Refine Drugs, Don’t Complete Them: Uniform-Source Discrete Flows for Fragment-Based Drug Discovery
Authors: Benno Kaech
Luis Wyss
Karsten Borgwardt
Gianvito Grasso
Venue: ICLR 2026 Poster (2026)
Keywords: Generative Chemistry
Discrete Flow Models
Molecular Optimization
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: Discrete flow model that iteratively refines random tokens to fragmented SMILES, achieving competitive results in various drug discovery tasks.

Abstract: We introduce InVirtuoGen, a discrete flow generative model for fragmented SMILES for de novo and fragment-constrained generation, and target-property/lead optimization of small molecules. The model learns to transform a uniform source over all possible tokens into the data distribution. Unlike masked models, its training loss accounts for predictions on all sequence positions at every denoising step, shifting the generation paradigm from completion to refinement, and decoupling the number of sampling steps from the sequence length. For \textit{de novo} generation, InVirtuoGen achieves a stronger quality-diversity pareto frontier than prior fragment-based models and competitive performance on fragment-constrained tasks. For property and lead optimization, we propose a hybrid scheme that combines a genetic algorithm with a Proximal Property Optimization fine-tuning strategy adapted to discrete flows. Our approach sets a new state-of-the-art on the Practical Molecular Optimization benchmark, measured by top-10 AUC across tasks, and yields higher docking scores in lead optimization than previous baselines. InVirtuoGen thus establishes a versatile generative foundation for drug discovery, from early hit finding to multi-objective lead optimization. We further contribute to open science by releasing pretrained checkpoints and code, making our results fully reproducible.

Published as a conference paper at ICLR 2026
REFINE DRUGS, DON'T COMPLETE THEM: UNIFORM- SOURCE DISCRETE FLOWS FOR FRAGMENT-BASE DRUG DISCOVERY
Benno Kaech* *
Luis Wyss"
Karsten Borgwardt
Gianvito Grasso"
ABSTRACT
We introduce VirtuouGenn, a discrete flow generative model for fragmented SMILES for de novo and fragment-coonsraaned generation, and target- prgettprpperty/lead optimization small molecules. The model learns to transform a uniform source over all possible tokens into the data distribution. Unlike masked models, its train- ing loss accounts for predictions on all sequence positions at every denoising step, shifting the generation paradigm from completion to refinement, and decoupling the number of sampling steps from the sequence length. For de novo genera- tion, In Virtuoeen achieves a stronger quality-divere pareto frontier than prior fragment- based models and competitive performance on fragment-come conttrrnne tasks. For property and lead optimization, we propose a hybrid scheme that combines a genetic algorithm with Proximal Property Optimization fine-tuning strategy adapted to discrete flows. Our approach sets new state-of-the-art on the Practical Molecular Optimization benchmark, measured by top- 10 AUC across tasks, and yields higher docking scores in lead optimization than previous baselines. In VirtuoGen thus establishes versatile generative foundation for drug discovery, from early hit finding to multi-objective lead optimization. We further contribute open science by releasing pretrained checkpoints and code, making results fully reproducible
INTRODUCTION
Fragment-base based drug discovery (FBDD) widely used in both academia and industry for its efficient exploration of chemical space (Kirkman et al. (024).. FBDD relies on fragment-consstaiied design, which new candidate molecules are generated by preserving specific substructures, such as active scaffolds pharmacophores, and modifying surrounding regions to tune properties (Kirsch et al.) 2019). However, FBDD is typically guided by expert-defined heuristics based on chemical intuition, limiting exploration of the vast chemical space. In contrast, in silico molecular generation seeks to formalize and automate this intuition, leveraging data-driven generative models to navigate chemical space more systematically. While many such models have emerged as promising candidates to accelerate the drug discovery pipeline (Zeng et al. 2022), their adoption in practice remains limited. key barrier is that their molecular representations are often poorly aligned with medicinal chemistry workflows, making them difficult to integrate into existing pipelines. Although graphs provide natural representation for molecules, generative frameworks tailored graph-structured data remain limited in performance. For instance, the state-of-the-art AutoGraph (Chen et al., (025) sidesteps direct graph generation by linearizing graphs into sequences via depth-first traversal and relying next token prediction. Similarly, the Simplified Molecular Input Line Entry System (SMILES) /Weininger 1988) commonly used when working with small molecules. SMILES encodes molecular graphs as sequences via depth- first traversal of spanning tree with annotations for branches and ring closures. However, both linearizations disrupt chemically meaningful substructures, offering limited control over scaffold retention fragment assembly and making them poorly suited for fragment- bbased drug discovery (Tinsong et al. 2024). We propose In VirtuoGen, continuous-time discrete flow model (Campbell al. 2024 Gat SMILES.
2024) that operates directly on fragmented
II Virtuo Laboratories
Max Planck Institute of Biochemistry
httpps//ght thub. com/ invi rtuol http://iiiittooe_eeeeeeell

---

Published as a conference paper at ICLR 2026
f
1= t=3 1=4
t=1
t=
1=
1=4
(c) Discrete Flow & Uniform Source Figure 1: Comparison of generation paradigms: (a) autoregressive models generate tokens sequen- tially (here simplified by omitting BOS/EOS tokens), (b) masked diffusion models iteratively reveal masked positions, and (c) discrete flows refine all positions starting from uniform souree distribution, where shading indicates the transition from random tokens to data.
(a) Autoregressive
(b) Masked Diffusion
2 RELATED WORK
While numerous generative models have been proposed for small-molecule drug design (Jensen
2019
Olivecrona et al. 2017 Morrison et al. 2024; Gao et al. 20226 (iggam et al.) 2020;] Bou et al.
few are explicitly designed for fragment-level control. In this work, focus approaches that operate on sequential fragment-based representations. Several alternative approaches construct molccules via graph-based operations on substructures, for example by adding deleting fragments through Markov Chain Monte Carlo sampling (Xie et al.) (20T)) using graph-base Variational
2024
Auto-Encoders conditioned on identified substructures (Jin et al.] 2020 2018 Maziarz et al. 2024). or applying truph-based genetic algorithms (GA) (Jensen 2019) Tripp and Hernández-Lobar
2023). Although these models encode domain-specinf priors, they often suffer from poor scalability and limited generalization beyond known chemical regions, in part due to their reliance graph operations and discrete mutation strategies. By contrast, generative models operating on linear sequential representations of fragmented SMILES, such as SAFE-GPP (Noutahi et al. (203)) and GenMol (Lee et al. 2025). offer a more scalable and expressive alternative, and form the primary baselines for our work
Autoregressive Models Autoregressive approaches, such as SAFE-GPT (Noutahi et al. 2023).
generate molecular sequences token by token in fixed left-to-right order. This ordering is arbitrary with respect to molecular structure, which is inherently unordered
Masked Diffusion Models Masked discrete diffusion models, such as GenMol (Lee et al. 2025). iteratively unmask tokens starting from a fully masked input. While predictions are produced for the entire sequence at each denoising step, the training objective accounts for errors only the masked positions. As a consequence, once a token is unmasked during sampling, it is treated as fixed and no longer updated. This introduces fundamental limitation: the number of sampling steps is bounded by the number of initially masked tokens, unless arbitrary remasking heuristics are included.
Our Contributions Our method departs from completion-stye generation and instead refines all positions simultaneously at every denoising step (Figure I This training paradigm enables coordi- nated updates across the molecule and decouples sampling steps from sequence length, aligning with central principle: refine drugs, don't 't complete them. Concurrent to work (Schiff al. 2025) proposed Uniform Discrete Language Models, which similarly allow simultaneous token updates but remain within diffusion- based framework. Coneretely, present the first discrete flow model for fragmented SMILES with refinement-basee training paradigm, show state-of-the-arr performance in de novo generation and competitive performance fragment-conntrainedd generation tasks, and introduce a brid optimization framework combining Proximal Property Optimization (Schulman al. (017). adapted to discrete flows, with a genetic algorithm. Our framework achieves state-of- the-art results on the Practical Molecular Optimization (PMO) benchmark (Gao et al., 2022a) and improved results in lead optimization over prior baselines (Lee et al. 2025).
We compare against GenMol using the results reported in their paper. While the source code is publicly available to the best of knowledge, the pretrained checkpoints are only distributed through NVIDIĀ NIM/NGC under the NVIDIA Open Model I. License, which currently does not allow unrestricted download. As a result, we were unable to run GenMol directly and rely on the published numbers for comparison. Athhhhg,, there exist canonical SMILES encoding scheme, it is still arbitrary imposed ordering.
2

