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One Sequence, Many Decodings: CAGenMol-2 Recasts Drug Design as Masked Molecular Inference

Yanting Li, Enyan Dai, Lei Wang, Wen-Cai Ye, Li Liu

Year: 2026Venue: arXiv preprintArea: cs.LGType: PreprintEmbeddings: 113

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Abstract

Abstract:Drug design couples property evaluation, conditional generation, structure-based design, and local optimization, yet machine learning systems typically address these capabilities with separate task-specific models. We introduce CAGenMol-2, a masked diffusion molecular language model that represents molecules, continuous scalar properties, and 3D protein pockets within a single wrapped sequence. Within this pretrained interface, downstream operations are selected by which sequence regions are observed or masked at inference, allowing one checkpoint to perform property prediction, property- and pocket-conditioned generation, and partial-constraint design without task-specific architectures or backbone fine-tuning. We further propose Adaptive Fragment Optimization (AdaFO), a gradient-free mask-and-refill search that turns the masked decoder into an iterative local molecular optimizer. On CrossDocked2020, AdaFO increases Success Rate from 30.2\% to 70.8\%, the best reported under this protocol, while largely preserving drug-likeness and diversity. Finally, scaffold-preserving directional editing and CRBN/VHL case studies demonstrate its use in compound design workflows spanning local molecular editing, structure-based prioritization, and downstream simulation-based screening.

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One Sequence, Many Decodings: CAGenMol-2 Recasts Drug Design as Masked Molecular Inference Yanting LI 1 , Enyan DAI 1 , Lei WANG 2 , Wen-Cai Ye 2 , Li LIU 1 , 1 The Hong Kong University of Science and Technology (Guangzhou), 2 Jinan University, Guangzhou Correspondence: avrillliu@hkust-gz.edu.cn Abstract Drug design couples property evaluation, con- ditional generation, structure-based design, and local optimization, yet machine learning sys- tems typically address these capabilities with separate task-specific models. We introduce CAGenMol-2, a masked diffusion molecular language model that represents molecules, con- tinuous scalar properties, and 3D protein pock- ets within a single wrapped sequence. Within this pretrained interface, downstream opera- tions are selected by which sequence regions are observed or masked at inference, allow- ing one checkpoint to perform property pre- diction, property- and pocket-conditioned gen- eration, and partial-constraint design without task-specific architectures or backbone fine- tuning. We further propose Adaptive Frag- ment Optimization (AdaFO), a gradient-free mask-and-refill search that turns the masked decoder into an iterative local molecular op- timizer. On CrossDocked2020, AdaFO in- creases Success Rate from 30.2% to 70.8%, the best reported under this protocol, while largely preserving drug-likeness and diversity. Finally, scaffold-preserving directional editing and CRBN/VHL case studies demonstrate its use in compound design workflows spanning local molecular editing, structure-based pri- oritization, and downstream simulation-based screening.Code:https://github.com/ Lee612-1/CAGenMol-2 1 Introduction Drug design is a multi-step process that repeatedly combines property evaluation, conditional gener- ation, structure-based design, and local molecu- lar optimization. Yet most machine learning ap- proaches address these capabilities with separate task-specific models (Gómez-Bombarelli et al., 2018; Jin et al., 2018; Olivecrona et al., 2017; Polykovskiy et al., 2020). This fragmentation com- plicates design workflows, where molecules and constraints must be transferred across models with different representations, objectives, and inference procedures. A unified model is therefore useful for making these operations directly composable within a shared molecular representation. Molecular language models offer a natural route to such unification, and prior autoregressive or instruction-tuned models have shown that regres- sion, generation, and other molecular tasks can be cast as sequence prediction or prompting (Born and Manica, 2023; Fang et al., 2024; Yu et al., 2024). However, composing prediction, condition- ing, generation, and local editing within a single inference interface remains challenging. In partic- ular, molecular strings cannot naturally represent 3D protein pockets; ordinary tokenization does not explicitly preserve numerical proximity for contin- uous objectives (Golkar et al., 2023; Zhou et al., 2025); and left-to-right decoding is ill-suited to arbitrary observation patterns or local molecular infilling. Masked diffusion instead allows arbitrary sequence regions to be observed or hidden and par- tially masked molecules to be reconstructed with- out a fixed generation direction (Sahoo et al., 2024; Lou et al., 2024). This motivates our central prin- ciple: treating the task as a property of the mask rather than the architecture. We introduce CAGenMol-2, a masked diffusion molecular language model that instantiates this principle through a unified wrapped-sequence inter- face. CAGenMol-2 represents molecules, continu- ous scalar properties, and optional protein-pocket information within a single wrapped SAFE se- quence (Noutahi et al., 2024). Scalar properties occupy continuous value slots, while 3D protein pockets are compressed into a small set of learn- able pocket tokens using a frozen structural en- coder (Gao et al., 2023; Zhou et al., 2023). Rather than training a separate sequence format for each task, we expose the model during pretraining to the same region-level observation patterns used at infer- arXiv:2609.34301v1 [cs.LG] 28 Sep 2026 Properties PocketSAFE Tokens 3D Pocket Encoder SAFE Tokenizer QED SA MW logP MR Value Encoder Sequence Properties PocketSAFE Tokens SAFE TokensPocket PocketSAFE Tokens PocketSAFE Tokens Properties PocketSAFE Tokens De novo Property-conditoned Ligand Ligand with Properties Properties Properties Properties Property Prediction Value Decoder Value: ... Confidence: .... LM Head F1c(NC=O)c1 Pocket Token Property Token Masked Token Unmasked Token Transformer Blocks Different Heads F c 1 c ( ) N C = O c c c c 1 c ( c F c 1 c ( ) N = c c c 1 F c 1 ( N = c c c F c 1 ( = c t=1t=0 (A)(B) Figure 1: Overview of CAGenMol-2. (A) Molecules, scalar properties, and 3D protein pockets are mapped to role-tagged blocks within a single wrapped SAFE sequence via a tokeniser, value encoder, and frozen 3D encoder, respectively. At inference, varying the visible and hidden (grey) blocks recovers multiple tasks from a single checkpoint, where target blocks (colored borders) are decoded into tokens or continuous scalars with confidence. (B) The wrapped sequence is processed by a shared transformer backbone. The lower timeline illustrates a masked- diffusion trajectory unmasking the molecular block from t=1 to t=0 under a fixed condition prefix. ence. Consequently, property prediction, property- conditioned generation, pocket-conditioned gener- ation, and partial-constraint design become differ- ent masking configurations of the same pretrained model rather than separately trained task pipelines. The same masked reconstruction operator natu- rally supports local molecular optimization. We therefore introduce Adaptive Fragment Optimi- sation (AdaFO), a gradient-free inference-time optimiser that adaptively masks and refills lo- cal fragments while preserving their surround- ing context. Combined with external docking and drug-likeness objectives, AdaFO turns