot Bx xN
Fepoot R x xNxN
(10)
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Node head. We flatten Xooo along its channel axis, concatenate the residual building block one-hot matrix Xt, and pass the result through a two-layer MLP to obtain
LØ E &R" Bx
(11)
Edge head. We concatenate Epool with the residual building block-edge one-hot tensor E,, apply an analogous two-layer MLP, and symmetrize to produce
E Lg ER BRBB.NxXIII
max
(12)
Atom Features. The SEMLAFLOW (Irwin et al. node features Xgrom E (NN( x dhadk which are incorporated into Egtom via a bond refinement message-passing layer. We find that extracting both building block and edge logits directly from the refined features Eg marginally improves performance relative separately predicting Lg from X Xasom and Lg from Ligton
2025) backbone additionally outputs atom-level
B.11 DISCRETE NOISING SCHEME
Following (Sahoo et al. 2024), we adopt an absorbing (masked) state noising scheme for Xo and Es: (X, (x) Cat( X,; o + (1 xx)x,), q( (E Fo) Cat( E.g; ar Eo (1 az)
(13)
where (av))eju.1j is the monotonically decreasing noise schedule introduced in Section Reverse categorical posterior.
For node identities, we have
(at((x;xx));
X₂ + TX,
(X,, Xx, Xo)
Cat(Xxi (1- 1-a,)TxX + aos xx
(14)
X, = ax,
1- 0t
and, analogously, for edge labels
Cat(FEg; Fe),
Fg # π
(E. Es, Eo)
Cat (1-a,) .,)TE as Laa
(15)
E, = nF
Ot
where t. Equations (14 and (5) are the direct translation of the reverse denoising process described by (ahooo et al. 2024) into SYNCOGEN's 's node-edge representation.
B.12 NOISE SCHEDULE PARAMETERIZATION
2024 we parameterize the discrete noising schedule via a, e (t)) where a (t): : [0, 1] > IRT. In all experiments, we adopt the linear schedule:
Following MDLM (Sahoo et al.
(tt) maxx
(16)
where max a large constant; we use Fmax = 10 as in the original MDLM setup.
Edge Symmetrization. After drawing the upper-triang entries of the one-hot edge tensor E, in either the forward or reverse (de)noising process, we enforce symmetry by copying them to the lower triangle:
Eajic
Eajjes
0 0Si<j < n, 6 E RV2 R
B.13 POSITIONAL EMBEDDINGS
Though SEMLAFI OW Irwin positions, SYNCOGEN dataset molecules require that atom order be fixed and grouped by building block for reconstruction purposes. To enforce this during training, we intentionally break permutation invariance by generating and concatenating to each input coordinate sinusoidal positional embeddings representing both global atom index and building block index.
et (rwin
al. 2025) is permutationally invariant by design with respect to atom
B. HYPERPARAMETERS
We train SYNCOGEN for 100 epochs with batch size of 128 and global batch size of 512. Note that SEMLAFLOW and Midi are trained for 200 epochs, and EQGAT-diff is trained for up to 800 epochs. All models are trained with linear noise schedule (see Appendix B.12), with the SUBS
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parameterization enabled. During training, random conformer for each molecule is selected, then centered and randomly rotated to serve as the ground coordinates Co. All atomic coordinates normalized by constant Ze describing the standard deviation across all training examples. For the pairwise distance loss Lpairs we set d to 3A, adjusted for normalization. During training, for each recentered input-prior pair (C1, Co) rotationally align Ci to Co. When training with noise scaling and the bond loss time threshold, we set the noise scaling coefficient to 0.2 and the time threshold to 0.25, above which bond length losses are zeroed. When training with auxiliary losses, we set the weights for the pairwise, sLDDT, and bond length loss components to 0.4, 0.4, and 0.2, respectively.
B.15 COMPUTATIONAL RESOURCES USED
We train models on 2 HI00-80GB GPUs.
B.16 TRAINING LOSSES
Here, we define several loss terms that have proved useful for stabilizing training on 3-D geometry. By default, SYNCOGEN is trained with LMSE and Lair as coordinate losses.
For prediction (Lg LØ Ed) =fdXe, Ee, C,, X² softmax L) E softmax(1... T
Graph loss.
Let Xo and Eg be the clean node and edge tensors. Following the MDLM implemen- tation (Sahoo et al. 2024), we weigh the negative log-likelihood at step by
Do:
W/ exp(or)
Ao: = oi Ot-1, og =0 0,
(17)
where o, is the discrete noise level. The discrete (categorical) loss is then
Egraph = w2 (-log X [x]] -log (Fl)) iee. the cross-entropy between the one-hot ground truth and the predicted distributions for both nodes and edges.
(18)
MSE loss. Let So {0, N mask the atoms that exist in the clean structure and C₁ be the noisy coordinates. Denote As, {(i, a [od]=1]] 11..
MMSE
Σ
[Colia - Coli, al
(19)
Aso
(1,0)
Pairwise loss.