---

Published as a conference paper at ICLR 2026
2.1 DISCRETE FLOW MODELS
We adopt the discrete flow model framework of Gat et al. (2024), where the goal is to transform samples from a source distribution Xo ~<p into samples from a target distribution X1 ~ q. Training data consists of interpolation pairs (Xo. X1) sampled independently from the source and target. We
choose the linear scheduler niÿ of Gat et al. (2024). resulting in following the probability path:
(e(e' (1) (1 t) 600 (z") t62, (x'),
E [0.
(1)
During sampling, each token X; is updated according to the discrete-time Markov update
Xita ~ 6x;(6 (-) + u/( X²),
where is the probability velocity and h > 0 is the step size. Following Gat et al. satisfy the validity constraints
2024). must
Σ x'E
u 2 0 for all and a² + z.
(3)
For our scheduler choice, the training objective becomes
(()) (X.
12 Σ log r(x Xx),
where P1/T denotes the model prediction and the sum over the sequence. The time-dependent loss weighting term, not present in its original formulation, inspired by |Shoo et al. (2024) and places greater emphasis on later timesteps, encouraging higher accuracy near the end of the trajectory. As backbone model, leveraging its bidirectional self-attention to capture long-range dependencies between fragments while predicting the target token distribution at each position. More details about experimental setup is given in Appendix A.I
diffusion transformer (Peebles and Xie 2022) to parameterize P1 IT
2.2 FRAGMENTED SMILES NOTATION & PREPROCESSING
Our molecule representation is based and marginally extends the Sequential Attachment- Based Fragment Embedding (SAFE) framework Noutahi et al. (2023) by encoding molecules as sequences of fragment blocks with explicit attachment points, improving readability and di- rect control over molecular substructures. To produce chemically meaningful fragments, the molecules are decomposed using the revised BRICS algorithm (Degen et al., 20088., with the locations of bond breaks marked by attachment points of the form [i=]. where enumerates the broken bonds and we separate fragments with spaces. In Fig. 2 we illustrate the difference between the SMILES, SAFE, and our notation. To remove any implicit ordering bias, the result- ing fragments are randomly shuffled rather than ordered by their attachment point in the original molecule. The resulting fragmented SMILES strings are tokenized at the atomic leve yielding a vocabulary of 204 tokens.
[2')
SMILES: CC/Co Topojea OOJOCC
SAFE: e 12ooc33c11 -/).c////
Ours: [c]]cc][[[2 (*100000000)0011100000
Figure 2: Comparison between SMILES, SAFE, and our notation for the same molecule. Our nota- tion preserves fragment integrity while providing explicit attachment point numbering that facilitates bidirectional modeling of molecular structure.
2.3 FINETUNING
While de novo generation or fragment-constrainee generation of small molecules certainly an inter- esting and challenging topic, its practical utility in drug discovery is limited. A central contribution of our work is therefore the exploration of tasks with direct real world relevance, such as property optimization, docking score improvement, and lead refinement. These tasks require models not only
Note that do not tokenize e.g. 'CI' as two tokens, but as single one. The same holds for the attachment point tokens.

---

Published as a conference paper at ICLR 2026
to generate chemically valid structures, but navigate chemical space in goal directed manner under realistic computational constraints. Because the finetuning strategies we employ are tightly coupled to the requirements of each experimental setting, we introduce them directly within the corresponding sections (Sec. 3.3 onwards).
3 EXPERIMENTS
We evaluate In VirtuoGen four molecular design tasks: (i) de novo generation of diverse, synthe- sizable, drug-like molecules; (ii) fragment-constrained design with predefined scaffolds or pharma- cophores; (iii) target property optimization on the PMO benchmark (Gao al. 2022a), assessing sample efficiency and oracle performance; and (iv) lead optimization, optimizing docking scores under similarity, synthesizability and drug-likeness constraints.
For fair comparison, we pretrain on the same datasets as GenMol (Lee et al. 2025) and SAFE- GPT (El Mesbahi and Noutahi 2024): ZINC (Sterling and Irwin 2015) and UniChem (Chambers) et al. 2013), containing roughly one billion molecules.
The non-autoregressive formulation enables bidirectional attention, making the model well-suited for the inherently unordered representation. However, this also implies that we explicitly decouple sequence length from the generation process by factorizing the output distribution as
po(x) = p(n) (x n),,
(5)
where p(n) models the sequence length. To compare with GenMol, our base distribution is also chosen to be the empirical length distribution of ZINC250K, curated subset of ZINC (Sterling and Irwin 2015) containing synthesizable, drug-like compounds.
3.1 De Novo GENERATION
For drug discovery, generated molecules must be diverse, synthesizable, and drug-like. We evaluate these aspects with four metries, following prior work on fragmented SMILES: Validity (fraction of valid SMILES), Uniqueness (fraction of unique valid molecules), Diversity (average Tanimoto distance of Morgan fingerprints (Polykovskiy al. 2018 Rogers and Hahn 2010). and Quality (Lee)
et al. 2025) (fraction of valid, unique molecules with QED 2 0.6 (Bickerton et al. 2012) and
SAS (Ertl and Schuffenhauer, p009)) ). Quality and diversity are the main criteria, but they trade off against each other. As in GenMol, we tune this balance via the softmax temperature T and a noise scale r (modulating Gumbel n During generation, is damped as (1 - t) and annealed, promoting early exploration and late refinement. Empirically, sampling directly from the predicted
token-wise distribution
X4th (X.),
(6)
outperforms Eq. 2 significantly. Importantly, our update departs from masked discrete diffusion mod- els: instead of replacing only masked tokens, all sequence positions possibly change simultaneously at every step, leading to refinement process rather than arbitrary order completion. We provide
more details and investigate the benefits of our sampling method Appendix B.
Results In Figure 3] we present and compare our results to other state-of-the-ee fragment-
generative models. Increasing the time-granularity (i.e., using smaller timestep sizes h) consistently improves both quality and diversity. In VirtuoGen consistently achieves a superior pareto frontier, with the largest gains at high time-granularit (h- 0.001), outperforming all baselines across the full quality-diversig spectrum. As described in Appendix B.I] sampling with h = 0.01 yields a comparable number of model calls, while still showing modest performance increase over GenMol, particularly in the lower-diversity regime. We provide the ZINC250K sequence length distribution, non-curated samples, timing studies and additional results in Appendix B.1 including the pareto frontier obtained by sampling according to Eq. 2
3.2 FRAGMENT- CONSERRINND GENERATION
A core task in FBDD is to generate molecules given one or more fragments the molecule should contain. However, both next-token prediction models and masked discrete diffusion models such as GenMol can be prompted in straightforward manner by using prefix. In contrast, our model predicts a potential completely different sequence at every timestep. Thus strictly requiring the presence of the exact prompt significantly impacts the performance model, since to ensure that the
'GenMol instead perturbs the order of the confideece-bbsee token unmasking
4

---

Published as a conference paper at ICLR 2026
100
01.01
90
11.21
12.41
Quality
60
59
GenMol
50
SAFE-GPT
InVirtuoGen (h=0.1)
40
InVirtuoGen (h=0.01)
InVirtuoGen (h=0.001)
0.750
0.775
0.800
0.825
0.850
0.875
0.900
0.925
Diversity
Figure 3: Quality-diversity trade-off for GenMol, SAFE-GPT (single point, as no quality- diversity scan data is available), and our model at different simulation time granularities (h {0.1, 0.01, 0.001 Curves correspond to varying sampling noise (T, where T is the softmax temperature and the Gumbel noise scale.
generated molecules remain consistent with given fragments, the corresponding positions are naively overwritten every timestep of the simulation. We note that Tragment-constraine generation is fundamentally at odds with our refinement philosophy. It requires fixing certain positions, preventing the holistic refinement that makes our approach powerful. Nevertheless, we include additional results in Appendix [B.2] That said, prompting remains an important feature of our model. Unlike strict fragment enforcement, soft prompting enables controlled exploration the neighborhood of input molecule, making it useful mechanism for guided search and local optimization, as we show in the following section.
3.3 TARGET PROPERTY OPTIMIZATION
The PMO benchmark evaluates molecular optimization under conditions that mirror practical drug discovery, with limited oracle calls and diverse pharmacologically relevant objectives. We introduce hybrid approach that combines genetic algorithm, which provides fast convergence through recombination of high-scoring molecules, with PPO-based reinforcement learning adapted to discrete flows, which enables gradient-guides refinement under shaped reward signals. Importantly, combination of the two methodologies is simplified by our model's ability to accept full sequences as input. Note, that for this experiment we used the standard discrete flow sampling from Eq. short explanation for this choice given in App. B.3.1
Genetic Algorithm Because our model operates on full-length sequences, the initial state Tı=o is constructed as mixture of top-performing molecules. We maintain vocabulary of high-scoring molecules with pairwise Tanimoto distance 2 0.7 on Morgan fingerprints. To produce an offspring, two parents are sampled without replacement using rank-based probabilities p(m) = (/(rank(m) k.)), where M is the vocabulary size and и controls the contribution of lower-ranked entries. Parents are then decomposed by the fragmentation rule, and offspring are formed by replacing one fragment of the first parent with fragment from the second, joined by separator token in the fragmented SMILES space (i.e. simple string concatenation). GenMol joins fragments at fixed dummy attachment points, while refinement method can adjust the local context and explore structural variants around the fragment. Naturally, most resulting offspring are not valid molecules, but they only provide the starting state 2r=0 for model. While in traditional GA the offspring is mutated, adopt the
5

---

Published as a conference paper at ICLR 2026
mutation operators of Jensen (2019) and apply them the best-perforning molecules found far to explore their neighborhood.
Reinforcement Learning We adapt PPO (Schulman et al., 2017 to fine-tune the discrete flow policy. Unlike autoregressive models, where the policy log-probability is directly available the sum of next-token log-likeliban likelihoods, discrete flows do not yield a tractable log p(z)) over entire sequences. Instead, following the discrete flow matching framework Gat et al. (2024). log-probability via Monte Carlo estimation over perturbed states. For every sequence, we draw timesteps (O, (0, 1), apply the noise schedule to obtain a partially noised state 2, and optimize the time-weighted loss
approximate the
log To (x 2z, t).
12
muised positions
Our rewards are computed as o. where is the oracle scores, F denotes the batch mean, or the standard deviation and provides numerical stability. The clipped PPO surrogate p(0)
exp (log m log Tota) is optimized in the standard way.
Adaptive Sequence Length Sampling As mentioned previously, our model requires a sequence length as input during generation. To accelerate convergence to well-performing molecule lengths, we employ an adaptive bandit that favors lengths with consistently high rewards while still retaining exploration through the prior distribution. We use a peak peak-seeking variant that blends best-so-far performance, reward quantiles, and an exploration bonus (see Appendix AA.3.I).
Combined Optimization Algorithm The overall procedure, combining GA exploration with PPO fine-tuning of the discrete flow, is summarized in Alg. [ and additional implementation details are provided in Appendix A.3] Unlike GenMol or f-RGG, our method uses single hyperparameter configuration across all tasks, highlighting that the performance gains arise from the algorithmic design rather than extensive hyperparameter tuning.
Algorithm 1 Target-Property Optimization (GA + PPO)
Require: Model frozen prior Told. oracle O population P, bandit B, maximum oracle calls N Nmax. fragmentation rule R. mutation op, PPO params (c, Cneg, (3)
while oracle calls NNuxx do
sample parent pairs from P; draw lengths & B
Port + {X ~ T- (rossover(R((1)) R(22)), E)} Por <- Poι U (mutate(I)
E top (P)}
r T (
for k 1 to K do
0 - 0 (oL(O;r, r, no. Tota)
end for
update B with (e,r); P - UP
Told f
end while
return top molecules
Results The PMO benchmark comprises 23 single-objective molecular optimization tasks. Evalua- tion considers the achieved score and sample efficiency, summarized by the top10 AUC metric: the area under the curve of the mean score of the top ten molecules as a function of oracle calls. The scores are normalized to [0. 1]. and each run is limited 10,000 oracle evaluations. GenMol (Lee) et al. (025) and f-RAG (Lee et al. 2024) initialize their populations by screening the entire ZINC250K dataset, i.e. performing 250,000 additional oracle calls before optimization begins. Thus, while they nominally report results with 10k oracle calls, the effective budget is closer to 260,000. To ensure comparability, we evaluate our method under both setups: with prescreening on ZINC250K (Tab [). directly comparable GenMol and f-RAG, and without prescreening (Tab) 2}. directly comparable to baselines such as REINVENT (Olieecoona et al. 2017). MolGA (Trip and Hernández-Lobarr 2023), and Genetic GFN (Kim et al.) (2024), which do not any prior oracle information. Due to space constraints, we only include up to three top- performmnn basclines, ranked by the sum of AUC-top10 scores across all benchmark tasks. In both setups, In VirtuoGen consistently achieves the