pocket- conditioned generation into iterative molecular op- timization (Trott and Olson, 2010; Alhossary et al., 2015; Bickerton et al., 2012; Ertl and Schuffen- hauer, 2009). On 100 held-out CrossDocked2020 pockets (Francoeur et al., 2020), it improves the base model’s Success Rate from30.2%to70.8%, while largely preserving drug-likeness and diver- sity.AdaFO-S further combines native prop- erty prediction, confidence, and contrastive token saliency for scaffold-preserving directional edit- ing, while CRBN and VHL case studies connect AdaFO-generated molecules to downstream dock- ing and simulation-based candidate prioritization. Our contributions are: (1) a unified wrapped- sequence formulation and masking-consistent pre- training strategy that represent molecular structures, continuous properties, and protein pockets within a shared observation-and-reconstruction interface; (2) AdaFO, which reuses masked reconstruction for gradient-free local search and extends it with confidence- and saliency-guided molecular edit- ing; and (3) the composition of these capabili- ties across unconditional and conditional gener- ation, native property prediction, structure-based drug design, directional editing, and CRBN/VHL candidate-prioritization workflows. 2 Related Work Molecular Language and Diffusion Models. Molecular language models support multi-task prediction and generation through masked or instruction-based sequence modeling, including joint regression, conditional generation, and broader prompted molecular tasks (Born and Man- ica, 2023; Fang et al., 2024; Yu et al., 2024). Dis- crete diffusion further enables flexible non-left-to- right reconstruction, including molecular sequence generation, fragment remasking, and condition- aware optimization (Austin et al., 2021; Lou et al., 2024; Sahoo et al., 2024; You et al., 2025; Noutahi et al., 2024; Lee et al., 2025; Li et al., 2026). Our work extends these ideas by unifying continuous properties, protein-pocket conditions, and molec- ular regions within a shared masking-based infer- ence interface. Structure-Based and Optimization-Driven De- sign. Structure-based molecular generation of- ten models explicit 3D atomic geometry in protein pockets (Guan et al., 2023a; Peng et al., 2022; Jain et al., 2023; Liu et al., 2022; Zhang et al., 2023), while fragment-sequence methods combine molec- ular fragments with pretrained pocket representa- tions (Fu et al., 2025). Non-differentiable molec- ular objectives are commonly optimized using re- inforcement learning (Loeffler et al., 2024; Zhou et al., 2019; Wang et al., 2024) or evolutionary search (Yoshikawa et al., 2018; Spiegel and Dur- rant, 2020; Jensen, 2019). AdaFO instead reuses the masked decoder as a local mutation operator for inference-time fragment refinement without per- target parameter updates. Property Prediction and Uncertainty Quantifi- cation. Molecular property prediction typically fine-tunes graph or transformer representations for regression (Chithrananda et al., 2020; Zhou et al., 2023). Continuous-value representations instead preserve numerical structure beyond ordinary tok- enization (Golkar et al., 2023; Zhou et al., 2025). Gaussian likelihoods and selective prediction fur- ther show that confidence can support ranking even when imperfectly calibrated (Nix and Weigend, 1994; Geifman and El-Yaniv, 2017; Amini et al., 2020; Fort et al., 2019). In CAGenMol-2, contin- uous scalar prediction and rank-useful confidence are learned jointly with molecular generation and reused by AdaFO-S for adaptive local editing. 3 Method CAGenMol-2 is a masked diffusion molecular language model operating on wrapped SAFE se- quences. Its core principle is to treat the task as a property of the mask rather than the architecture: depending on slot visibility, the same sequence can be decoded as a molecule, scalar properties, or a partially observed design query. We first define this sequence interface, followed by the encoding components for numbers and protein pockets, the masking-consistent pretraining objective, and the AdaFO inference-time optimiser. 3.1 Wrapped Molecule Sequence Following prior work, we represent molecules us- ing SAFE (Noutahi et al., 2024), a fragment-based notation that imposes strong chemical priors and prevents local invalidity, overcoming the limita- tions of SMILES (Weininger, 1988; Krenn et al., 2020). Lets 1:L denote the SAFE tokens of a molecule. We wrap each example into a single unified sequence containing three role-tagged re- gions: an optional pocket block, a scalar-property block, and a molecular block. The molecule-only layout is defined as: [BOS]b 1 v 1 e 1 ·b K v K e K [BOM]s 1:L [EOM] [EOS], where each scalar property occupies an address- able value slotv k bounded by a property-specific begin markerb k and end markere k . We employ K = 6property slots: logP, MW, QED, SA, MR, and one reserved slot. When a protein target is present, a pocket block[BOPK]q 1 q 2 q 3 q 4 [EOPK] is prepended to the property block. Molecule-only examples omit this pocket block, whereas pocket- conditioned examples whose structural condition is dropped replace the pocket features with learned unknown embeddings. Within this predefined interface, native predic- tion and generation operations are selected by the visibility of the corresponding sequence regions without changing the model or sequence. Specifi- cally, masking the molecular block while observing property slots enables property-conditioned gen- eration; conversely, masking the properties while keeping the molecule visible yields property predic- tion. Partial observations naturally support multi- constraint or pocket-conditioned molecular design. 3.2 Model Architecture The model backbone is a standard bidirectional Transformer encoder operating as a shared se- quence processor, following design of BERT (Vaswani et al., 2017; Devlin et al., 2019). Task be- havior is therefore determined primarily by how heterogeneous scientific signals are represented within the wrapped sequence and which regions are observed at inference. Continuous Value Encoding. To preserve the continuous structure of scalar properties, each raw value is firstz-normalised using fixed statistics. The normalised scalarzis then mapped to a con- tinuous embedding via z-space Fourier features: φ(z) = sin(2πz/T i ), cos(2πz/T i ) 4 i=1 ∥z, followed by a two-layer MLP to match the hidden dimension. This design adapts Fourier number em- beddings (Zhou et al., 2025) and continuous value encoding (Golkar et al., 2023) to the scalar slots while retaining the raw normalised magnitude. We use periodsT i ∈0.5, 1, 2, 4in normalised space. Unobserved or masked properties are replaced by learned unknown embeddings at their respective slots, explicitly distinguishing prescribed numeri- cal targets from unspecified conditions. Pocket Representation. For protein targets, we leverage the per-atom representations from a frozen DrugCLIP encoder (Gao et al., 2023) backed by a 3D Uni-Mol architecture (Zhou et al., 2023). To maintain a compact and constant sequence foot- print, a lightweight adapter projects the per-atom features and pools them into exactly four tokens via cross-attention. Specifically, four learnable query vectors attend over the per-atom representations, utilizing a key-padding mask to exclude padded atoms, followed by a feed-forward block with resid- ual layer normalisation. This fixed-token bottle- neck allows pocket-conditioned and molecule-only examples to coexist in the same training batch. For pocket-conditioned rows whose structural condi- tion is dropped, the pocket slots are filled with learned unknown embeddings. Property Decoder. The hidden states at the scalar slots are read by a dual-headed MLP prop- erty decoder. For each property, this shared head parameterises a Gaussian output by directly predict- ing a meanμand a log variancelogσ 2 in the nor- malised space. During inference, these are mapped back to physical units, and the normalised standard deviation is converted into a bounded confidence scorec = exp(−σ norm ), which serves as a ranking signal for downstream editing. Crucially, all conditions are injected directly into their reserved sequence positions via embedding replacement. Consequently, different task config- urations reuse the same backbone and modality- specific output heads; they differ primarily in which sequence regions are observed or hidden. 