Cpair
Σ
Soli, a) Sob. (I[Co[i,a] Coli. 6]|2 |[oo al b11)2
(20)
(L.))
where d is the distance cut-off for pairwise terms. The default total loss value for the model is therefore
LSyNCOGEN = Egraph + LMSE + Lpair-
(21)
Smooth-LDDT loss (Abramson et al. 2024a). Let Let ||Co[ Cobilla and d ||A,
čobill2 be ground-truth and predicted inter-atomic distances, respectively. For each pair of atoms within a 15 cutoff in the reference structure, we compute the per-put per-pair score
sLDDT, = Σ oTT prod 12
T1, T2, Ta, Ta = [0.5, 1,2, 4] A
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where (2) 1/(1 =)* is the logistic function. The smooth-LDDT loss averages 1 sLDDT,; over all valid pairs,
Σ Idd < 15) Soli] (1 sI.DDT,))
LLDDT
(22)
1 < 15] Soli Sobi]
Given set of intra-fragment bonds bonds {(p,4) extracted from the vocabulary, we penalize deviations in predicted bond lengths:
Bond-length loss.
Lrand
Σ
|||olo] - Colalll2 |[Co[p] - Co(a]lla-
(23)
|bonds|
(p-n)
Self-Conditioning
The modified SEMLAFLOW (Iwiin et al. 2025) backbone operates on node and
edges features at the atomic level, but outputs unnormalized prediction logits Xo E {0. [] and
Eo {0, x We therefore implement modified self-conditioning for SYNCOGEN that projects previous step graph predictions X Xocond and Frcond to the shape of X and Extom using an MI..
B.17 CONFORMER GENERATION
We randomly assembled 50 molecules with the reaction graph and used the standard conformational search (iMTD-GC) in CREST with GFN-FF find all reference conformers. For both SyNCOGEN and RDKit ETKDG, we sampled 50 conformers per molecule and computed the coverage and matching scores. We used relatively strict RMSD threshold of t = 0.75 A.
Formally, COV is defined as:
N
COV
min RMSD(m,, 9j) ST ISSS
(24)
where [ is the indicator function, m, the N generated conformers and gj the M reference conformers. And MAT is defined as:
MAT
min RMSD(m;; 9s).
(25)
IS5M
B.18 MOLECULAR INPAINTING
we keep two fragments D = (D(L), D(2)} and their coordinates fixed and sample the remaining part of the molecule. We follow Appendix B.S and initialize the graph prior X, with the one-hot encoding of the desired fragment at a specified node index in the graph (decided at random based the structure of the original molecule, so that it matches its scaffold). For each denoised fragment ((i), replace its coordinates at each time t > 0.03 during sampling by
For the inpainting experiments in Section 5.2
c. - (1-1) + t0
where ((() and 5(t) are the centered ground-truth and prior coordinates fragment i, respectively, and all other fragments are updated as shown in Appendix [B8] For any t < 0.03, which for 100 sampling steps amounts to the last three steps in the path, we follow normal Buler steps as shown in Appendix B.8 to allow refinement of the fixed coordinates in line with the rest of the predicted ones for the rest of the fragments. We empirically observed that this led to molecules with lower average energies.
C BASELINE COMPARISONS.
C.1 UNCONDITIONAL GENERATION.
For baselines, we sampled 1000 molecules with random seeds on an A.00 GPU and reported averaged results over three runs.
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SemlaFlow We evaluated SemlaFlow using the sampling script in the official codebase on GitHub'. We reported results for a model trained on the GEOM (Axelrod & Gomez- Bombbreelbi 2022) dataset (by sampling from the checkpoints provided in the repository) and from model trained dataset (see Table DT We trained SemlaFlow using the default hyperparameters for 150 epochs on a single conformer per molecule.
EQGAT-diff, MiDi, JODO, FlowMol We evaluated EQGAT-diff, Midi, JODO, using their official implementations provided GitHub". We modified the example sampling script to save molecules as outputted from the reverse sampling. without any post-processing. For MiDi, we evaluated the uniform model. For FlowMol, both CTMC and Gaussian models were evaluated and reported.
C.2 CONDITIONAL GENERATION.