---

Published as a conference paper at ICLR 2026
Table 1: Comparison of models on the PMO benchmark that screen ZINC250K before initialization. We report the AUC-top10 scores, averaged over three runs with standard deviations. Best results and those within one standard deviation of the best are indicated in bold. The scores for f-RAG (Lee) et al. 2024) and GenMol (Lee et al. 2025) are taken from the respective publications.
Oracle
In VirtuoGen
GenMol
f-RAG
albuterol similarity
0.975 (1:0)
0.937 0.010)
0.977 (#: 0.00)
amlodipine mpo
0.836 n031)
0.810 0.13)
0.749 (1: 0019)
celecoxib rediscovery
0.839 (4 0.013)
0,826 (#: 0.018)
0.778 (à: 0.007)
deco hop
0,968 (4 0012)
0.960 0.010)
0.936 0.011)
drd2
0.995 ( 0.000)
0.995 (# 0.000
0.992 (+: 0.000)
fexofenadine mpo gsk3b
0.904 ( 0.00))
0.894 (# 0.028)
0.856 (:: 0.016)
0.988 ( 0.001)
0.986 (#: 0.003)
0.969 + 0.003)
isomers c7h8n202
0.988 (1: 0.002)
0.942 (# 0.004)
0.955 (:: 0.008)
isomers c9h 122222f2ell
0.898 (1: 0.018)
0.833 (# 0.014)
0.850 (# 0.00))
jnk3
0.898 (+ 0.031)
0.906 (+: 0.023)
0.904 (4: 0.004)
medianl
0.386 (4: 0.003)
0.398 0,000)
0,340 (à: 0.007)
median2
0.377 (:
0.359 (= 0.004)
0.323 (+: 0.005)
mestranol similarity
0.991 (+ 0.002)
0.982 (#
0.671 (:: 0.021)
osimertinib mpo perindopril mpo qed ranolazine mpo scaffold hop
0.881 0.012)
0.876 (1: 0.008)
0.866 (1: 0.009)
0.753 (1 0.943 (1: 0.000)
0.718 (2: 0.012)
0.681 (1: (017)
0.942 (2: 0.000)
0.939 (#: 0.00))
0.854 (+ 0.012)
0.821 (#
0.820 r 0.066)
0.711 (+ 0.081)
0.628 (#: 0.008)
0.576 (è: 0.014)
sitaglintin mpo thiothixene rediscovery
0.743 ( 0.022)
0.584 (# 0.034)
0.601 ( 0.01)
0.652 ( 0.24)
0.692 (#: 0.123)
0.584 (#: 0.009
troglitazone rediscovery
0.853 (1: 0.003)
0.867 (t: 0.022)
0.448 (1: 0.017)
valsartan smarts
0.935 (1 0.01))
0.822 (:: 0,042)
0.627 (1: 0.058)
zaleplon mpo
0.624 (+ 0.40))
0.584 (d: 0.013)
0.486 (+: 0.004)
Sum
18.993 (:: 0.219)
18.362
16.928
best overall performance, considering the sum over all tasks. Ablations in Appendix B.3.1 show that all components of our optimization stack matter. In particular, PPO without prescreening and any genetic algorithm yields higher performance than REINFORCE, common baseline used in industry.
3.4
LEAD OPTIMIZATION
Given initial seed molecule, the goal in lead optimization is to generate leads that exhibit improved binding affinity to a target protein while satisfying constraints on the generated molecules. For the following experiments, the constraints are QED > 0.6, SA S 4, and Tanimoto similarity 2 to the seed molecule, where 5 E (0.4, 0.6). We follow the benchmark of et al. (2025) and evaluate on five target proteins (parpl, 1, fa7, 5ht1b, braf, jak2), each with three active ligands as molccule seeds. Performance is measured by the docking score (DS) of the most optimized lead (lower is better). We use the same optimization method as in the previous section, but we scale the docking score DS by constraint satisfaction:
DS (1 penalty(QED(m)) (()() (A(m))
S(m) = 15
(8)
where the penalty increases when QED < 0.6, SA 4, or SIM < 8.
Results Table 3 compares our approach against GenMol, RetMol, and GraphGA Our model consistently achieves competitive or superior docking scores across most proteins and similarity thresholds. Notably, our method remains effective even under the stricter 8 = 0.6 constraint, where baseline methods frequently fail to produce improved leads. For example, on parpl and jak2, our model obtains substantially better docking scores than the baselines. The use of a soft-constraint oracle during training proves advantageous, allowing our model to explore chemical space more effectively while still converging to molecules that meet all constraints. While Tanimoto similarity is standard proxy for structural similarity, it has known limitations as it reduces complex molecular relationships to a single fingerprint overlap score. To give a more complete view, we also report results without this constraint in Appendix B.4
7

---

Published as a conference paper at ICLR 2026
Table 2: The results of the best performing models on the PMO benchmark, where we quote the AUC- top10 averaged over 3 runs with standard deviations. The best results are highlighted in bold. Values within one standard deviation of the best are also marked in bold. The results for Genetic GFN (Kim) et al. (024) and Mol GA (Tripp and Hernández-Lobate 2023) are taken from the respective papers. The other results are taken from the original PMO benchmark paper by (Gao et al. 2022a).
Oracle
In Virtuoenn (no prescreen)
Gen. GFN
Mol GA
REINVENT
albuterol similarity
0.950 (4 0.017)
0.949 (# 0.010)
0.896 (4: 0025)
0.882 (4: 0.066)
amlodipine mpo celecoxib rediscovery deco hop drd2
0.733
0.761 0.019)
0.688 (4: 0039)
0.635 0.03))
0.798 ( 0.028)
0.802 0.029)
0.567 (+ 0.08))
0.713 (#: 0.067)
0.748 ( 0.109)
0.733 (# 0.109)
0.649 0.025)
0.666 (# 0.44))
0.985 ( 0.002)
0.974 ( 0.006)
0.936 (+: 0016)
0.945 (+ 0.007)
fexofenadine mpo gsk3b
0.845 ( 0.016)
0.856 (#: 0.039)
0.825 0.019)
0.784 (:: 0.006)
0.952 (1: 0.016)
0.881 (# 0.042)
0.843 (:: 0.039)
0.865 (#: 0.043)
isomers ch882202
0.968 (+ 0.005)
0.969 (#t 0.003)
0.878 (+: 0.026)
0.852 (+: 0.036)
isomers c9h 1nno0222l
0.874 (4: 0.013)
0,897 0,007)
0.865 (4: 0.012)
0.642 (+: 0.054)
jnk3
0.825 0.016)
0.764 (# 0.069)
0.702 (+: 0.13)
0.783 (+: 0.023)
medianl
0.342 (#: 0.08))
0.379 0.010)
0.257 (+: 0.09)
0.356 (:: 0.099)
median2
0.288 (1: 0.008)
0.294 (: 0.007)
0.301 (# 0.021)
0.276 (1: 0.008)
mestranol similarity
0.797 (1 0.033)
0.708 (1
0.591 0.53)
0.618 0.048)
osimertinib mpo
0.870 (1: 0.005)
0.860 (1: 0.008)
0.844 (+ 0015)
0.837 (:: 0.009)
perindopril mpo qed ranolazine mpo scaffold hop
0.645 + 0.092)
0.595 ( 0.014)
0.547 (+ 0022)
0.537 0.16))
0.942 (+ 0.000)
0.942 (#: 0.000)
0.941 (+: 0.001)
0.941 (+ 0.000)
0.848 ( 0.100)
0.819 ( 0.018)
0.804 (+: 0011)
0.760 (:: 0.009)
0.589 ( 0.21))
0.615 5 0.103)
0.527 ( 0.025)
0.560 (# 0.019)
sitagliptin mpo thiothixene rediscovery
0.709 (1: 0.029)
0.634 (1 0.039)
0.582 (1: 0.00)
0.021 (4: 0.003)
0.625 (1 0.014)
0.583 (# 0.034)
0.519 (1 0011)
0.534 (1: 0.013)
troglitazone rediscovery
0.595 ( 0.053)
0.511 ( 0.054)
0.427 (t: 0031)
0.441 (+: 0.032)
valsartan smarts
0.210 ( 0.297)
0.135 0.271)
0.000 (t 0.000)
0.178 (+: 0.358)
zaleplon mpo
0.536 (+ 0.006)
0.552 (th 0.053)
0.519 (# 0.029)
0.358 (+: 0.062)
Sum
16.676 (+ 0.256)
16.213
14.708
14.184
4 CONCLUSION
We have presented In VirtuoGen, discrete flow-based generative model for fragmented SMILES. versatile model employable in various stages of common practical drug discovery tasks allowing fragment-leve control. By decoupling sequence length from token generation, we can show that finer granularity during the simulation trajectory leads to more diverse and drug-like molecules in de novo generation. The uniform-source formulation also enables seamless integration with a genetic algorithm and PPO-motivated fine-tuning. Across de novo generation, mugment-constraile design, and target property optimization, our approach advances the state-of-the--rr, achieving a new pareto frontier in -iivesyy trade-offs, with competitive quality and diversity in fragment- constrained tasks, a higher sum of top10 AUC in the PMO benchmark and similarly better results in lead optimization, where docking scores are optimized under constraints.
5 LIMITATIONS
Our fragmented SMILES representation discards stereochemistry, preventing modeling of stereospe- cifie interactions. The rBRICS decomposition may miss chemically relevant fragmentation patterns, and the SA/QED metrics are coarse heuristics that poorly correlate with actual drug-likeness (Sko- raczyński et al., 2023 Chen and Jung 2024). Missing ADMET assessments limit our conclusions and all results remain base,- requiring experimental validation. However, these issues are shared by all compared baselines.
Our sampling modification (Eq. lacks theoretical justification despite strong empirical evidence. For Tagment-coostraiin
generation, employ naive overwriting that disrupts the learned flow dynamics by forcing certain positions to remain fixed throughout the trajectory, contradicting the refinement paradigm central to our approach.
8