3.3 Masking-Consistent Pretraining The wrapped interface defines native tasks through region-level visibility, so pretraining exposes the model to the corresponding observation patterns used at inference. We jointly train molecular recon- struction and property prediction using two asym- metric masking regimes: (1) Prediction Regime (p clean = 0.15): the dif- fusion time is sampled ast∼U (ε, 0.05), keeping the molecular block nearly intact, while allK = 6 property slots are hidden. This regime trains the model to predict physical properties from an ob- served molecular structure. (2) Conditional-Generation Regime (1 − p clean = 0.85 ): the molecular block is corrupted via masked discrete diffusion att∼U (ε, 1), while each property slot is independently observed with probabilityp keep = 0.75. This trains the decoder to reconstruct molecular structures under arbitrary subsets of observed property constraints. Superimposed on both regimes, with probabil- ityp uncond = 0.10, the entire conditioning prefix (pocket and properties) is replaced by unknown em- beddings, providing the unconditional path used for classifier-free guidance (CFG) (Ho and Salimans, 2021) at inference. The full objective isL = L tok + λL prop with λ = 0.4. The token lossL tok is the standard continuous-time MDLM negative log-likelihood restricted to the molecular block. The property lossL prop is active on hidden, loss-active prop- erty slots within the prediction regime:L prop = Huber δ (μ,z) + w n 2 h logσ 2 + (z−μ) 2 σ 2 i +w r L rank . whereμis the predicted mean for a normalised targetz. We clamplogσ 2 to[−10, 4]for numer- ical stability. The pairwise margin lossL rank pe- nalises incorrect relative orderings of property mag- nitudes, discouraging degenerate solutions that fail to preserve target ordering. We setw n = 0.5and w r = 0.2. The reserved sixth property slot carries no property loss. 3.4 Adaptive Fragment Optimisation Because the pretrained model supports partial ob- servation, its masked reconstruction mechanism can also serve as a local proposal operator for molecular search.We build on this property with Adaptive Fragment Optimisation (AdaFO), a gradient-free evolutionary inference-time opti- mization loop that treats mask-and-refill decoding as a structured mutation operator. Formally, AdaFO maintains a candidate pool P t at iterationt. To select elite parents while preventing a greedy sort from collapsing popu- lation diversity, we rerank the pool using Maxi- mal Marginal Relevance (MMR) (Carbonell and Goldstein, 1998) over Morgan fingerprints (Rogers and Hahn, 2010). This explicitly penalizes near- duplicates, preserving diverse molecular scaffolds during search. For each parents, a local fragment of lengthαLis masked, and children are sampled: s ′ ∼ p θ (s mask | s ,c),wherecis the observed condition. The mutated children are filtered by score to prevent low-quality variants from diluting the pool before being merged back. The mutation radiusαis adaptive, with its sched- ule determined by the optimization setting. For pocket-conditioned molecular optimization, the external reward balances binding affinity with drug-likeness:r(s;p) = − V (s;p)− V ref (p) + w q Q(s) + w a A(s)− η⊮[dock fails]whereV,Q, andArepresent affinity, QED, and SA scores, re- spectively. The upper bound of the mask fraction αis linearly annealed across iterations, allowing broader edits early in the search and progressively more local edits later. When the model itself acts as the oracle, AdaFO- S performs directional editing using only its in- trinsic signals. Given a seeds 0 and targety ⋆ = y j (s 0 )± ∆σ j , candidates are scored byr j (s) = −|ˆy j (s)− y ⋆ |/σ j + β,τ (s,s 0 ) whereτ (s,s 0 )de- notes the Tanimoto similarity to the seed andβ controls scaffold preservation. The mutation radius α(s)is adapted from target error and predictive confidence: u(s) = min |ˆy j (s)− y ⋆ | σ j , 3 + (1− c j (s)), α(s) = α min + u(s) 4 (α max − α min ). AdaFO-S localises the edit using contrastive to- ken saliency, s i = logp θ (x i | x ,∅)− logp θ (x i | x ,y ⋆ ), which measures how strongly the target condition disfavors the current token. It masks the width- α(s)Lwindow with the largest summed saliency and regenerates it undery ⋆ . So confidence controls the edit size, while saliency controls its location. 4 Experiments We evaluate whether CAGenMol-2 can support both basic and compound molecular-design be- Fragment Vocabulary Score Vocabulary Evolution Generate &Filter Expand MMR Top-K Parents ... Seed Pool Scored Pool AdaFO Figure 2: AdaFO Refinement Loop: score the pool, rerank by MMR diversity, keep Top-Kparents, and mask-and-refill fragments to generate children. Mask- ing is annealed for pocket-conditioned optimization and confidence-driven by unsuretyufor directional editing. Top children are filtered back into the pool. haviors. Our experiments address five core ques- tions: (1) whether joint training preserves uncon- ditional molecular generation; (2) whether arbi- trary subsets of property constraints can control generation; (3) whether the model provides accu- rate native property prediction, rank-useful confi- dence, and transferable molecular representations; (4) whether AdaFO transforms pocket-conditioned generation into competitive structure-based design; and (5) whether these capabilities compose into local-editing and design-to-screening workflows. Unless stated otherwise, all results are based on the same pretrained model. Implementation and experimental details not covered in the main text are provided in Appendix. 4.1 De Novo Generation A unified model should preserve its foundational generative capacity while acquiring additional con- ditioning and prediction capabilities (Brown et al., 2019).Following the GenMol protocol (Lee et al., 2025), we sampled 1000 molecules over three random seeds per setting to evaluate valid- ity, uniqueness, quality (QED≥ 0.6, SA≤ 4), and fingerprint-based diversity. As shown in Figure 3, CAGenMol-2 closely tracks the GenMol quality–diversity frontier across decoding settings, matching or slightly exceeding it in the high-quality regime. This indicates that the model largely preserves its unconditional gen- 0.820.840.860.880.90 Diversity 40 50 60 70 80 Quality (%) (0.5, 0.5) (0.5, 1.0) (0.5, 10.0) (1.0, 10.0) (1.5, 10.0) De novo qualitydiversity trade-off SAFE-GPT GenMol CAGenMolv2 Figure 3: Quality–diversity Pareto frontier for de novo generation. Despite joint training with property and pocket conditioning, CAGenMol-2 closely tracks the GenMol frontier. erative capability despite only limited de novo gen- eration data during joint training with property pre- diction and pocket conditioning. 