In the pharmacophore- condiiioonc generation setting, we compare SyNCOGEN against Syn- former (Jocys et al. 2024), CGFlow (Shen al. 2025), and ShEPhERD (Adams et al.] 2025). SynFormer was conditioned on the native ligand for synthesizable analogue generation. We used the official implementation on GitHub', and changed the following inference settings to allow for higher quality designs compared to the default: sear Bearch_we dthh=3,, exhaust veness=128, For ShEPhERD, we use the p(z1 (x3,44) x4) conditional setting from the paper experiments where denotes molecular structure, 23 denotes the reference ligand charge surface, and æt denotes the reference ligand pharmacophore profile. We provide ShEPhERD with the refer- ence ligand and generate 100 analogs evenly split between 36, 38, 40, 42, 44, 46, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 64, 66, 68, 70, 75, and 80 atoms (4 each). To prepare molecules for ShEPhERD conditioning, et al. 2019). For CGFlow-7S experiments, we generate molecules setting using TacoGFN (Shen et al., 2024) first implemented by Seo et al.(Seo al., 2024 Shen et al. 2024) Molecules are generated using the web app described in the GitHub repository', which inherits the sampling hyperparameters specified the original CGFlow manuscript. For each target, we conditionally generate using a cleaned PDB and centroid derived from reference ligand heavy atoms. See Appendix D.6 for details of DiffLinker linker design experiments.
generate partial charges for each reference ligand using (TBnBanwa
zero-shot protein- conditionne
D EXTENDED RESULTS AND DISCUSSION
D.1 TRAINING ABLATIONS
Table 3: Training ablations. We incrementally remove inference annealing, auxiliary losses, self- conditioning, scaled-noise, and constraints to see the performance difference. All results shown are 50 epochs rather than 100 epochs in Table [ Here, "Constraints" refers to both training-time compatibility masking and sampling constraints. See Sections 4.3 and 4.4, (Appendices B.7 B.14 and B.
Method
Valid.
GFN-FF
Base
93.5
4.871
Inference annealing
93.5
4.933
Auxiliary losses
85.3
5.194
Self cofficonditoninng
69.0
6.424
Scaled noise
70.4
5.091
Constraints
42.4
67.006
D.2 SAMPLING ABLATIONS
By default, SYNCOGEN implements a linear noise schedule and samples for 100 timesteps. To evaluate the effect of step count and noise schedule choice on performance, we provide experiments
available under the MIT License
com/ cvi gwa.i/aac/iiii Dii cwmpb/nmmmmmmmmm///m/// FloMo, available
under the MIT License
'https: http://gg...tbb.coomm/a///////at
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with step count decreased 50 and 20, as well modified noising to follow log-linear and geometric schedule. All results listed subsequently can be assumed to use the default noise schedule and step count.
We additionally follow FoldFlow to implement inference annealing, a time-dependent scaling on Fuler step size that was found to empirically improve in-silico results protein design [Bose et al. (2024). We studied multiplying the Euler step size at time by 5t, 10t, and 50t. In practice, employ 10t for our experiments unless otherwise noted.
We find that noising and de-noising building blocks according to linear noise schedule generally achieves good performance, which during inference sees most unmasking occur in the final steps. An aggressive denoising schedule for the discrete fragments yields significantly worse validity (Geometric and Loglinear). Inference annealing that speeds up continuous denoising in the beginning but slows it down near the end helps to inform discrete unmasking and can slightly improve discrete generation validity, energies, and PoseBusters validity. As sanity check to evaluate whether simultaneous generation is necessary for good performance using SYNCOGEN, we evaluate an inference configurations where all building blocks and reactions noised until single final prediction step (FinalOnly) where we find performance using the default parameters to be superior.
Table 4: Sampling ablations. Results are averaged over 1000 generated samples, except retrosynthesis solve rate (out of 100). All results shown are at 50 epochs rather than 100 epochs in Table
Primary metries
Secondary metries
Method
Valid. AiZyn. 1 Synth. 1 GEN-FF GFN2-XTB 4
PB
Div. f Nov. f
Linear-100
93.5
55
70
4.933
-0.92
78.3
0.79
94.1
Linear-20
82.4
56
68
5.102
-0.91
71.3
0.78
94.9
Linear-50
92.0
50
4.890
-0.91
78.9
0.78
93.6
Geometric- 100
48.2
61
68
5.206
-0.84
72.0
0.80
91.7
Loglinear-100 100
60.3
56
64
5.182
-0.87
70.1
0.80
91.7
Annealing-5t
94.7
52
5.001
-0.93
79.1
0.78
94.1
Annealing-101 (default)
93.5
42
68
4.870
-0.91
82.8
0.78
94.2
Amnealing-50t
85.1
51
64
4.972
-0.82
86.7
0.76
94.6
FinalOnly
69.7
39
68
5.260
-0.92
70.1
0.76
94.1
To examine the effect of de-noising edges probabilistically ("Default") against exclusively selecting the highest-probabilis edge (" ("Argmax") during sampling, we sample 1000 molecules unconditionally for each setting.
Table 5: Comparison of sampling strategies. All results are at 100 epochs (same with Table without inference annealing.
1 but
Sampling Mode
Validity f
PB f
Diversity +
Novelty (%)
Default
0.947
0.8425
0.7811
95.24
Argmax
0.956
0.8483
0.7797
93.41
We there is relatively insignificant differences (small improvement in the proportion of valid molecules is slightly higher in the "Argmax" " setting, at the cost of slightly lower diversity and novelty). Note that the proportion of molecules with 3, 4 and 5 building blocks are sampled according to their respective distributions in SynSpace.