---

Published as a conference paper at ICLR 2026
Table 3: Docking scores (lower better) averaged over random seeds. Bold indicates the best result seed molecule. Values in parentheses indicate solutions with QED>> 0.6 and SA< 4 that do not improve the docking score over the seed. For each seed molecule, its docking score, the quantitative estimate of drug-likeness and synthetic accessibility is given.
Protein (DSQUENISA)
== 0.4
8 = 0.6
GenMol
RetMol
GraphGA
Vi
GenMol
RetMol
GraphGA
VirtuoGen
parp1
8.3008982.61
-10.6
-9.0
-8.3
-1,11 (#0.4)
-10.4
-8.6
-12.3 (=0.2)
75880.7582.77
-11.0
-10.7
-8.9
-1.4 (#0.6)
-9.7
-8.1
-11.7 (=0.6)
8.2X0438/2.91
-11.3
-10.9
-9.0 (1:1.3)
-9.2
-10.7 (:10.9)
fa7
6.4022802.29
-8,4
-8.0
-7.8
-8.4 (10.4)
-7.3
-7.6
-7.6
-7.7 (1:0.4)
66700 186/3.39
-8.4
-8.2
-8.9 (20.5)
-7.6
-7.6
-7.5 (20.3)
(-8.0 (#0.3))
(-7.4 (10.4)
5htlb
4..00.438/3995
-12.9
-12.1
-11.7
13.3 (#-0.1)
-12.1
-11.3
-2244 (=0055)
-74807633.29
-12.3
-9.0
-12.1
12.0 (#d.7)
-12.0
10.00
-12.0
1220 (#0.4)
9.800716/4.69
-1..6
10.9
-10.5
-0.6
braf
-..30.235/2.66 89
-10.8
-1.66
-9.8
10.1 (20.00
.9.7 (20.1)
-9400346/2.40
-10.8
-10.8 (2:0.)
-9.7
-10.4 (200.)
9.8802555/2338
-10.6
-11.6
10.6 (10.4)
-10.5
-10.4
10.3 (1:0.)
jak2
-7.7X0725/2.88 89
-10,2
-10.2 (20.8)
-9.3
-9.7 (20.3)
3.000.12/3.99
-10.0
-9.0
-9.2
-10.5 (#0.3)
-9.4
-9.2
-10.4 (20.1)
86804823.10
-9.8
-10.2 (1002)
-0.33 (200.2)
Sum
-148.7
-88.5
-96.3
1-2.64
-117.7
-25.7
-74.8
-145.7 (-153.1)
IMPACT, REPRODUCIBILITY & LLMS USAGE
The method enables efficient fragment-based design with potential benefits for drug discovery but carries risks if misused for harmful molecule design.
Impact
Reproducibility We release model checkpoints, scripts, Dockerfile, and instructions to replicate the experimental results.
LLM Usage We used language models for text polishing and LaTeX/coding assistance. However, all experiments, analyses, and results were designed and conducted by the authors.

---

Published as a conference paper at ICLR 2026
REFERENCES
P. Auer, N. Cesa-Bianchi, and P. Fischer. Finite-time analysis of the multiarmed bandit problem. Machine Learning, 47:235-256, 05 2002. doi: (0200//:10336970000000
R. Bickerton, G. Paolini, J. Besnard, S. Muresan, and A. Hopkins. Quantifying the chemical beauty of drugs. Nature chemistry, 4:90-8, 8, 02 2012. doi: 10. 10.1038/nchem.1244 1243.
A. Bou, M. Thomas, S. Dittert, C. N. Ramírez, M. Majewski, Y. Wang, S. Patel, G. Tresadern, M. Ahmad, V. Moens, W. Sherman, S. Sciabola, and G. D. Fabritiis. Acegen: Reinforcement learning of generative chemical agents for drug discovery, 2024. URL/attaa://rxxivvoo
04657
A. Campbell, J. Yim, R. Barzilay, T. Rainforth, and T. Jaakkola. Generative flows discrete state-spaces: Enabling multimodal flows with applications to protein co-design, 2024. URL
https://arxi org/ abs 20Dp//2400 2402. 2402.04997
J. Chambers, M. Davies, A. Gaulton, A. Hersey, S. Velankar, R. Petryszak, J. Hastings, L. Bellis,
S. McGlinchey, and Overington. Unichem: a unified chemical structure cross-referencing and identifier tracking system. Jourmal of Cheminformattics, 5(1):3, 2013. doi: 10.1186/1758-2946-5
URL htt.:httt:://oottt org/10 11w.11.1111111111111111
D. Chen, M. Krimmel, and K. Borgwardt. Flatten graphs as sequences: Transformers are scalable graph generators, 2025. URL
wtt.:ggggbb/////// 02216
S. Chen and Y. Jung. Estimating the synthetic accessibility of molecules with building block and reaction-aware sascore. Journal of Cheminformuttics 16(1):83, 2024. doi: 10. 186/ sl13321-024000879-00 URLhttts://doo/ http://///....ooo.0...111////11/
Y. David and N. Shimkin. Pure exploration for max-quantile bandits. volume 9851, pages 556-571, 09 2016. ISBN 978-3-319-46117-4, doi:
Degen, Wegscheid-Gerluee 'drug-like' chemical fragment spaces. ChemMedChem: Chemistry Enabling Drug Discovery, 3 110):1503-1507, 2008
Zaliani, and M. Rarey. On the art of compiling and using
Y. El Mesbahi and E. Noutahi. Safe setup for generative molecular design. arXiv preprint arXiv:2410.20232. 2024. preprint.
P. Erd and A. Schuffenhauer. Estimation of synthetic accessibility score of drug-like molecules based on molecular complexity and fragment contributions. Journal of cheminformatics, 1:8, 06 2009. doi: 10.1 1188/6188-29666 29---1-8--
W. Gao, T. Fu, J. Sun, and C. W. Coley, Sample efficiency matters: A benchmark for practical molecular optimization, 2022a. UtL/tttsss//az///oo////// 20000 1211_/11122220.2111 12411
W. Gao, R. Mercado, and C. W. Coley. Amortized tree generation for bottom-up synthommmuuppythssitii planning and synthesizable molecular design, 2022b. URL
I. Gat, T. Remez, N. Shaul, F. Kreuk, R. T. Q. Chen, G. Synnaeve, Y. Adi, and Y. Lipman. Discrete flow matching. arXiv preprint 2rXiv:2407.15595, 2024.
J. H. Jensen. A graph-based genetic algorithm and generative model/monte carlo tree search for the exploration of chemical space. Chem. Sci., 10:3567-3572, 2019. doi: 10.1039/c3sc05372c. URL http:/ //t::///xxxcoo doi. org 10.
W. Jin, R. Barzilay, and T. Jaakkola. Junction tree variational autoencoder for molecular graph generation. Proceedings of the 35th International Conference on Machine Learning. 80:2323- 2332, 2018.
W. Jin, D. Barzilay, and T. Jaakkola. Multi-objective molecule generation using interpretable substructures. In H. D. III and A. Singh, editors. Proceedings of the 37th International Conference Machine Learning. volume 1 119 of Proceedings of Machine Learning Research, pages 4849- 4859. Pmlr, 13-18 Jul 2020. URL htt http::::/pppcceeiiioeooo mlr. mml..ppees//119///12000 html
10