4.2 Property-Conditioned Generation We next evaluate whether CAGenMol-2 can pre- cisely control molecular properties through the con- tinuous scalar slots within the wrapped sequence. We selected five core properties (Landrum, 2018) and defined five target values per property from the empirical distribution: three in-distribution (ID) percentiles and two out-of-distribution (OOD) tail values. For each target, 200 molecules were sampled while conditioning solely on that specific slot. A molecule is counted as a “hit” if its calcu- lated value falls within0.5σof the requested target, where σ denotes the corpus standard deviation. As shown in Table 1, CAGenMol-2 achieves a mean hit rate of0.89on ID targets and retains sub- stantial control on OOD targets with a mean hit rate of0.72. To distinguish active steering from passive filtering of an unconditional pool, we ad- ditionally measure the directional shift, defined as the displacement of the conditional mean from the unconditional mean in standard-deviation units and oriented toward the requested target. The consis- tently positive shifts in Table 1, together with the distributions in Figure 4, show that conditioning moves the sampled molecular distributions toward the requested targets. Our architecture features decoupled yet jointly processed scalar slots, enabling simultaneous con- Figure 4: Representative property-conditioned distribu- tion shifts. Conditioning moves the sampled molecular distributions toward the requested scalar targets. PropertyHit-IDHit-OODMAE-IDMAE-OODShift logP0.960.860.130.27+1.07 MW0.930.470.140.95+0.59 QED0.810.680.310.46+1.27 SA0.940.890.200.25+1.58 MR0.840.690.210.43+0.92 Mean0.890.720.200.48+1.09 Table 1: Single-property conditional generation. ID and OOD denote targets within the empirical distribution and its tails, respectively. MAE and directional Shift are reported in corpus standard-deviation units. trol over multiple property constraints. The model achieves a joint hit rate of0.76on a three-property Lipinski-like profile and0.84on a two-property lead-like target, while retaining non-trivial control under out-of-distribution conditions. Full metrics for all evaluated combinations are provided in the supplementary material. 4.3 Property Prediction and Representation Transfer We next evaluate two complementary capabilities: native physicochemical property prediction from the pretrained scalar head and transfer of the shared molecular representation to external ADMET end- points. For native prediction, CAGenMol-2 directly pre- dicts the five pretraining properties by observing the molecule and masking the scalar slots, with- out fitting an additional regressor. For context, we compare against predictors based on Morgan fin- gerprints, GIN, and ChemBERTa with separately fitted regression heads. On the 5k held-out set, CAGenMol-2 achieves a macroR 2 of0.910and Pearson correlation of0.974across the five proper- ties (Table 2). Per-property MAE and RMSE are reported in the supplementary material. MethodMacro R 2 ↑Macro Pearson↑ Morgan + GBR0.5250.720 GIN + GBR0.2190.550 GIN + MLP0.4770.678 ChemBERTa + MLP0.7620.880 CAGenMol-2 (native)0.9100.974 Table 2: Physicochemical property prediction on the 5k held-out set. CAGenMol-2 uses its pretrained native scalar head without downstream fitting; reference pre- dictors use separately fitted regressors. Macro averages are reported for the dimensionlessR 2 and Pearson met- rics. The native property head also provides rank- useful confidence scores. Sorting molecules by confidence reduces MAE for all five properties; on the top-25% highest-confidence subset, the relative error reduction ranges from29.1%to59.9%(Ta- ble 3). This ranking signal is subsequently used by AdaFO-S to adapt local molecular edits. PropertyFull MAE↓Top-25% MAE↓Relative drop logP0.2350.16729.1% MW3.892.1046.0% QED0.0360.01459.9% SA0.3640.22338.9% MR0.9810.68330.3% Table 3: Selective prediction using confidence from the native scalar head. Molecules are ranked by confi- dence, and MAE is reported for the top-25% highest- confidence subset. Finally, we assess transfer to MoleculeNet end- points (Wu et al., 2018) using standard scaffold splits and small MLP readouts trained on frozen molecular representations. As summarized in the compressed comparison in Table 4, when compared against a specialized transformer-based prediction model ChemBERTa3 and GenMol, CAGenMol-2 achieves the strongest performance among the dis- played methods on BBBP, Tox21, and HIV, while the regression tasks show a mixed but competitive transfer profile. These results demonstrate that the shared representation remains useful beyond its na- tive physicochemical objectives. The full ten-task benchmark and additional baselines are provided in the supplementary material. 4.4 Structure-Based Drug Design We evaluate pocket-conditioned molecular genera- tion on the CrossDocked2020 benchmark using the MethodBBBP↑Tox21↑HIV↑ESOL↓Lipo↓ ChemBERTa30.7000.7180.7400.9200.758 GenMol0.8970.7530.7680.7250.948 CAGenMol-20.9310.7890.7920.7890.790 Table 4: Representative MoleculeNet transfer results. Classification tasks report ROC-AUC and regression tasks report RMSE. CAGenMol-2 and the GenMol use frozen representations with trained MLP readouts. standard protocol (Guan et al., 2023b,a), sampling 100 molecules per pocket for evaluation. Perfor- mance is measured via Vina score, High Affin- ity rate (Vina gen ≤ Vina ref ), QED, SA, diver- sity, and Success Rate (defined byVina <−8.18, QED > 0.25, and SA > 0.59). As shown in Table 5, we compare against re- cent structure-based design methods (Zhang et al., 2025; Peng et al., 2022; Qu et al., 2024; Fu et al., 2022; Guan et al., 2024; Zhou et al., 2024). The pretrained CAGenMol-2 produces highly drug-like and diverse structures but has limited docking affin- ity. AdaFO allocates inference-time search to local structural refinement, improving the mean Vina score to−8.76kcal/mol and increasing Success Rate from30.2%to70.8%, the best reported result under this protocol. Importantly, QED, normalized SA, and diversity remain close to the pretrained baseline. The RL variant provides a parameter- updating optimization reference, whereas AdaFO performs inference-time search without updating model parameters. MethodVina↓HA↑ (%)QED↑SA↑Div↑SR↑ (%) Reference-7.45–0.480.73–25.0 Pocket2Mol-7.1548.40.560.740.6924.4 DecompDiff-8.3964.40.450.610.6824.5 MolCRAFT-9.2559.10.460.620.6136.1 RGA + Vina-8.0164.40.570.710.4146.2 DecompOpt-8.9873.50.480.650.6052.5 MolChord-8.5974.60.560.780.7153.4 CAGenMol-2-7.3253.50.730.840.8430.2 with RL-8.5175.40.610.810.8257.5 with AdaFO-8.7685.10.700.830.8270.8 Table 5:Structure-based drug design on Cross- Docked2020, averaged over 100 held-out pockets. Suc- cess Rate jointly requires affinity, drug-likeness, and synthesizability thresholds. The RL and AdaFO rows represent parameter-updating and inference-time opti- mization, respectively. 