D.3 LARGER VOCABULARY
Appendix D.3 show unconditional generation results after training SYNCOGEN on SYNSPACE-Lfo 50 epochs, and as compared to SYNCOGEN on SYNSPACE for 50 epochs. We note that given a thousand fold increase search space, longer training would typically be expected, and may further improve the results. Under this conservative setting, scaling to the larger search space yields very similar overall behavior. We observe a small decrease in RDKit validity and a moderate decrease in PoseBusters validity, and the molecules still retain good conformer energies and high
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retrosynthesis solve rates. These indicate the molecules synthesizable, and the local geometry remains reasonable. Diversity is essentially unchanged, while novelty increases substantially from 94.2% to 99.1%, showing that the enlarged vocabulary is effectively used to explore new regions of chemical space.
Primary metrics
Secondary metries
Method
Valid. f AiZyn. Synth. 1 GFN-FF L GFN2-XTBE | PBt Div. f Nov. f
SYNCOGEN SYNSPACE
93.5
42
68
4.870
-0.91
82.8
0.78
94.2
SYNCOGEN SYNSPOCE-L
87.0
52
77
5.502
-0.81
65.0
0.79
99.1
D.4 METRICS
We here describe metric computation details that are absent in the main text.
For synthesizability evaluation, we used the public AiZynthFinder and Syntheseus models. Due to the speed of these models, we only evaluate 100 randomly sampled generated examples. For AiZynthFinder, we used the USPTO policy, the Zinc stock, and we extended the search time to 800 seconds with an iteration limit of 200 seconds. For Syntheseus, we used the LocalRetro model with Retro* search under default settings, with Enamine REAL striet fragments as the stock. We additionally appended our building blocks as the stock, but found no meaningful difference in solved rates, presumably as most of our building blocks are already in the utilized stock. We note that we replaced all boranes with boronic acids due to simplifications made in our modeling (see Appendix A.2).
For energy evaluation, all results are from single-poing point calculations. For GFN-FF, we report the total energy minus the bond energies (equivalent to the sum of angle, dihedral, bond repulsion, electrostatic, dispersion, hydrogen bond, and halogen bond energies) as the intramolecular non-bond energies, and average it over the number of atoms. For GFN2-xTB, as the intramolecular non-covalent energies. We note that the total energies and bonded energies follow very similar trends. We note that MMFF94 energies not parameterized for boron; therefore. we report them only for the Wasserstein distances in Appendix D.5 and inpainting task in Table S Figures and 14 show distributions obtained from 1,000 molecules generated by each generative method, along with 50,000 subsampled molecules from their respective training datasets. Gaussian kernel density estimation (bandwidth = 0.15) was used for linear distributions, while von Mises kernel density estimation (k 25) was applied for circular distributions. Wasserstein-1 distances (computed linearly for lengths and energies, and the circle for angles and dihedrals) were calculated using the Python Optimal Transport Package (Flamary et al. 2021)
report the dispersion interaction energies
D.5
De novo 3D MOLECULE GENERATION
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0).
xP2C-4p2N
70
37.5
sysbaace
15.0
Pleylee CTHC
104
Danelty
1000
Nol
2.5
1.2
1.3
1.4
Length A
1.2
1.3
1.6
Longet /A
3.5
1.0
1.7
SympaGen
-22
-10
-08
-08
0.4
-22
0.
5 58.000
Energe/ looll mo-
Band langth AA
Bonglong A.
sp3C sp3C 203C
SO2C sp20 sp2C
d))
300
100
182'
300
130
250
250
50
:00
350
200
250
Angle
sp2C- Spp0ppppp-p
FlowMol- Gauss
FlowMoi-CTMC
MIDI
80"
200
RCP
EQGAT-DIff
SemlaFlow
SemiaFlow retrrained
SynCoGen
SynSpace
Geam Drugs
240
127
247
L27
100
200
120
250
Figure 14: Additional conformer bond length, angle, dihedral, and energy distribution compar- isons. a-b) Bond lengths, e) GFN2-xTB energy distribution, d-f) bond angles, g-h) dihedral angles. Solid curves denote training data densities; lower subpanels show deviations between generated samples and data.
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Figure 15: Unconditionally sampled random molecules from SYNCOGEN.
SynCoGen
GFN2-XTB optimized
0.85 A
0.96 Á
0.79
suroz oduoo
SynCoGen
GFN2-XTB optimized
1.28 A
0.56
A
Figure 16: A subset of randomly sampled molecules from SYNCOGEN and further optimized by GFN2-XTB until convergence. Alignment RMSD is shown below the molecular structures.
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Table 6: Wasserstein-I distance (W1) and Jensen-Shannon divergence (JSD) for the generative models (lower is better). For bond lengths, angles, and dihedrals, we computed the average Wi and JSD for the top 10 prevalent lengths/angles/dhhhrraasss Comparisons are made the respective training set.