---

Published as a conference paper at ICLR 2026
S. Jinsong. J. Qifeng, C. Xing. Y. Hao, and L. Wang. Molecular fragmentation crucial step in the ai-bused drug development pathway. Communicaations Chemistry, 7(1):20, 2024, doi: 10.1038/ +42004-024-01109-
H. Kim, M. Kim, S. Choi, and J. Park. Genetic-guided gftownets for sample efficient molecular optimization, 2024. URL http:: http:///axxxvvoooo. abs wttp://owr/p///22.......
Kirkman, C. Silva, M. Tosin, and M. Dias. How to find a fragment: Methods for screening and validation in fragment-basedt drug discovery. ChemMedChem, 19, Nov. 2024, doi: 10. 1000/mmc 202400342.
Kirsch, A. M. Hartman, A. K. H. Hirsch, and M. Empting. Concepts and core principles of fragment- based drug design. Molecules, 24(23), 2019. ISSN 1420-3049. doi: 10.390/mmbbculee222435599 URL https:://///...... /wwp://wwwwwww// http://wwwpppp....mmmmm/.m www.ccmm/////oooo /ttp://///000003////23333334//33
S. Lee, K. Kreis, S. P. Veccham, M. Liu, D. Reidenbach, S. Paliwal, A. Vahdat, and W. Nie. Molecule generation with fragment retrieval augmentation, 2024. URL httpa://arxiv..oo
2411.12073
Lee, K. Kreis, S. P. Veccham, M. Liu, D. Reidenbach, Y. Peng. S. Paliwal, W. Nie, and A. Vahdat. Genmol: A drug discovery generalist with discrete diffusion, 2025. URL https://arxiv org/ arg/abs// 2501. 06158
J. Lim, S.-Y. Hwang, S. Moon, S. Kim, and W. Y. Kim. Scaffold-based molecular design with graph generative model. Chemical Science, 11(4):15331164, 2020. ISSN 2041-6539, doi: 10.1039/c9sc44503a URL
doi http://o............11/////00/..
I. Loshchilov and Hutter. Decoupled weight decay regularization, 2019. URL https: /axxiv org/abs/ 711.11111 05101
K. Maziarz, H. Jackson-Flux Cameron, F. Sirockin, N. Schneider, N. Stiefl, M. Segler, and M. Brockschmidt. Learning to extend molecular scaffolds with structural motifs, 2024. URL 03864
https://arxiv org/
O. M. Morrison, F. Pichi, and J. S. Hesthaven. Gfn: A graph feedforward network for resolution- invariant reduced operator learning in multifidelity applications, 2024. URL hhttss://arx: org htgg/bba/20 2406. 03569
A. Nigam, Friederich, M. Krenn, and A. Aspuru- Guzik, Augmenting genetic algorithms with deep neural networks for exploring the chemical space, 2020.
1909. 11655
H. Nisonoff, J. Xiong, S. Allenspach, and J. Listgarten. Unlocking guidance for discrete state-space diffusion and flow models, 2025. URL
wttp://///a/b////o///b///// 01572
E. Noutahi, C. Gabellini, M. Craig. J. S. C. Lim, and P. Tossou. Gotta be safe: A new framework for molecular design, 2023. URL 30070/
org/ httgg//b/bb/../1/.....
M. Olivecrona, T. Blaschke, O. Engkvist, and H. Chen. Molecular de-novo design through deep reinforcement learning. Journal of Cheminformatics, 9(1):1-14, 2017.
W. Peebles and S. Xie. Scalable diffusion models with transformers. arXiv preprint arXiv:2212.09748. 2022.
D. Polykovskiy, A. Zhebrak, B. Sanchez-Lengeling S. Golovanov, O. Tatanov, S. Belyaev, R. Kur- banov, A. Artamonov, V. Aladinskiy, M. Veselov, A. Kadurin, S. Johansson, H. Chen, S. Nikolenko, A. Aspuru-Guzik and A. Zhavoronkov. Molecular sets (moses): A benchmarking platform for molecular generation models, 2018.
D. Rogers and M. Hahn. Modeling, 50(5):742-754 754, 05 2010. doi: 10.102//c1100000. URL 1021/ci 100050E
fingerprints. Journal of Chemical Information and / http::::/doii..rg/////
11

---

Published as a conference paper at ICLR 2026
S. S. Sahoo, M. Arriola, Y. Schiff, A. Gokaslan, E. Marroquin, J. T. Chiu, A. Rush, and V. Kuleshov. Simple and effective masked diffusion language models, 2024. URL https: Btllaattp://axaaaa http::://rxxivoooo.. abs/2406. 07524
Y. Schiff, S. Sahoo, H. Phung, G. Wang, S. Boshar, H. Dalla-torre, P. de Almeida, A. Rush, T. Pierrot, and V. Kuleshov. Simple guidance mechanisms for discrete diffusion models, 2025. URL
wwtpi//..oo/////222....... 10193
Schulman, Wolski, P. Dhariwal, A. Radford, and Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv: 170.::/777.6347,20111
S. Seo, J. Lim, and W. Kim. Molecular generative model via retrosynthetically prepared chemical building block assembly. Advanced Science, 10, 01 2023. doi: 10. 20.10022advv.2222266744
G. Skoraczyúski, M. Kitlas, B. Miasojedow, and A. Gambin. Critical assessment of synthetic accessibility scores in computer-assisted synthesis planning. Journal of Cheminformatics. 15(1);6, 2023. doi: 10.118864133211002-0077777 913321-023-00678-2
URL
Sterling and Irwin. Zine 15 ligand discovery for everyone. Journal of chemical information and modeling, 55, Oct 2015. doi: 11.0://ac.ccim.500055555
J. Su, Y. Lu, S. Pan, A. Murtadha, B. Wen, and Y. Liu. Roformer: Enhanced transformer with rotary position embedding, 2023. UtI.httss://arat /ttp:::///aaxvvv.// obtpa////rrr///////////////
09864
A. Tripp and J. M. Hernández-Lobato. Genetic algorithms are strong baselines for molecule genera- tion, 2023. URL /tL./a/pss///aax....rr/////////p
09267
D. Weininger. Smiles, chemical language and information system. 1. introduction to methodology and encoding rules. Journal of Chemical Information and Computer Sciences, 28(1):31-36 02 1988. doi: 10. 10:102//00005570005. URL httph::////oiiii
10. 1ttp:///....002/00000000000
Z. Xi, X. Guo, Y. Nan, E. Zhou, J. Shen, W. Chen, Liu, Huang, Z. Zhang, H. Guo, X. Deng. Z. Lei, M. Zheng. G. Wang, S. Zhang. P. Sun, R. Zheng, H. Yan, T. Gui, Q. Zhang, and X. Huang. Bapo: Stabilizing off-policy reinforcement learning for llms via balanced policy optimization with adaptive clipping, 2025. URL httt::://arxiiiiiee org http:/bb//21..11222
Y. Xie, Shi, H. Zhou, Y. Yang, W. Zhang, Y. Yu, and L. Li. Mars: Markov molecular sampling for multi-objective drug discovery, 2021. URL htt.t::tt//:xiiiii www.:iiiorrr.//// www.////1... 10432
X. Zeng, F. Wang, Y. Luo, S. gu Kang, J. Tang, F. C. Lightstone, E. F. Fang, W. Comnell, R. Nussinov, and F. Cheng. Deep generative molecular design reshapes drug discovery. Cell Reports Medicine, 3(12):100794 2022.
12

---

Published as a conference paper at ICLR 2026
A EXPERIMENTAL DETAILS
A.1 IMPLEMENTATION DETAILS
The backbone model, adapted from Peebles and Xie (2022), has 36 layers 12 heads, the hidden dimension is chosen 768, and uses rotary positional embeddings (Su et al. 2023). Training is performed for one epoch with batch size of 300. Sequences of similar length are bucketed together to reduce the padding per batch. The maximal number of tokens per batch limited to 25, 000. The AdamW (Loshchilov and Hutter 2019) optimizer, with (Bi 0.99, 82 0.999) is used with learning rate of 10 Additionally, the learning rate is varied according to a linear warm-up cosine annealing scheduler.
A.2 TRAGMENT-CONSTRANN
GENERATION PARAMETERS
The time-granularity of 0.01 is used together with our proposed sampling from Eq. 6 We see a slight performance increase when increasing the sampling time-granularity, as demonstrated in Appendix B.2
A.3 TARGET-PROPERTY OPTIMIZATION PARAMETERS
smaller model is used in this setting, with 12 layers instead of 36. The population for the genetic algorithm, which provides the starting points of the trajectory {zr=a), is updated every 50 scored samples. Out 80 generated samples, 20 are obtained by mutating the top 20 candidates generated so far, using the mutation operators from Jensen (0119). For rank-base based sampling. For the calculation of the Tanimoto distance, we use Morgan fingerprints with 2048 bits and a radius of 2 nodes. The model is updated with PPO after every 100 scored SMILES. For each sequence, 50 timesteps t. ~ (0, 1) are sampled to construct the training dataset { by interpolating hetween a sequence of random tokens and the sampled values. During each epoch, 10 optimization steps are performed with a learning rate of 10-4 The clipping coefficient for PPO is set to 0.2. When constructing the initial population by prescreening ZINC250K, no experience replay used. Otherwise, an experience replay buffer of 300 samples is maintained.
set 0.001.
A.3.1 PEAK-SEEKER BANDIT
Our peak-seeking bandit, given in Alg. iis heuristic that combines elements of UCB bandits (Auer ct al. 2002) with quantile-based bandit updates (David and Shimkin 2016).
Algorithm 2 Peak-Seeker Bandit for Adaptive Length Sampling
Require: Candidate lengths {m prior x:(0), quantile target 7. learning rate 7g- weights
(Wbest, Wquant), bandwidth a, exploration bonus c, temperature floor probability
1: while generating molecules do
2: For each arm k, track visit count Ng, best reward by, and rumning quantile estimate 9R.
3: Compute score $ş + Wbest b + Wquant + UCB(NN) + neighborhood Lbest, n4%))
4: For unvisited arms: use prior (0) as fallback
5:
Convert scores to probabilities pk x exp(sx/T). apply floor e, normalize
6:
Sample sequence length L ~ Categorical(p)
7:
Generate molecules of length and obtain reward r
8: Update Ng, by + max(b2, r). År by quantile SGD
9:
Update global best (Lbest; Tbest) if > Thest
10: end while
FFor the results in the consrandt generation and target property/lead optimization smaller model with 12 layers was used improve speed and reduce memory use.
13