4.5 Compound Design Workflows While the previous sections evaluate individual ca- pabilities, practical molecular design requires them to operate together. We therefore test two com- pound workflows that reuse the same pretrained model and its masked reconstruction interface. Directional property editing. Given a seed molecules 0 , a property axisj, a direction, and a target magnitude∆σ j , the goal is to move the property in the requested direction while retaining similarity to the seed. A scaffold-preserving suc- cess requires a property shift of at least0.5∆σ j together with a Tanimoto similarity of at least0.20. AdaFO-S uses the model’s native predictions as reward, confidence to adapt the edit radius, and contrastive token saliency to localise each edit. Across six directional axes, a single saliency- guided edit moves the target property in the re- quested direction in 76.3% of cases, compared with 41.1% for random-span editing. Under the full three-iteration protocol across 12 configura- tions, the mean directional-and-similarity success rate is 61.2%. Figure 5 shows a representative trajectory. logp = 3.45logp = 2.38 sim = 0.82 logp = 1.77 sim = 0.52 logp = 1.77 sim=0.55 Seed Figure 5: Representative three-iteration directional- editing trajectory. AdaFO-S decreases logP through local molecular edits while retaining similarity to the seed scaffold. CRBN and VHL candidate prioritization.We further evaluate a design-to-screening workflow on two E3-ligase ligand-binding sites: CRBN (PDB 4CI1) and VHL (PDB 6GFZ) (Fischer et al., 2014; Testa et al., 2018). For each target, three AdaFO iterations generate 200 candidates. Structural-alert filtering and consensus docking with QuickVina 2, smina/Vinardo, and GNINA (Koes et al., 2013; Quiroga and Villarreal, 2016; McNutt et al., 2021) prioritize 50 candidates per target for 10-ns MD and M-GBSA analysis. The crystal ligands are evaluated under the same simulation protocol. The resulting computational shortlists contain 25 CRBN and 21 VHL candidates. All shortlisted molecules pass the recorded structural-alert filters, retain more than80%of their initial buried sur- face area, exhibit polar contacts in at least half of the analyzed frames, and have negative M- GBSA energies. The CRBN and VHL shortlists span 22 and 18 Bemis–Murcko scaffolds, with me- dian ECFP Tanimoto similarities to the reference ligands of0.141and0.116, respectively. These re- sults demonstrate a design-to-screening workflow that prioritizes chemically diverse candidates using molecular quality, contact retention, and energy- based criteria. Appendix C.6 provides the complete screening definitions and candidate-level results; Figure 6 illustrates representative pose inspection. Figure 6: Representative binding-pose inspection for CRBN. CAGenMol-2 candidates is shown together in the binding site, illustrating the structures carried for- ward by the design-to-screening workflow. Together, these workflows show how the shared masked-inference interface supports local molec- ular revision and connects pocket-conditioned search with downstream structure-based screening. 5 Conclusion We introduced CAGenMol-2, a masked diffusion molecular language model that frames native pre- diction and generation as different observation pat- terns over a shared wrapped sequence. Contin- uous property slots provide numerical condition- ing and readout, while compact pocket representa- tions incorporate 3D structural context. The result- ing model preserves its generative capability while supporting property-conditioned generation, native property prediction, and transferable molecular rep- resentations. Building on the same masked recon- struction mechanism, AdaFO turns partial molecu- lar decoding into adaptive local search guided by ei- ther model-native signals or external objectives. Di- rectional editing and candidate-prioritization work- flows further demonstrate how this shared infer- ence interface can connect molecular generation, assessment, and revision across design workflows. Limitations CAGenMol-2 remains most reliable within the property and structural regimes represented dur- ing pretraining. Steering can weaken for strongly out-of-distribution targets, particularly when re- quested changes conflict with learned fragment priors. The native confidence score is useful for ranking and adaptive editing, but is not intended as a calibrated posterior uncertainty estimate. In ad- dition, AdaFO relies on inference-time evaluation signals, such as docking or model-based objectives, whose quality and computational cost affect the re- sulting search. 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Zhenpeng Zhou, Steven Kearnes, Li Li, Richard N Zare, and Patrick Riley. 2019. Optimization of molecules via deep reinforcement learning. Scientific reports, 9(1):10752. Appendices The appendices provide the method, data, and ex- perimental details accompanying the main paper. They are organised into three sections. Appendix A specifies the method to the level required for a from-scratch reimplementation: the exact wrapped- sequence layout, the masked discrete-diffusion pro- cess and its training loss, every neural module with pseudocode, the joint pretraining procedure, and the two inference-time optimisers. Appendix B lists the pretraining corpora, their sizes and con- struction, the normalisation statistics, and batch- level mixing. Appendix C documents every ex- periment: datasets, whether any component was trained, baselines, protocols, metrics, and the com- plete result tables and figures, including the ones summarised or omitted in the main text. Native prediction and generation use the single pretrained checkpoint from the main paper. Reference regres- sors and MoleculeNet readouts are fitted separately, while the reinforcement-learning baseline of Ap- pendix C.4 updates model parameters and is re- ported as a separate row. The CRBN/VHL study additionally reports the supplied docking and MD screening results. SymbolMeaning s 1:L SAFE token sequence of a molecule, length L y k ,z k raw / z-normalised value of property k K=6number of scalar property slots t∈ [0, 1]diffusion time (0 clean, 1 fully masked) α t survival probability at time t mmask token cconditioning context (pocket + observed properties) f θ shared Transformer backbone μ,σpredicted mean / std of a property (normalised) p clean fraction of rows routed to the prediction regime p keep per-property keep probability (generation regime) αAdaFO mask fraction (mutation radius) s i contrastive token saliency (edit-localisation signal) Table 6: Recurring notation. A Method Details A.1 Notation and Overview CAGenMol-2 is a masked discrete-diffusion lan- guage model (Austin et al., 2021; Sahoo et al., 2024) over SAFE tokens (Noutahi et al., 2024). A single wrapped sequence carries three role-tagged regions: an optional pocket block, a scalar-property block, and a molecular block. The native inference operation is selected by which regions are observed and which are masked. Lets 1:L denote the SAFE tokens of a molecule,y ∈ R K the vector ofK=6 scalar properties, andPan optional protein pocket. The backbone is a bidirectional Transformer en- coderf θ shared across all tasks. Two read-out heads sit on top off θ : a masked-language-model head that predicts token logits over the molecular block, and a property head that predicts a Gaus- sian(μ,σ)per scalar slot. Table 6 lists recurring symbols. A.2 Wrapped Sequence: Full Specification A.2.1 Special Tokens The base SAFE-GPT tokenizer (Noutahi et al., 2024) of1880tokens is extended with19 marker tokens, giving a vocabulary of1899: six begin/end pairs for the property slots (⟨bop 1 ⟩,...,⟨eop 6 ⟩), one begin/end pair for the pocket block (⟨bopk⟩,⟨eopk⟩), one begin/end pair for the molecule block (⟨bom⟩,⟨eom⟩), one shared value token⟨val⟩overwritten at its position by the encoded scalar/pocket features, and two reserved markers kept for checkpoint compatibility. The to- kens⟨bos⟩,⟨eos⟩and the pad token complete the set. Slot Mol-only position Pocket position pocket (×4)—2, 3, 4, 5 logP28 MW511 QED814 SA1117 MR1420 reserved1723 prefix length2026 suffix length22 Table 7: Absolute value-slot positions in the wrapped sequence. Maximum length320(≤ 26prefix+≤ 256 SAFE tokens+2suffix, with slack). Properties in order: logP, MW, QED, SA, MR, reserved. Special tokens and the prefix are never noised. A.2.2 Two Layout Variants Every example is one of two variants.The molecule-only layout has a prefix of 20 tokens: ⟨bos⟩ b 1 v 1 e 1 ·b 6 v 6 e 6 |z 6 property blocks ⟨bom⟩ s 1:L ⟨eom⟩⟨eos⟩, withb k = ⟨bop k ⟩,e k = ⟨eop k ⟩,v k = ⟨val⟩. The pocket layout has a prefix of26: a block ⟨bopk⟩⟨val⟩ 4 ⟨eopk⟩is inserted after⟨bos⟩. Both coexist