(a) Bond dihedrals
(b) Bond angles
(c) Bond lengths
Method
Wi
JSD
Method
Wi
JSD
Method
Wi
JSD
SYNCOGEN
7.01
0.29
SYNCoGEN
1,36
0.22
SYNCOGEN
0.0171
0.34
SEMLAFI.ON SYNSPACH
6.50
0.22
SEMLAFFLOW SYNSPACE:
1.64
0.28
SEMLA SYNSPACH
0.0320
0.48
SEMLAFI.OW
7.76
0.28
SEMIAAFLONN
1.18
0.21
SEMLAFILOW
0.0200
0.38
EQGAT-Diff'
8.48
0.29
EQGAT-Diff
1.37
0.16
EQGAT-Dif
0.0039 0.13
MiDi
9.32
0.38
MiDi
1.41
0.21
MiDi
0,0142 0.31
JODO
5.47
0.31
JODO
0.59
0.12
JODO
0.0034 0.12
FlowMol-CTMCC
13.69
0.35
FlowMol-CTMC
1.90
0.24
FlowMol-CTMM
0.0089 0.20
FlowMol-Gauss
18.85
0,46
FlowMol-Gauss
3,68
0.30
FlowMol-Gauss
0,0152 0.28
(d) GPN2 XTB non-covalent E
(c) GEN-FF non-bonded E
(f) MMFE total E
Method
W1
JSD
Method
W1
JSD
Method
Wi
JSD
SYNCOGEN
0.0838
0.33 SYNCOGEN
1.37
0.28
SYNCOGEN
6.59
0.089
SEMLAFLOW SYNSPACI
0.0125 0.16 SEMLAFLOW SYNSPACH
1.09
0.22
SEMLAFLOW SYNSracH
54.63
0.22
SEMLAFLOW
0.0249
0.16 SEMLAFLOWW
1.52
0.16
SEMLAFLOW
69.56
0.24
EQGAT-Diff
0.0073 0.12 EQGAT-Diff
1.69
0.18
EQGAT-Diff
4.80
0.076
MiDi
0.0084 0.14 MiDi
0.19
MiDi
19.00
0.11
JODO
0.0031 0.11 JODO
1.33
0.12
JODO
22.07
0.11
FlowMol-CTMCC
0.0605 0.26 FlowMol-CTMC
1.53
0.17
FlowMol-CTMC
41.95
0.15
FlowMol-Gauss
0.0322 0.19 FlowMol-Gauss
2.13
0.17
FlowMol-Gauss
26.96 0.14
Table 7: With given reaction graphs, comparison of mean coverage (COV) and matching accuracy (MAT) for RDKit ETKDG and zero-shot conformer generation using SYNCOGEN.
Method
COV (%) 1
MAT (Å)
RDKit
0.692
0.657
SYNCOGEN
0.614
0.693
D.6 MOLECULAR INPAINTING EXPERIMENTS
Three protein-ligand complexes (PDB IDs 7N7X*, 51.25 and 4EYR²) were selected for molecular inpainting of the ligand structures. These ligands were chosen because they are prominent FDA- approved drugs, and they are typically challenging synthesize, but the key functional groups present in our building blocks. Specifically, 4EYR contains ritonavir, a prominent HIV protease inhibitor the World Health Organization's 's List of Essential Medicines: 5L2S contains abemaciclib, an anti-cancer kinase inhibitor that amongst the largest selling small molecule drugs; 7N7X contains berotralstat, recently approved drug that prevents hereditary angioedema. Note that for 4EYR, the inpainting was done using the ligand geometry from the PDB entry 8 but docking was performed with 4EYR because the protein structure in 3NDX contained issues nonetheless, both entries contain the same protease and ligand.
In addition to the experiments in Section 5.2 we evaluate SYNCOGEN's conditional sampling perfor- mance for the fragment linking framework against the state-of-the-arr model DiffLinker (Igashov ct al. 2024). While DiffLinker is trained for fragment-linking our model performs zero-shot fragment linking without any finetuning. For both models, the size of the linker was chosen that it matches
htttpp::/ww..rcsboorr/////t///e/
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that of the original ligand: 2 extra nodes were sampled for SYNCOGEN and 15 linking atoms for DifeLinker in the case of 5L2S, while 3 extra nodes and 25 linking atoms were sampled for 4EYR and 7N7X. We specified leaving groups (for SYNCOGEN) and anchor points (for DiffLinker) so that the fragments are linked at the same positions as the ligand. Results are shown in Table 8 No retrosynthetic pathways were found for the molecules in DiffLinker, while SYNCOGEN models synthetic pathways and synthetic pathways can be easily drawn, with examples for 4EYR shown in Figure 18 This out-of-distribution task for SYNCOGEN leads to fewer valid molecules; however, for the valid candidates, SYNCOGEN has lower interaction energies and achieves 100% connectivity as uses reaction-basee -based assembly, whereas DiffLinker can sample disconnected fragments.