---

Published as a conference paper at ICLR 2026
B ADDITIONAL EXPERIMENTAL RESULTS
B.1 DE Novo GENERATION
Validity and Uniqueness versus Diversity. Since the Quality metric represents combined sum- mary of Uniqueness and Validity, here we report the individual relationships between Uniqueness. Validity, and Diversity, as shown in Figures
102.0
100.0
97.5
95.0
Uniqueness
Validity
92.0
00.0
Gentol
SAFE-GPT
SAFE-GPT
85.0-
85.0-
InVirtoGeen (h=0:1)
(h=0.1)
IiVituoGen (hm0.01)
InVirtuGGen (hm0.01)
WVirtuoGen (h=0.001)
InVirtoGenn
80.0
0.750
0.775
0.000
0.255
0.850
0.500
8:525
800
0.750
0.775
0.800
0.855
Diversity
Diversity
(a) Validity versus Diversity
(b) Uniqueness versus Diversity
Figure 4: Trade-offs between Validity, Uniqueness, and Diversity in the generated molecules.
Sequence Length Distribution In Fig. 5 we show the sequence length distribution of ZINC250K. The maximum observed length 84, which implies that masked model would require up to 84 steps to produce a sample. In contrast, our discrete flow model with a uniform source decouples the number steps from the sequence length, allowing shorter sequences be refined more within the same compute budget.
Probabiiity
0.03
0.01
Sequence Length
Figure 5: Sequence length distribution of ZINC250K. The maximum observed length is 84, which implies that a masked model requires at least 84 sampling steps, putting close to our step size 0.01.
Non-Curated Samples In Fig. 6 provide non-curated samples from de novo generation with temperature T = 1 and randomness r = 0.
14

---

Published as a conference paper at ICLR 2026
Eoo andy aoto
goso grop Poft Xoo
plo aloa
Loso Pid soar cot play
poro cora ooooo
Figure 6: Non curated samples for de novo generation
15

---

Published as a conference paper at ICLR 2026
compare the quality versus diversity trade-off generated by sampling according to our proposed sampling method (Eq. and for the one proposed by Gat al. (2024) (Eq. 2 The benefit of increasing the sampling granularity disappears when standard sampling is used. In the following, we investigate possible causes for this.
Comparison of Sampling Methods In Fig.
90
Quality
Quality
70-
GenMal
GenMal
SAFE-GPT
50-
SAFE-GPT
InVirtunEen (h-0.1)
InvrrtuGeen (h=0.1)
40
InVirtuaGen (h-0.01)
40
InVrtunGan (h-0.01)
InVirtunGen (h-0.011)
InVirtuGeen (h-0.003)
5.925
0.000
Diversity
Diversity
(a) Our Sampling (Eq. 6
(b) Discrete Flow Model Sampling (Eq.
Figure 7: Comparison of the different sampling methods in terms of quality diversity.
Avg. token changes sequence
Durs i- 0.01
DFM é 0.003
0.003
Mean Piglk))
DFM
Ours 0.01
DFM h 0.001
Ours
5.2
0.5
1.
2.8
Time
Time:
(a) Evolution mean token probabilities (z.). (b) Average number of token changes per sequence. Figure 8: Dynamic behavior during sampling. Our method rapidly concentrates token probabilities and progressively reduces the number of token changes, while standard sampling (DFM) increases confidence linearly and keeps changes nearly constant.
We provide statistics aggregated from the sampling trajectories. As shown in Fig. 8a for our sampling method the probability density of the current tokens (1,)(x,) quickly saturates I, while for standard sampling (Eq(2 it increases almost linearly across steps. This difference is mirrored in the dynamics of token changes (Fig. (8)): our approach begins with many parallel updates that gradually decay into refinement phase, whereas standard sampling maintains nearly constant but low rate of changes throughout. Our decay pattern is closer to the intuitive notion of refinement, where the number of modifications decreases the sequence converges towards high-probabilit solution. Finally, the cumulative number of token changes (Fig. (9) highlights a fundamental distinction: DFM sampling yields step-size-invariant total number of modifications, effectively fixing the update budget, while our method scales with the granularity h. allowing more structured refinements when smaller steps used. The observation that the number of token changes independent of time granularity for standard DFM sampling provides a plausible explanation for the lack of improvement in standard sampling at higher resolutions.
Additionally, Figs. 10a and show QED and SA distributions across time resolutions h. Under sampling (Eq.6)) (). the QED distribution shifts markedly upward to higher values, while SA also seems to move smaller values (Figs. [0a [Obb.. In contrast, the standard discrete flow update (Eq, 2 more closely follows ZINC250K for both metrics (Figs. Ta ITb). This upward shift in QED and downward shift in SA under sampling method is consistent with the stronger quality-
16

---

Published as a conference paper at ICLR 2026
DFM
Ours
Total #Changes
500
500
100
1////A
0.001
0=0.11
Figure 9: Cumulative number of token changes per sequence for different time resolutions h. DFM sampling shows step-size invariance, while our method scales the number of refinements with stepsize
h.
distribution
distribution
Granularity
Time Granularity h- 0.001
h m00000
0.7
0.00
ZINC250K
0.6
2IC250K
Density
3-
Density
0.5
0.4
1-
1.0
QED
SA
(a) QED distributions (ours).
(b) SA distributions (ours).
Figure 10: Distributions of QED and SA for molecules generated with our sampling rule (Eq. at different time resolutions h. ZINC250K is shown dashed baseline.
frontier reported earlier. Although one might expect the generated distributions overlap with ZINC250K, it is important to emphasize that ZINC250K contributed only small fraction of the training data (2.5 x 10 molecules vs. 10 in total). The training dataset contains biological compoinds, which tend to be longer and complex and therfore exhibit higher synthetic accessibility. Moreover, the objective of our framework is not to reproduce the underlying training distribution but to generate drug- like molecules with optimized properties. Figure 12 compares standard sampling (Eq. 2 and
QED distribution
distribution
3.5
Time Granularity
Time Granularity b 0.003
0.00001
0.00
ZINC250K
ZNC2
2.5
Density
Density
1.5
1.0
0.5
0.1
0.0
0.0
0.4
0.8
1.0
QED
SA
(a) QED distributions (DFM).
(b) SA distributions (DFM).
Figure 11: Distributions of QED and SA for molecules generated with the standard discrete flow
update (Eq. 2 across different time resolutions h. ZINC250k is shown dashed baseline.
17

---

Published as a conference paper at ICLR 2026
sampling (Eq. 6 (T 1, 0). The left panel shows the average number of carbon atoms per sequence. Our sampling results in slightly higher carbon frequency. though the difference is modest.
The right panel reports the distribution of the number of fragments sequence, estimated from the maximal attachment index observed. Standard sampling produces higher fraction of sequences with many fragments, whereas our sampling shifts weight toward intermediate fragment counts. We hypothesize that this structural difference translates into improved drug-likeness, but further investigation is necessary.
Carbon Frequency
Number Fragments Sequence
26.0
17.5
Average per sequence
0.35
Stondard Sampling
Sampling
2cquente
15.0
0.30
Our Sompling
12.5
0.25
10.0
7.5
0.35
0.30
Standard Sampling
Semping
Number Fragments
Figure 12: Sampling comparison at temperature 1 and noise r O. Left: average number of carbon atoms sequence. Right: distribution of the number of fragments per sequence.
18

---

Published as a conference paper at ICLR 2026
show results obtained by training the same model as for the other novo generation experiments, but without timewtiigting the loss terms. While the performance under sampling with Eq. i nearly unchanged, the results with Eq. are significantly worse without time-weighting, showing that our modification has significant impact on the result.
Impact of Time- Weighting Loss In Fig. 13
100
100
80
80-
Quality
Quality
GenMol
GenMol
50-
SAFE GPT
50-
SAFE-GPT
InVrrtuGenn (h=0.1)
IntrruoGeen (h=0.1)
42
InVirtunGen (h-0.01)
InVrruuGeen (h-0.01)
InVirtuGGin 0.00.)
InVirtuEeen (h=0.003)
0.750
0.775
0800
0825
3.850
0.875
0.000
0.625
0,750
0.775
0
0825
0.550
0.875
0.000
0.525
Diversity
Diversity
(a) Our sampling (Eq.6))
(b) Discrete Flow Model sampling (Eq. 1
Figure 13: Quality-diversit trade-off without using the time-weighting T-yz of the loss, given in Eq.
Left: results from sampling with Eq. 6 Right: results from sampling with Eq.
Timing Studies To compare with GenMol, we also report results for the smaller 12-layer model used in the target-property optimization section. Its quality-diversity frontier is shown in Fig. [14] Sampling with time granularity h = 0.01 on an RTX 4090 yields 20.2 = 0.3 for 1000 samples. Using the same setup with GenMol (instantiated from the provided configuration rather than released checkpoint) we obtain 33.2 + 0.3 We emphasize, however, that speed is minor factor in drug discovery, since downstream steps such as docking or wet-lab experiments typically dominate runtime.
100
Quality
70-
60
GenMal
50
SAFE-GPT
InVirtunGen (h=0.1)
40
InVirtuoGen (h=0.01)
InVirtuoGen (h=0.001)
0.750
0.775
a 0.800
0.825
0.550
0.575
0.900
0.925
Diversity
Figure 14: Quieity-diversity frontier for the 12-layer model. At h = 0.01, Vn achieves higher maximum quality to GenMol while attaining substantially higher diversity in the high-quality regime.
19