in every batch. Table 7 gives the exact value-slot positions. A.3 Masked Discrete Diffusion We adopt absorbing-state masked discrete diffu- sion (Austin et al., 2021) in the stabilised form of MDLM (Sahoo et al., 2024); this section restates it because it definesL tok and is prior work, not a contribution. A.3.1 Forward Process For clean tokensx 0 over a vocabulary augmented with a mask symbolm, each token is independently sent towardmwith survival probabilityα t decreas- ing from 1 at t=0 to 0 at t=1: q(x i t | x i 0 ) = α t δ x i 0 (x i t ) + (1− α t )δ m (x i t ). We use a log-linear schedule in continuous time (T =0), sampling floorε=10 −3 , and antithetic time sampling to reduce gradient variance. Only molecular-block positions are noised. Algorithm 1 Confidence-based decoding 1:Input: conditionc, stepsN, temperatureτ, randomness r, guidance γ 2:initialise molecular block to all-mask; build prefix from c 3: for n = 1...N do 4: ℓ← f θ (seq,c) at masked positions 5:if γ ̸= 1 then 6: ℓ← ℓ uncond + γ(ℓ− ℓ uncond ) 7:end if 8: p ← softmax(ℓ/τ ) ; commit top-k n confi- dent positions (k n set by r) 9: end for 10: decode SAFE→SMILES; keep largest frag- ment A.3.2 Training Loss MDLM reduces the diffusion NELBO to a time- weighted cross-entropy over masked positions: L tok = E t∼U(ε,1) E q(x t |x 0 ) " α ′ t 1− α t X i:x i t =m logp θ x i 0 | x t ,c # , withα ′ t = dα t /dt andcthe prefix condition. The sum runs only over masked molecular positions; special tokens are excluded. We use the global- mean reduction across the batch. A.3.3 Confidence-Based Decoding At inference we generate by iterated denoising with the confidence-based unmasking schedule of GenMol (Lee et al., 2025) (Algorithm 1). Each ofNsteps scores masked positions, softmaxes logits at temperatureτ, and commits the most confident positions; the number committed per step grows with randomnessr. Classifier-free guidance mixes conditional/unconditional logits, ℓ = ℓ uncond +γ(ℓ cond −ℓ uncond ), withγon a linear- up schedule (Ho and Salimans, 2021; Schiff et al., 2025). Default (τ,r) = (0.5, 0.5). A.4 Modules A.4.1 Continuous Value Encoder Each raw valuey k isz-normalised with fixed model statistics (Appendix B.1) toz k = (y k − μ k )/σ k , then mapped to a Fourier feature vector whose pe- Algorithm 2 Pocket adapter (per-atom→4 tokens) 1:Input: atom featuresH ∈ R L a ×512 , atom mask M , has-pocket flag 2:KV ← LayerNorm(Linear 512→768 (H)) 3: Q← LayerNorm(4 learned queries) 4: A ←MHA(Q,KV,KV ; key_pad= ¬M, heads = 8) 5: X ←LayerNorm(Q + A) ;X ← LayerNorm(X + FFN ×2 (X)) 6: returnXif has-pocket else 4 learned unknown embeddings riods are chosen in z-space: φ(z) = sin(2πz/T i ), cos(2πz/T i ) 4 i=1 ∥ z, T i ∈0.5, 1, 2, 4. a nine-dimensional vector fed through a two-layer MLP (9→ 768→ 768, GELU). Choosing periods in normalised space adapts Fourier numerical fea- tures (Zhou et al., 2025; Golkar et al., 2023) to the scalar interface. The raw-value feature preserves magnitude alongside the periodic components. A masked slot receives a learned unknown embed- ding instead of φ(z). A.4.2 Pocket Adapter The per-atom output of a frozen DrugCLIP en- coder (Gao et al., 2023) (Uni-Mol backbone (Zhou et al., 2023)) gives featuresH ∈ R L a ×512 for up toL a =400atoms. A learned adapter (Al- gorithm 2) pools these to four tokens via cross- attention. Molecule-only rows omit this block; a pocket-layout row whose condition is dropped re- ceives four learned unknown embeddings. Padded mixed batches share one forward pass. DrugCLIP is frozen while the adapter trains. A.4.3 Property Head and Its Loss The hidden states at the six scalar slots are read by a shared two-branch head (Algorithm 3): a Lay- erNorm then an MLP (768 → 768 → 2, GELU) outputting(μ, logσ 2 )per slot in normalised space, trained with L prop = Huber δ (μ,z) + w r L rank + w n 2 logσ 2 + (z− μ) 2 σ 2 . The Huber term (δ=1) is a robust mean anchor. The Gaussian NLL (Nix and Weigend, 1994) (w n =0.5) supplies the variance branch;logσ 2 is clamped Algorithm 3 Property head (per scalar slot) 1: Input: slot hidden state h∈ R 768 2: (μ, logσ 2 ) ←MLP(LayerNorm(h)); logσ 2 ← clamp(logσ 2 ,−10, 4) 3:train:Huber 1 (μ,z) + 0.5 NLL(μ,σ,z) + 0.2L rank 4:infer:value= μσ k + μ k ;std =exp( 1 2 logσ 2 )σ k ;conf= exp(− exp( 1 2 logσ 2 )) to[−10, 4]so the NLL cannot diverge (a variance collapse that would explode the gradient). The pairwise-margin ranking loss (w r =0.2, margin0.1) penalises within-batchμorderings that disagree with the target ordering, penalizing constant pre- dictions that fail to preserve target orderings. To avoid variance-head feature collapse under weight decay (Andriopoulos et al., 2024), the LayerNorm precedes the head and the head sits in a zero-weight- decay group. At inference the head returns a physi- cal value, a physical std, and a bounded confidence c = exp(−σ norm ) ∈ (0, 1]used only as a ranking signal. A.4.4 Condition Injection by Embedding Replacement Encoded property vectors (6 × 768) and pocket tokens (4× 768) are written directly into the in- put token embeddings at their reserved value po- sitions, plus a learned conditioning bias. A stan- dard bidirectional Transformer processes the se- quence (Vaswani et al., 2017; Devlin et al., 2019). Conditional and unconditional passes share the backbone and heads, differing at the observed value positions. Section C.2 evaluates classifier-free guid- ance for this interface. The per-row scatter handles mixed batches in one pass. A.5 Joint Masking-Consistent Pretraining Pretraining optimises generation and prediction jointly so one representation learns both mapping directions. A per-row Bernoulli routes each in- stance into one of two regimes (Algorithm 4): •Prediction regime (p clean = 0.15): the diffu- sion time is drawn near zero,t∼U (ε, 0.05), keeping the molecule essentially intact, and all six property slots are hidden. The model must read properties off the visible structure, matching the inference-time prediction distri- bution where the molecule is fully clean. Algorithm 4 One joint pretraining step (per row) 1: draw clean flag∼ Bernoulli(p clean =0.15) 2: if clean then 3: t∼U (ε, 0.05); hide all 6 property slots 4: else 5: t ∼ U (ε, 1) ; keep each property w.p. p keep =0.75 6: end if 7: w.p.p uncond =0.10: drop pocket+all proper- ties to unknown 8:build wrapped sequence; apply MDLM noise to the molecular block only 9: ℓ,h k ← f θ (seq) 10: L tok from ℓ on masked molecular positions 11: L prop fromh k on hidden slots (clean rows, loss-active properties) 12: update onL tok + 0.4L prop •Generation regime (1− p clean = 0.85): the molecule is corrupted att∼U (ε, 1)and each property slot is independently kept with prob- abilityp keep = 0.75. The model must denoise the structure under any of the2 6 subsets of observed properties. Superimposed on both,with probability p uncond = 0.10the entire conditioning prefix (pocket and all properties) is dropped to unknown embeddings, training an unconditional path for classifier-free guidance. The full objective is L =L tok + λL prop , λ = 0.4, whereλprevents the token loss (an order of mag- nitude larger early in training) from drowning the property signal. The property loss is active only on hidden slots of prediction-regime rows and only for the five loss-active physicochemical properties (the reserved sixth slot carries no loss). Both terms update the shared backbone. A.6 Inference-Time Optimisers A.6.1 AdaFO for Pocket Optimisation AdaFO (Algorithm 5) is a gradient-free evolution- ary loop that treats the model’s mask-and-refill as a structured mutation operator, in the spirit of diffu- sion inpainting (Lugmayr et al., 2022). It maintains a scored pool; each iteration reranks