Table 8: Molecular inpainting task. Results are averaged over 1000 generated samples, except retrosynthesis solve rate (out of 100). SYNCOGEN-FT denotes light fine-tuning model for 5 epochs on in-painting with randomly fixed fragments from SYNSPACE.
Method
Target
AlZyn.
Synth.
Valid. 1
Connect.
MMFF
GEN-FF
GFN2-xTB
Diversity
PB 1
SL2S
0
95.8
95.09
14.22
7.52
-0.95
0.60
49.3
DiffLinker
4EYR
93.7
81.86
20.01
-1.03
35.0
7N7X
0
95.8
74.65
20.51
7.99
-1.09
0.78
37.5
5L28
73
79
57.6
100
10.11
6.77
-0.78
0.62
27.3
SYNCOCIEN
4EYR
72
58
46.9
100
12,80
6.58
-0.86
0.64
32.0
7N7X
53
50.6
100
4.243
6.60
-0.80
0.67
56.1
5L2S
77
75.3
100
4.25
6.58
-0.81
0.632
56.2
SYNCOGEN-FT 4EYR
42
62.0
100
10.13
5.33
-0.78
0.604
19.8
7N7X
57
77
73.6
100
4.09
6.86
-0.83
0.664
47.9
Table 9: Percentage of hard-to-syniie hard-to-synthesize chemical features in generated "valid" molecules from SYNCOGEN versus DiffLLinker in fragment linking (out of 1000). Exotic bonds include hydrazine, nitro, nitramine, azide, diazo, peroxide, nitrate ester, fulminate. Fused large/small rings where fused ring contains sub-ring that is larger than atoms or smaller than atoms.
DiffLinker
SYNCOGEN
Chemical features
5L2S
3NDX
7N7X
5L2S
3NDX 7N7X
Macrocycles (>=9)
1.0%
72.6%
12.6%
0.0%
0.0%
0.0%
Fused rings with large/small rings
13.3%
81.4%
37.0%
0.0%
0.0%
0.0%
Large rings (7,8)
12.1%
9.9%
22.2%
0.0%
0.0%
0.0%
Disconnected
4.9%
18.1%
25.4%
0.0%
0.0%
0.0%
Exotic bonds
0.2%
1.2%
1.7%
0.0%
0.0%
0.0%
Total problematic %
22.8%
86.0%
61.5%
0.0%
0.0%
0.0%
(a) 51.28
(b) 3NDX/EEYR
(c) 7N7X
Figure 17: Structural overlays of the native protein (gray) and its native ligand (blue) with AlphaFold3- predicted folds of a subset of generated ligands (green) for (a) 51.2S, (b) 3NDX//EER, and (c) 7N7X.
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DM
6n
m
10
No
NO
HUN
am+
wa
44
Figure 18: Synthetic pathways for molecules generated in the molecular inpainting task for target 3NDX/4EYR. The final product is shown in blue, and the inpainted fragments shown in red.
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D.7 PHARMACOPHORE CONDITIOOED GENERATION EXPERIMENTS
Table 10: Percentage of taantto-synttheize chemical features pharmacophore generation for CGFlow-ZS, Shepherd, Synformer, and SYNCOGEN 100 per target, 10 targets in total). Exotic bonds include hydrazine, nitro, nitramine, azide, diazo, peroxide, nitrate ester, fulminate. Fused large/small rings where fused ring contains sub-ring that is larger than 6 atoms smaller than 5 atoms.
Chemical features
CGFlow-Z5
Shepherd
Synformer
SYNCOGEN
Macrocycles (>=9)
0.0 %
4.7%
1.8%
0.0
Fused rings with large/small rings
31.1% %
39.2%
1.9%
0.1 %
Large rings (7,8)
1.2%
31.2%
4.0%
0.0%
Disconnected
0.0 %
0.0%
0.0%
0.0%
Exotic bonds
0.0% %
0.3%
1.3%
0.0%
Total problematic %
31.3%
46.8%
8.3%
0.1%
Score (kcalmol)
SynCoGen
Random Syrspace
Random FDA
ligand
Zlak
4zzn
5Fv7
Figure Docking score box-plot comparisons on pharmacophoor--condiiiioo SyNCOGEN samples, randomly selected SYNSPACE samples, and randomly selected FDA-approved small molecules (100 for each target). Pharmacophorr-condiie outperforms FDA-approved molecules. These results suggest that the reason why pharmacophore- conditioned SyNCoGEN can outperform other baselines may partially stem from the careful curation of building blocks, SYNSPACE samples perform well in docking experiments. Lastly, caution that docking is a merely a proxy for binding affinity, and we emphasize that the primary results are that SYNCOGEN generates synthesizable molecules with reasonable poses when conditioned pharmacophore profiles. Note all SyNCoGEN sampling runs were performed using building block count fixed to 3.