---

Published as a conference paper at ICLR 2026
B.2 FRAGMENT-CONSTRANG GENERATION
We follow the benchmark of Noutahi et al. 2023). which uses fragments from ten known drugs, and evaluate five subtasks: linker design (connecting two or more terminal fragments with feasible linker), scaffold morphing (modifying the core scaffold while preserving pharmacophoric features), motif extension (growing a fixed motif with new substituents), scaffold decoration (attaching func- tional groups at predefined positions), and superstructure generation (assembling multiple fragments into a coherent larger molecule). In our notation, as for GenMol, linker design and scaffold morphing yield identical prompts and therefore identical results.
Updated comparison to prior work. In contrast to the results reported in the original GenMol paper, our analysis of the public implementation shows that the official Tugment-constraingg results for linker design and scaffold morphing are produced through a multi-step rejection- -iltiiiiniiiiigg proce- dure. This procedure discards invalid, unparsable, or non- matching generations and therefore inflates the observed quality and validity. To ensure a fair comparison, we instead report the more relevant single-step linker-design results released in the GenMol repository update, which do not rely on this filtering. We include these values for completeness and comparability with prior work only.
In Table[4 we present the fragment-constraine generation results for all methods. Averaging over all five tasks and three random seeds, our model achieves competitive performance in terms of both quality and diversity. While the validity is lower across all tasks, we emphasize that validity in isolation not the most informative metric in this benchmark. Validity and uniqueness contribute symmetrically to the quality metric, which more effectively captures the tradeoff between producing valid molecules and producing diverse ones. This avoids degenerate cases, such as models that repeatedly generate the same valid molecule. Moreover, lower validity can be compensated by generating additional samples, whereas low diversity or low quality cannot. For these reasons, we regard quality as the more practically meaningful metric. Finally, we note that GenMol tunes its generation parameters separately for each task, whereas our method uses a single unified parameter setting across all tasks.
Table 4: Performance across five fragment-constran generation tasks, averaged over three random seeds: motif extension, linker design, superstructure generation, scaffold morphing, and scaffold decoration. In our setup, similar as for GenMol, scaffold decoration is identical to linker design, so results are shared.
Task
Method
Diversity
Quality
Uniqueness
Validity
SAFE-GPT
0.56 0.003
18.60 + 2.100
66.80 1.200
96.10 1.900
Motif Extension
GenMol
0.62 0.002
30.10 + 0.400
77.50 0.100
82.90 + 0.100
InVirtuoGen
0.62 0.005
39.27 + 1.078
96.83 = 0.290
68.97 + 0.759
SAFE-GPT
0.55 0.007
21.70
1.100
82.50 = 1.900
76.60 + 5. 5.100
Linker Design
GenMol
0.53 0.002
4.30 1 0.400
97.80 = 0.500
16.70 0.2
InVirtuoGen
0.52 0.004
22.33 1.250
84.76
1.620
60.37 + 0.573
SAFE-GPT
0.51 + 0.011
16.70 + 2.300
70.40 5.700
58.90 + 6.800
Scaffold Morphing
GenMol
0.53 0.002
4.30 1 0.400
97.80 + 0.500
16.70 1 0.2
Vn
0.52 + 0.004
22.33 1.250
84.76 1.620
60.37 + 0.573
SAFE-GPT
0.57 + 0.028
14.30 + 3.700
83.00 5.900
95.70 + 2.000
Superstructure Design
GenMol
0.60 + 0.009
34.80 + 1.000
83.60
1.000
97.50 + 0.900
InVirtuoGen
0.73 = 0.001
27.43 1 0.953
99.41 = 051
75.70 1 0.898
SAFE-GPT
0.57 - 0.008
10.00 + 1.400
74.70 2.500
97.70 0.300
Scaffold Decoration
GenMol
0.59 0.001
31.80 - 0.500
82.70 1.800
96.60 + 0.800
VaVirtoGenn
0.56 + 0.003
36.37 1 1.096
88.58 = 1.130
90.70 1 0.616
SAFE-GPT
0.55 0.006
16.26 + 1.031
75.48 1.773
85.00 1.788
Average
GenMol
0.57 + 0.002
21.06 + 0.263
87.88 0.436
62.08 + 0.242
VnVirtuoGen
0.59 0.001
29.55 + 0.813
90.87 = 0. 0.445
71.22 + 0.399
In Fig. [5] we provide non-cherry picked samples for the fragment-conssraained generation task. The left-most figure in every row depicts the starting fragment(s).
20

---

Published as a conference paper at ICLR 2026
(a) Motif Extension
(b) Linker Design/Scaffold Morphing
(c) Superstructure Generation
(d) Scaffold Decoration
Figure 15: Non cherry-picked samples generated by VirtuoGen on fragment-constrained design tasks. The left-most figure in every depicts the starting fragment(s).
21

---

Published as a conference paper at ICLR 2026
B.3 TARGET-PROPERTY OPTIMIZATION
B.3.1 ABLATION STUDIES
In Table we show the results of ablation studies of the core components of our optimization framework. We include results for the following ablations:
Including the experience replay in the prescreened setting.
Sampling according to eq. [6 but with start time istart = 0.2.
Sampling according to eq.
Sampling sequence lengths from the Zinc250K distribution instead of using our Peak-Finder Bandit.
No mutation applied to the best performing molecules.
No PPO, relying only on the genetic algorithm.
No presereening, but leaving out the experience replay, yielding significantly lower performance.
A baseline without GA, mutation, or prescreening, which allows a fair comparison to REINVENT (Olivecrona et al. 2017) and slightly better performance.
As the table shows, the results obtained with our sampling method depend strongly on the start time of the trajectory simulation. We attribute this sensitivity to the dynamics in Fig. [b) at early times many positions are simultaneously updated, which can diminish the performance gains provided by the genetic algorithm component. And because we did not want to tune our parameters, we stuck to sampling according to Eq 2
22

---

Published as a conference paper at ICLR 2026
No Prescreen, No Prompler, No Mutation, No Prescreen
0. 0.851
0.547
0.768
0.659
0.950
0.735
0.867
0.857
0.798
0.701
0.308
0.241
0.764
0.802
0.463
0.941
0.762
0.522
0.324
0.465
0.418
0.150
0.458
14.349
Table 5: Ablation study results on the PMO benchmark. We report the AUC-1op10 scores from single runs. Best results are highlighted in bold.
No Experience Replay
0.969
0.679
0.834
0.651
0.984
0.852
0.949
0.971
0.888
0.825
0.342
0.304
0.723
0.864
0.627
0.943
0.840
0.619
0.693
0.620
0.434
0.000
0.520
16.131 131
No PPO
0.881
0.755
0.815
0.943
0.986
0.853
0.972
0.974
0.834
0.889
0.363
0.363
0.962
0.858
0.682
0.943
0.816
0.595
0.546
0.526
0.836
0.715
0.653
17.758
No Mutation
0.928
0.777
0.758
0.970
0.986
0.834
0.976
0.967
0.851
0.807
0.370
0.331
0.963
0.857
0.695
0.943
0. 0.807
0.790
0.457
0.588
0.833
0.766
0.576
17.831
No Bandit
0.991
0.764
0.785
0.988
0.995
0.913
0.992
0.978
0.919
0.917
0.385
0.377
0.983
0.868
0.710
0.944
0.866
0.657
0.738
0.625
0.855
0.927
0.605
18.782
Sampling with eq. 6
0.972
0.801
0.795
0.973
0.995
0.879
0.987
0.986
0.871
0.881
0.370
0.367
0.986
0.870
0.696
0.943
0.843
0.648
0.613
0.542
0.812
0.891
0.643
18.364
Sampling with oq. 6 fsttrt = 0.2
0.975
0.795
0.866
0.965
0.995
0.870
0.989
0.986
0.882
0.917
0.379
0.386
0.986
0.868
0.753
0.943
0.840
0.632
0.766
0.625
0.859
0.906
0.654
18. 836
With Experience Replay
0.993
0.813
0.872
0.960
0.995
0.908
0.990
0.989
0.876
0.892
0.382
0.333
0.992
0.878
0.733
0.943
0.878
0.654
0.772
0.685
0.870
0.870
0.617
18.893
isomers e9h Onmoo2ppeel
sitagliptin mpo thiothixene rediscovery
troglitazone rediscovery ever
celecoxib rediscovery
mestranol similarity
albuterol similarity
fexofenadine ipo
isomers ch8n222
amlodipine mpo
osimerinib mpp
perindopril mpoo ged
ranolazine mpo scaffold hop
valsartan smarts zalep paleplon mpo
Oracle
deco hop
modianl
median2
drd2
gsk3b
jnk3
Sum
23

---

Published as a conference paper at ICLR 2026
100
MM
-08550
0.825
0.800
70-
Avg Top 10 AUC
Validity
-0.775
60
-0.750
50
0.725
40
30
Validity (Seed=0)
-0.700
Validity (Seed=2)
AUC (Seed=00
AUC (Seed=2)
-0.675
2000
2000
10000
Number of Oracle Calls
Figure 16: Validity versus Number Oracle Calls
B.3.2 VALIDITY VS ORACLE CALLS
In Fig. 16 we illustrate the potential instability of our optimization routine. The plot shows both the fraction of valid samples and the top-10 AUC as functions of the number of oracle calls. We report two runs with identical configurations that differ only in their random seed. While one run remains stable throughout optimization, the other exhibits signs of policy collapse. Interestingly, the collapsing achieves higher top-10 10 AUC, pattern repeatedly observed. We attribute this behavior to an overly exploitative optimization regime, and addressing this this- pots--tlll through stabilizing techniques such proposed by Xi et al. 2025 is an important direction for future work.
B.4 LEAD OPTIMIZATION
We provide the results obtained when not requiring similarity to the seed molecule in Tab. showing that performance improves significantly when this restriction is removed. Constraints on diug-liseness and synthesizability are still enforced.
24

---

Published as a conference paper at ICLR 2026
Table 6: Docking scores (lower is better) averaged over 3 seeds. Bold indicates the best result per seed. For each seed molecule, its docking score, quantitative estimate drug-likeness and synthetic accessibility is given.
Protein (DSQEENSSA
No sim
In VirtuoGen
5htlb
03510-438/3.05
-12.5 (21.0)
29
-13.4 (10.5)
13.0 (20.3)
braf
29.30.238/2009
-12.5 (#00.2)
.9.40.346/249
-12.3 (#0.8)
988025552.3
12.2 (1:0.)
fa7
6.00.264/2.29
-9,9 (1:0.4)
4.700 186/3.90
-10.2 (2:0.5)
1662.1556..66
-9.4 (1:02)
jak2
7..00.225/288
-2.0 (+-0.3)
8.00.712/3.09
-12.1 (+:0.2)
3.600.92/3110
-1.66 (+0.7)
parp1
-7.00.8882.61
-13,5 (2:0.2)
778007582..74
-13.3 (2:0.7
4220438221
-13.5 (#:0.5)
Sum
-181.4
25