by maximal marginal relevance (Carbonell and Goldstein, 1998) over Morgan fingerprints (Morgan, 1965; Rogers and Hahn, 2010) to preserve diversity, selects Top- Kparents, masks a fragment span of lengthαL Algorithm 5 AdaFO inference-time refinement 1:Input: conditionc, budgetT, poolK, chil- drenM, mask range[α min ,α max ], diversityλ, score r 2:seedNsamples underc; score byr;P 0 ← MMR-TOP-K 3: for t = 1...T do 4: α max t ← α max −(α max −α min )t/T anneal (pocket mode) 5: C ←∅ 6:for all parent s∈P t−1 , repeated M× do 7: α ← draw in[α min ,α max t ](pocket) or target-error/confidence rule 8:choose span: random (pocket) or max- saliency window 9: mask theαL-span ofs; refill underc; add toC 10:end for 11:scoreC; keep top K (elite) 12: P t ← MMR-TOP-K(P t−1 ∪ elite(C)) 13: end for 14: return best ofP T per parent and refills it under the pocket condition, filters children by score (elite), and merges. The mask-fraction upper bound anneals linearly with the iteration so early iterations restructure scaffolds and late iterations polish. The reward is r(s;p) = − V (s;p)− V ref (p) + w q Q(s) + w a A(s) − η⊮[dock fails]. withVthe QuickVina 2 score (Trott and Olson, 2010; Alhossary et al., 2015),QQED (Bickerton et al., 2012),Anormalised SA (Ertl and Schuffen- hauer, 2009),w q =w a =0.7,η=5. Hyperparame- ters are in Table 9. A.6.2 AdaFO-S for Directional Editing The directional variant runs the same loop with three changes. (i) The reward uses only the model’s own predictions,r j (s) = −|ˆy j (s) − y ⋆ |/σ j + β τ (s,s 0 ), with targety ⋆ = y j (s 0 )± ∆σ j , Tan- imoto anchorβ=0.5, and no external oracle. (i) The per-parent mask fraction (how much to edit) is set by a score combining target error and predictive confidence: u(s) = min |ˆy j (s)−y ⋆ | σ j , 3 + (1− c j (s)), α(s) = α min + u(s) 4 (α max − α min ). (i) The mask location is chosen by contrastive token saliency. For each molecule token we mask it in isolation and read the log-probability of the original token under the target and unconditional prefixes: s i = logp θ (x i =tok i | x ,∅) − logp θ (x i =tok i | x ,y ⋆ ), The first child masks the contiguous width-α(s)L window with maximum summeds i , found using prefix sums. Additional children sample starts from a softmax over window scores, diversifying propos- als around salient regions. Saliency is computed with target-conditioned and unconditional batched forward passes. The reported localization com- parison uses random-span editing with the same confidence-dependent radius. B Pretraining Data B.1 Corpora Pretraining interleaves examples from two data sources at the sample level, so a single batch may contain both molecule-only and pocket- conditioned examples. Molecule corpus (molecule-only variant).The released data pipeline uses ten million property- annotated molecules drawn from the SAFE-GPT training corpus (Noutahi et al., 2024).All molecules are tokenised with the SAFE converter usingslicer=Noneandignore_stereo=True. Five physicochemical properties are precomputed for every molecule with RDKit (Landrum, 2018): logP using the Crippen estimator, molecular weight (MW), QED (Bickerton et al., 2012), synthetic ac- cessibility (SA) (Ertl and Schuffenhauer, 2009), and molar refractivity (MR). The resulting corpus is stored as a property-augmented table containing safe,smiles, and the five property columns. Dur- ing pretraining, molecule-only examples are sam- pled randomly from this corpus; the 100,000-step run with global batch size 2,048 processes approxi- mately2× 10 8 example presentations across both data sources, including repeated sampling. Pocket corpus (pocket-conditioned variant). The pocket corpus is constructed from all pro- tein pockets in the CrossDocked2020 training split (Francoeur et al., 2020) and the DrugCLIP training set (Gao et al., 2023). For each pocket, we PropertyMean μ k Std σ k logP2.3332.483 MW371.558131.271 QED0.6840.166 SA3.4910.860 MR98.64637.334 Table 8: Empirical corpus statistics used for evalua- tion target shifts, hit tolerances, and normalized errors. Model encoding uses the separate checkpoint statistics specified in the text. use the pretrained DrugCLIP model to retrieve can- didate ligands from the original DrugCLIP molecu- lar retrieval library. Specifically, we randomly sam- ple5× 10 5 candidate molecules for each pocket, score all pocket–molecule pairs with DrugCLIP, and rank the candidates by their retrieval scores. Candidates with a score below0.5are discarded, after which at most the top 200 molecules are re- tained as pseudo-ligands for that pocket. Each re- tained molecule is paired with the corresponding pocket and carries the same five precomputed RD- Kit properties as in the molecule-only corpus. Each pocket is additionally encoded offline by the frozen DrugCLIP pocket encoder, whose Uni- Mol backbone (Zhou et al., 2023) produces per- atom pocket features that are cached before train- ing. These examples train the pocket adapter and the pocket-conditioned generation pathway. The DrugCLIP encoder remains frozen throughout pre- training. Normalization and evaluation scales. The scalar encoder and decoder use fixed per-slot means and standard deviations stored in the checkpoint. Evaluation scripts separately use empirical corpus statistics to define requested shifts, hit tolerances, and normalized errors. Table 8 gives the empir- ical evaluation scales. In slot order (logP, MW, QED, SA, MR), the checkpoint stores model means (1.98, 363, 0.69, 2.8, 95)and standard deviations (1.49, 61.5, 0.16, 0.7, 25). The reserved slot uses mean 0 and standard deviation 1 and carries no active loss. Thus the model normalization inz k and the evaluation standard deviation in∆σ j have distinct roles. The empirical statistics are estimated from a 200,000-molecule sample of the property- annotated corpus. B.2 Batch Mixing and Optimisation Rows from the two corpora are interleaved so ev- ery global batch mixes molecule-only and pocket variants; the collator pads to the longest row and records per-row value-slot offsets. Table 9 lists every training and inference hyperparam- eter.The global batch size is2048, realised as four devices×a per-device batch of128 × four gradient-accumulation steps. Optimisation is AdamW (Loshchilov and Hutter, 2019) (learning rate3 × 10 −4 , betas(0.9, 0.999), no weight de- cay) under a constant schedule with a2500-step linear warmup, gradient clipping at1.0,bfloat16 precision with the scalar-head forward upcast to single precision for NLL stability, and an expo- nential moving average of weights (decay0.9999) used at evaluation. Training runs for10 5 steps on four A6000 (48 GB) accelerators for roughly three days. C Experiment Details and Full Results Every experiment below uses the single pretrained checkpoint of Appendix A. For each we state the dataset, whether any component was trained (ref- erence property regressors, MoleculeNet readouts, and the SBDD reinforcement baseline are trained downstream; native scalar prediction and genera- tion use the frozen checkpoint), the baselines, the protocol and metrics, and the complete tables. Fig- ures referenced here are the full-resolution versions of those summarised in the main paper plus addi- tional plots. Group / parameterValue Backbone layers / hidden / heads12 / 768 / 12 intermediate size3072 activationGELU dropout (hidden / attn)0.1 / 0.1 max position / vocab320 / 1899 Value encoder / property head Fourier periods (z-space) 0.5, 1, 2, 4 Huber δ1.0 NLL weight w n 0.5 rank weight w r / margin0.2 / 0.1 logσ 2 clamp[−10, 4] Pocket adapter atom dim / tokens / heads512 / 4 / 8 FFN expansion / max atoms ×2 / 400 Diffusion / masking regime noise schedule / timelog-linear / continuous