SyNCOGEN outperforms SYNSPACE, which
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Ziok
2p15
2v3d
3eme
4zzn
5tv7
Figure 20: Pharmacohhor-conndiiinnnng task. Examples of docked SYNCOGEN VYNCoGENN-enerated generated molecules (green) overlaid with PDB ligands (magenta) in their crystal structure pose.
39


Reviews:
[{"review_id": "lM6aWSLIav", "reviewer": "Reviewer_8SMJ", "summary": "The paper introduces a multimodal generative framework that jointly samples a reaction graph with masked graph diffusion and 3D atomic coordinates with flow matching under a unified time schedule. To enable training, the authors curate SYNSPACE, comprising synthesis-aware building-block graphs with associated low-energy conformations. Empirically, SYNCOGEN achieves strong validity and retrosynthetic solve rates while producing low-energy, PoseBusters-plausible conformers. It further demonstrates fragment linking and pharmacophore-conditioned generation with competitive docking scores and markedly higher retrosynthesis success than baselines.", "questions": "1. SYNCOGEN shows lower diversity and novelty. Is this mainly due to using fixed 93 building blocks and 19 reaction templates? How were these number chosen?\n2. Can the model generate molecules with more building blocks than seen in training? How does performance changes for larger N?\n3. For a fairer baseline, it would be more convincing to compare with other synthesis-aware models, such as CGFlow.\n4. In SAMPLEEDGES, the authors draw parents stochastically. Did the authors test deterministic sampling for example argmax? How does this affect diversity and validity?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- Well-motivated co-generation: Jointly models reaction graphs and 3D coordinates, explicitly aligning “makeability” with structural plausibility in one framework.\n- Diversified application scenarios: Demonstrates fragment linking and pharmacophore-guided design, suggesting practical utility beyond unconditional generation.\n- Technical contribution: Clear integration of chemistry-aware constraints and templated reaction modeling that improve validity and retrosynthesis success. SYNSPACE is substantial, pairing reaction-level structure with optimized conformers, and includes pharmacophore annotations to support structure-informed tasks.", "weaknesses": "- Fixed reaction vocabulary: Reliance on fixed building blocks and templates restricts chemical diversity and may limit generalization performance.\n- Baseline comparability: Many 3D baselines reported are not synthesis-aware. Stronger comparisons with synthesis-aware methods would be more convincing.\n- Hard edge constraints can preclude valid chemotypes such as macrocycles.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "gYH1Xj6eb3", "reviewer": "Reviewer_7GM3", "summary": "This paper introduces SYNCOGEN, a generative framework for designing synthesizable small molecules directly in 3D Cartesian space. The core idea is to jointly model molecular building blocks and chemical reactions alongside the continuous 3D atomic coordinates. The method combines a masked graph diffusion model for the reaction graph with a flow matching model for the coordinates, trained on a newly curated dataset called SYNSPACE. The authors demonstrate SYNCOGEN's capabilities through experiments in unconditional generation, where it achieves state-of-the-art performance in both 3D geometry and synthesizability metrics, as well as in conditional tasks like fragment linking and pharmacophore-conditioned generation, where it shows competitive results.", "questions": "1. Could you please add an analysis of the SYNSPACE dataset's chemical property distributions to the appendix? This would help in understanding the chemical space your model operates in.\n2. Could you comment on the feasibility of adding an experiment that explicitly highlights the synergy of your joint approach? For example, a task involving conditioning on a 3D property where a 2D-first pipeline would likely fail. \n3. Could you comment on the generalizability of your findings, given the small number of targets?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. The primary contribution is the novel formulation of jointly generating a synthesizability-aware reaction graph and the corresponding 3D molecular conformation. This elegantly bridges two previously disconnected lines of research: 2D synthesizable generation and 3D all-atom generation. If successful, this approach could significantly accelerate drug discovery pipelines by producing spatially-aware designs that are also practically achievable in the lab. \n2. The technical execution is of high quality. The choice to combine masked discrete diffusion for the building block graph and equivariant flow matching for the 3D coordinates is a sophisticated and well-suited generative paradigm for this multimodal task. Furthermore, the curation of the SYNSPACE dataset, which explicitly links reaction graphs with low-energy 3D conformers, is a valuable resource contribution that could enable future research in this direction. \n3. The paper is well-written, clearly structured, and generally easy to follow. The methodology is explained with sufficient detail, and Figure 1 provides an excellent conceptual overview of the generative process. The experimental setup and evaluation metrics are well-defined.", "weaknesses": "1. While the creation of SYNSPACE is a commendable effort, its presentation as a key contribution is not fully supported by an analysis within the paper. The manuscript lacks a characterization of the dataset's properties. To understand the model's behavior and potential biases, it is crucial to see distributions of key molecular properties (e.g., molecular weight, logP, scaffold diversity) and how they compare to standard benchmarks like ZINC or GEOM-Drugs. It is difficult to assess the complexity and chemical scope of the space the model has learned.\n2. The de novo generation experiments (Table 1) compare SYNCOGEN only against all-atom 3D generative models. While this is a necessary comparison for evaluating 3D conformer quality, it omits a critical class of baselines: state-of-the-art synthesizable generators that operate on fragments in 2D or 3D.  