---

Published as a conference paper at ICLR 2026
Condition
QED=0.30
20
QED=0.40
QED=0.50
QED=0.60
QED-0.70
QED=0.80
15
QED=0.90
Density
10
5-
0.0
0.2
0.4
0.6
0.8
1.0
QED
Figure 17: QED Distribution for QED-Conditioned Samples
B.5
CONDITIONAL GENERATION VERSUS TARGET PROPERTY OPTIMIZATION
Here briefly clarify the conceptual and practical differences between conditional generation and our target-property optimization framework. Conditional generation provides a model with an explicit property value (for example, desired LogP or QED level) as additional input during training as prior work explored (Lim et al.] (2200] (Seo et al. (023). In our implementation, the condition passed through a small neural module and added the timestep embedding. Recent advances further introduce explicit guidance mechanisms for discrete flow models (Nisonoff et al. (025), which could potentially improve the results adherance further. Figure Figure depiicts the results obtained from fine-tur munitu model with conditional inputs. The model produces QED distributions that shift consistently with the provided conditioning input, confirming that the model can guided toward desired property regimes.
26


Reviews:
[{"review_id": "TC9O7jHY34", "reviewer": "Reviewer_EgpW", "summary": "This paper introduces InVirtuoGen, a novel generative model for fragment-based drug discovery. The core contribution is a paradigm shift from \"auto-regressive\" used by SAFE-GPT or \"completion\" used by GenMol to \"refinement.\" Authors investigate the model performance on four drug discovery tasks: de-novo generation, fragment-constrained generation, property optimization, and lead optimization. The method achieves a superior quality-diversity pareto frontier in de novo generation and sets a new state-of-the-art (SOTA) on the Practical Molecular Optimization (PMO) benchmark under both 260k and 10k oracle calls.\n\nHowever, there are some concerns, and I would like to increase the score depending on the response.\n\n---\n**Usage of LLM:** I wrote the entire review myself and only used the LLM to correct the grammar and improve readability.", "questions": "- Line 153: How is `c1ccccc1` tokenized? `c1` or `c`&`1`?\n- Line 283: As I know, GenMol cut an arbitrary single bond in molecules to create offspring. Since this cutting can be conducted with a reaction template, it does not restrict the chemical space.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 1, "contribution": 3, "strengths": "- **Novel & Versatile Generation Paradigm**: Authors proposed a novel paradigm for molecular generation. In particular, it is different previous auto-regressive approach or unmasking approach.\n\n- **Commitment to Fair Benchmarking**: A major strength is the paper's transparent and fair evaluation. For the PMO benchmark, the authors correctly identify that prior SOTA models (GenMol, f-RAG) used a 250,000-call pre-screening step without fully accounting for it. This paper reports results in both settings (with and without pre-screening), providing a much fairer comparison against all baselines (e.g., Genetic GFN) and restoring integrity to the benchmark.\n\n- **Transparency in Reporting Failures**: The authors are commendably transparent about the model's full capabilities, rather than cherry-picking only successful tasks. They include a detailed analysis of fragment-constrained generation, a task where the model performs poorly and its validity drops significantly. This transparency provides valuable insights into the model's \"philosophy\" and its operational boundaries.", "weaknesses": "**1. Lack of Conditional Generative Capabilities**\n\nThe paper successfully employs a PPO-based fine-tuning strategy for property optimization. However, unlike baseline model SAFE-GPT, authors do not investigate conditional generative capabilities proposed by Scaffold-GGM[1] and BBAR[2]. The ability to control key molecular properties directly (e.g., \"generate a molecule with LogP = 2\") is an important task. Demonstrating this capability would have significantly strengthened the paper's claim of being a \"versatile generative foundation.\"\n\n**2. Misleading Paper Structure**\n\nThe paper's structure is misleading. The fragment-constrained generation task is presented early (Section 3.2, Table 1), suggesting it is a core capability. However, this task yields extremely low molecular validity (e.g., 28.6% for superstructure design) and, as the authors rightly admit, fundamentally \"conflicts with the refinement philosophy.\" This prominent placement of a failed task creates significant doubt about the model's reliability. I suggest moving this section to the last section of manuscript or appendix in a camera-ready version.\n\n**3. Lack of validity metrics**\n\nRelated to W2, authors did not report independent validity metrics for its other, more successful tasks (de novo generation and property optimization). In the de novo task (Sec 3.1), validity is conflated with other metrics inside the \"Quality\" score, making it impossible to assess the base generative success rate. In the optimization tasks (Sec 3.3, 3.4), only the final scores of successful molecules are reported, giving no insight into the efficiency of the process (i.e., how many invalid molecules were generated and discarded to achieve those scores). This omission is significant, as it prevents a full assessment of the model's generative reliability in its primary use cases.\n\n---\n**References:**\n1. Lim, Jaechang, et al. \"Scaffold-based molecular design with a graph generative model.\" Chemical science 11.4 (2020): 1153-1164.\n2. Seo, Seonghwan, Jaechang Lim, and Woo Youn Kim. \"Molecular generative model via retrosynthetically prepared chemical building block assembly.\" Advanced Science 10.8 (2023): 2206674.", "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": "hHkjA7KhRu", "reviewer": "Reviewer_BEHY", "summary": "This submission investigates the problem of drug discovery, more specifically fragment-based drug discovery. The authors present a method called InVirtuoGen, which adopts the discrete flow model framework of Gat et al., 2024 and a slightly modified version of the SAFE framework of Noutahi et al., 2023 for molecule representation. The main contribution of the submission is the proposed method for Target Property Optimization on top of the Discrete Flow Model. This method combines a genetic algorithm for faster convergence with PPO-based Reinforcement Learning for gradient-based optimization. Experiments were performed on benchmarks for de novo (unconstrained) generation, fragment-constrained generation, target property optimization, and  lead optimization. Experimental results are supportive.", "questions": "InVirtuoGen proposes a discrete flow model that transforms a uniform source distribution over all tokens into molecular data. How is this different from starting with uniform prior, rather than a masked prior commonly done (https://arxiv.org/pdf/2402.04997)?\n\nMost experimental results for the baselines were copied from the original publications. How did you ensure that the experimental designs are identical and the experimental results comparable?\n\nPlease perform experiments with other SOTA methods!", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The submission focuses on the practically important tasks of molecule optimization instead of de novo molecule generation. \n\nInVirtuoGen proposes a discrete flow model that transforms a uniform source distribution over all tokens into molecular data. The simultaneous generation of the whole molecule is beneficial for optimization tasks.\n\nIt enables longer generation trajectories, where the quality improves with more refinement steps.\n\nInVirtuoGen integrates Genetic Algorithm + PPO for target-conditioned and goal-directed optimization, a novel hybrid scheme that combines the strengths of both ingredients.\n\nStrong experimental results on high-diversity generation benchmarks, in particular for property optimization and lead optimization.", "weaknesses": "The number of baselines compared with experimentally is small (2 and 3, respectively), and the credibility of the experimental results would be significantly strengthened by comparing with more SOTA methods.\n\nIt remains unclear whether the experimental results for the baselines copied from the original publications are comparable with the experimental results obtained for InVirtuoGen by the authors.\n\nLimited intuition for why validity is lower than GenMol or SAFE-GPT, even though quality metrics (valid, unique, QED ≥ 0.6) are higher.\n\nAppears better suited for de novo or goal-directed generation, rather than fragment-constrained generation — GenMol’s masked diffusion approach respects constraints more effectively.", "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": "xgKAqxNkph", "reviewer": "Reviewer_yXLN", "summary": "This paper presents InVirtuoGen, a discrete flow–based molecular generator that refines fragmented SMILES strings rather than completing them autoregressively. The model starts from a uniform source and learns a refinement process that updates all tokens simultaneously. It integrates a genetic algorithm for initial candidate recombination and a PPO-based fine-tuning scheme for property optimization, achieving state-of-the-art results on PMO and competitive lead optimization performance.", "questions": "1. How does the proposed refinement training compare in sample efficiency to off-policy methods like GFlowNets?\n\n2. Does the PPO fine-tuning use off-policy data reuse (e.g., replay) or purely on-policy updates, and how does that affect stability?\n\n3. Could the refinement framework be extended to stochastic sampling or energy-based objectives for better exploration?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Proposes a novel refinement-based discrete flow paradigm that departs from completion-style generation.\n\n2. Strong empirical results across de novo, fragment-constrained, and property optimization tasks.\n\n3. The GA + PPO hybrid optimization design is elegant and practically effective for sample-efficient molecular search.", "weaknesses": "1. The sampling modification (Eq. 6) lacks theoretical justification and deviates from formal flow definitions.\n\n2. Fragment-constrained generation is not well-aligned with the model’s refinement philosophy, showing lower validity.\n\n3. Limited analysis of training stability and efficiency vs. on-policy/off-policy baselines (e.g., GFlowNets, diffusion models).", "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": "y5ldNALiBd", "reviewer": "Reviewer_eGk6", "summary": "Through this paper, the authors propose InVirtuoGen, a discrete flow generative model for fragmented SMILES for de novo and fragment-constrained generation, and target-property/lead optimization of small molecules. Specifically, InVirtuoGen learns to transform a uniform source over all possible tokens into the data distribution by refining the sequence.", "questions": "Please see the *Weaknesses* section for my main concerns.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 1, "presentation": 1, "contribution": 1, "strengths": "- The authors provided the codebase.", "weaknesses": "I will combine the *Weaknesses* section and the *Questions* section. My concerns are as follows:\n- The main weakness of this paper is its weak novelty. The method section is completely missing. The proposed InVirtuoGen framework is a combination of a discrete flow model (Section 2.1) and the fragmented SMILES notation (Section 2.2). Only the latter corresponds to the invention of this work, but its contribution appears to be very minor.  The new notation is very similar to the SAFE notation [1], and its advantages over the SAFE notation is not described. The sentence “Our notation preserves fragment integrity while providing explicit attachment point numbering” is included in the caption of Figure 2, but this also applies for the SAFE notation. Overall, I am not convinced that this work provides a significant contribution from an ML perspective compared to previous methods in the domain.\n- The proposed InVirtuoGen framework shows very low molecular validity in the fragment-constrained generation tasks (Table 1).\n\n---\n\n**References:**\n\n[1] Noutahi et al., Gotta be safe: A new framework for molecular design, ArXiv, 2023.", "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)