Does the added complexity of generating 3D coordinates come at the cost of performance on the core task of synthesizable graph generation? This comparison is needed to fully contextualize the paper's contribution.\n3. A central motivation of the paper is the advantage of generating 3D coordinates alongside the synthesis plan. However, the experiments do not provide a clear, causal link demonstrating this advantage. The work successfully shows that it can be done, but not why it is better than alternative pipelines. For synthesizability alone, 2D methods suffice. \n4. The evaluation for pharmacophore-conditioned generation is performed on only three target proteins. This small sample size is insufficient to establish statistical significance or to claim general applicability. The results are promising but can be treated as anecdotal case studies rather than a robust validation of the method's capability.\n5. The model generates molecules conditioned on a pharmacophore without any information about the target protein pocket. It is therefore surprising that it produces molecules with docking scores superior to the native ligand and other baselines. A deeper analysis is needed to convince the reader that this is not a coincidental finding.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "htA9KtSMo8", "reviewer": "Reviewer_1Mne", "summary": "The authors introduce.  SYNCOGEN, a multimodal generative framework that jointly models 3D molecular geometry and synthetic accessibility through reaction templates. The key idea is to integrate masked graph diffusion and flow matching into a unified generative process that simultaneously samples both the reaction graph over molecular building blocks and the corresponding atomic coordinates. This coupling enables SYNCOGEN to generate 3D molecules that are not only conformationally realistic but also chemically synthesizable via known reaction templates. To support this framework, the authors curate SYNSPACE, a large-scale dataset of over 600K synthesizable molecules and 3.3M associated low-energy conformations, represented as building-block reaction graphs. The model supports conditional generation tasks such as linker design and pharmacophore-guided generation, showcasing its utility in practical drug discovery.", "questions": "- Fig 1 caption, what does non-linear node in this context mean?\n- why do authors disallow macrocycles?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 1, "contribution": 3, "strengths": "The paper tackles one of the central challenges in molecular generative models i.e. providing accessible synthetic routes for generated candidates. Additionally the proposed method is able to generate favourable conformers.", "weaknesses": "- The writing of the paper is convoluted makes it difficult to follow and appreciate the methodology. It would be beneficial if the authors explain their method more clearly. For example, there are several components in the proposed workflow, a better workflow diagram explaining end-to-end working of SYNCOGEN will be helpful to the readers. \n- for a complicated method as yours, with so many components, a more detailed workflow will he helpful. The message in current fig1 is unclear\n- To better understand the method, code could have helped. However the url provided (https://anonymous.4open.science/r/SynCoGen-13F7) does not have the code. Please provide reproducible code. \n- Another major issue I have that authors should benchmark their work against Shen et al (2025). It is the closest baseline to their work however haven't been benchmark against. I understand Shen et al, is conditional SBDD generation but their attempt to generate conformers while simultaneously providing reaction pathway is most similar to this work. In theory, the authors unconditional generation should be able to outperform Shen et al. Please include this experiment in your paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "WWaDdToi8c", "reviewer": "Reviewer_t7Yp", "summary": "This paper introduces SynCoGen, a framework that jointly generates synthesizable reaction graphs and 3D molecular coordinates using masked discrete diffusion and flow matching. The paper also introduces SynSpace, a new dataset with 600k synthesis-aware molecules. Experiments show strong results in unconditional 3D generation, fragment linking, and pharmacophore-conditioned tasks.", "questions": "1. How scalable is SynCoGen to larger or more diverse reaction vocabularies? Would the framework still function if reactions involved multiple leaving groups or more complex coupling patterns?\n2. The paper claims unified discrete–continuous time coupling. However, it seems that diffusion or flow updates on edge types may not take effect until the corresponding nodes are decoded. Did the authors experiment with decoupled or asynchronous schedules across modalities, and if so, how did that affect performance?\n\nI would consider raising my scores if authors could give some resonable explanations to the questions.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. Novel idea of coupling synthesizability with 3D coordinate generation.\n2. The dataset is well-curated and likely useful for future work.\n3. Results are convincing and demonstrate clear improvements over baselines.", "weaknesses": "1. There are many node/edge modeling constraints, heavy notation, and complex noise processes that make the method difficult to follow and reproduce. It’s also unclear which components contribute most to the final performance — the paper did not provide sufficient ablation studies or analysis isolating the impact of individual design choices (e.g., compatibility masking, visibility-aware noise, joint time coupling). As a result, the practical necessity of the full system remains uncertain.\n2. The reaction vocabulary is fixed and limits diversity. The model relies on a predefined set of 93 building blocks and 19 reaction templates, where each reaction involves at most one leaving group per reagent. While this makes synthesis simulation simpler and chemically reliable, it also restricts the model’s capacity to explore more diverse or complex chemical spaces.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)