sampling ε10 −3 p clean / clean t max 0.15 / 0.05 p keep / p uncond 0.75 / 0.10 property loss weight λ0.4 Group / parameterValue Optimisation optimiserAdamW learning rate / warmup3× 10 −4 / 2500 betas / weight decay(0.9, 0.999) / 0 grad clip / precision1.0 / bf16 EMA decay0.9999 global batch / steps2048 / 10 5 AdaFO (pocket) pool K / children M / iters T 32 / 4 / 5 mask range[0.05, 0.50] MMR λ / fingerprint0.3 / Morgan-r2, 1024b reward w q ,w a ,η0.7, 0.7, 5.0 Vina exhaustiveness (loop/final) 4 / 8 AdaFO-S (directional) pool K / children M / iters T 8 / 4 / 3 mask range[0.06, 0.20] similarity anchor β0.5 decoding (τ,r)(0.5, 0.5) CFG scale γ (default)1.5 Table 9: Complete hyperparameter listing for training and both inference-time optimisers. C.1 De Novo Generation Setup and dataset.Unconditional generation fol- lowing the GenMol protocol (Lee et al., 2025). No training: molecules are sampled directly from the frozen checkpoint with the property and pocket slots set to unknown.We generateN =1000 molecules per decoding setting and report mean ± std over three random seeds. Metrics. Validity (fraction of decoded SAFE strings yielding a valid SMILES), Uniqueness (unique canonical SMILES among valid), Quality (valid∧unique∧QED≥ 0.6∧SA≤ 4using the TDC oracles (Huang et al., 2021)), and Diversity (mean pairwise Tanimoto distance over Morgan fingerprints).τis the softmax temperature andr the confidence-sampling randomness; one token is unmasked per step. Baselines. SAFE-GPT (Noutahi et al., 2024), GenMol without confidence sampling, and Gen- Mol withN =1across five(τ,r)settings, all tran- scribed from the GenMol paper under the identical protocol. Results.Table 10 gives the complete five-setting comparison; Figure 3 is the quality–diversity Pareto frontier. At(τ,r) = (0.5, 0.5)our model reaches Quality85.2± 0.8%, above GenMol’s bestN =1 setting (84.6± 0.8%) at similar diversity (0.822 vs0.818). The two models trace similar quality– diversity frontiers. Uniqueness reaches100.0± 0.0%at the three mid-rsettings, retaining an effec- tive unconditional generation mode. Method / (τ,r)ValidityUniquenessQualityDiversity SAFE-GPT94.0±0.4100.0±0.054.7±0.30.879±0.001 GenMol w/o conf.96.7±0.399.3±0.253.8±1.70.896±0.001 GenMol (N =1) (0.5, 0.5)100.0±0.099.7±0.184.6±0.80.818±0.001 (0.5, 1.0)99.7±0.1100.0±0.183.8±0.50.832±0.002 (0.5, 10)99.8±0.199.6±0.179.1±0.90.845±0.002 (1.0, 10)99.8±0.199.6±0.163.0±0.30.873±0.008 (1.5, 10)95.6±0.398.3±0.239.7±0.50.911±0.004 CAGenMol-2 (N =1, ours) (0.5, 0.5)100.0±0.099.7±0.1 85.2±0.80.822±0.002 (0.5, 1.0)99.8±0.0100.0±0.083.3±0.70.832±0.001 (0.5, 10)99.7±0.0100.0±0.074.8±0.70.854±0.000 (1.0, 10)98.7±0.3100.0±0.060.2±1.30.883±0.000 (1.5, 10)96.6±0.599.7±0.137.5±1.70.908±0.001 Table 10: De novo generation, full five-setting comparison. N =1000 per setting, mean± std over three seeds. C.2 Property-Conditioned Generation Setup.Zero-shot from the frozen checkpoint. For each property we set three in-distribution targets (empirical p10, p50, and p90) and two tail targets listed in Table 11, and sample 200 molecules with only that property observed. Realised values are computed with RDKit (Landrum, 2018). Metrics: hit@0.5σ(fraction within half a corpus-σof tar- get), MAE, and mean shiftz(signed displacement of the conditional mean from the unconditional mean inσunits; positive means the prefix steered generation toward the target). CFG scaleγ=1.5, decoding (τ,r) = (0.5, 1.0). Full single-property results. Table 11 lists all 25(property, target) configurations. In-distribution conditioning averages hit@0.5σ = 0.89, out-of- distribution0.72; the mean shift is positive in all25 settings. At the demanding MW target of600Da (413± 151Da, hit0.24): the SAFE-token budget saturates before the target mass is reached, and the empirical distribution has a hard edge near the 97.5percentile (≈ 450Da). Figure 12 shows the realised distributions shifting toward targets. Multi-property results. Table 12 reports four drug-relevant combinations (500 molecules each), scoring the joint hit@0.5σ(within half aσon every targeted property simultaneously). The in- distribution Lipinski triple reaches0.76and the lead-like pair0.84; out-of-distribution combina- tions degrade gracefully. Classifier-free guidance ablation. Table 13 sweepsγ ∈ 1, 1.5, 2, 3, 4. The mean hit@0.5σ varies by only0.011across the range — smaller than the per-target seed noise — so guidance is not load-bearing in our model. The mechanism is the embedding-replacement conditioning of Sec- tion A.4.4: because the conditional and uncondi- tional forward passes share all parameters and dif- fer only in a few input embeddings, the guidance signal saturates once the prefix is expressive. We shipγ = 1.5(hit optimum with validity≥ 99.8%); γ = 1.0is equally good and avoids the doubled forward cost. Figure 13 plots the sweep. PropTarget (label)mean±stdMAEbiashitshift logP −2 (ood-lo) −1.78±0.630.47+0.220.93+1.85 logP0 (p10)0.08±0.550.38+0.080.95+1.10 logP2.3 (p50)2.14±0.490.34 −0.160.96+0.27 logP4.4 (p90)4.25±0.540.26 −0.150.95+0.58 logP7 (ood-hi)6.67±1.520.88 −0.330.81+1.56 MW180 (ood-lo)220±4954.3+40.20.69+0.81 MW290 (p10)276±3819.4 −14.20.88+0.39 MW360 (p50)353±3412.2 −6.50.96+0.21 MW450 (p90)444±4524.7 −6.20.94+0.89 MW600 (ood-hi)413±151196 −1870.24+0.66 QED0.25 (ood-lo)0.27±0.160.116+0.020.47+3.15 QED0.47 (p10)0.50±0.090.066+0.030.69+1.77 QED0.72 (p50)0.73±0.070.053+0.000.81+0.41 QED0.86 (p90)0.85±0.050.036 −0.010.94+0.32 QED0.95 (ood-hi)0.91±0.050.038 −0.040.88+0.72 SA1.8 (ood-lo)1.89±0.200.112+0.090.99+0.90 SA2.45 (p10)2.51±0.240.137+0.060.97+0.18 SA3.4 (p50)3.42±0.300.176+0.020.93+0.87 SA4.6 (p90)4.56±0.360.194 −0.040.91+2.20 SA6 (ood-hi)5.89±0.420.324 −0.110.79+3.75 MR50 (ood-lo)47.7±129.38 −2.40.85+1.16 MR76 (p10)73.1±9.44.28 −2.90.92+0.48 MR95 (p50)93.6±8.72.91 −1.40.95+0.07 MR121 (p90)125±2616.2+3.50.64+0.90 MR160 (ood-hi)166±3222.9+5.80.53+2.01 Table 11: Single-property conditional generation, all 25 configurations. hit = hit@0.5σ; shift is in σ units. ComboTargetsvalid/500joint hitregime LipinskilogP 2.5, MW 350, QED 0.754970.76ID Lead-likeQED 0.7, SA 2.55000.84ID Big-lipologP 5, MW 550, QED 0.5, SA 44930.52OOD Tiny-drugMW 200, QED 0.854950.44OOD Table 12: Multi-property conditional generation. Per-property hits for the Lipinski combo: logP0.92, MW0.85, QED 0.85; for lead-like: QED 0.87, SA 0.95. 0.30.40.50.60.70.80.91.0 QED 0 1 2 3 4 5 6 7 density qed 0.47 (p10) de novo prop-cond target = 0.47 0.30.40.50.60.70.80.91.0 QED 0 1 2 3 4 5 6 7 density qed 0.72 (p50) de novo prop-cond target = 0.72 0.30.40.50.60.70.80.91.0 QED 0 2 4 6 8 10 12 density qed 0.86 (p90) de novo prop-cond target = 0.86 0.00.20.40.60.81.0 QED 0 1 2 3 4 5 density qed 0.25 (ood_low) de novo prop-cond target = 0.25 0.30.40.50.60.70.80.91.0 QED 0.0 2.5 5.0 7.5 10.0 12.5 15.0 density qed 0.95 (ood_high) de novo prop-cond target = 0.95 Figure 7: Property distributions for single-property conditioned generation (QED). Results for in-distribution and out-of-distribution targets are shown. 123456 SA 0.0 0.5 1.0 1.5 2.0 2.5 density sa 2.45 (p10) de novo prop-cond target = 2.45 123456 SA 0.0 0.5 1.0 1.5 2.0 density sa 3.4 (p50) de novo prop-cond target = 3.4 1234567 SA 0.0 0.5 1.0 1.5 2.0 density sa 4.6 (p90) de novo prop-cond target = 4.6 123456 SA 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 density sa 1.8 (ood_low) de novo prop-cond target = 1.8 2468 SA 0.00 0.25 0.50 0.75 1.00 1.25 1.50 density sa 6 (ood_high) de novo prop-cond target = 6 Figure 8: Property distributions for single-property conditioned generation (SA). Results for in-distribution and out-of-distribution targets are shown. 100200300400500 MW (Da) 0.00 0.01 0.02 0.03 0.04 0.05 density mw 290 (p10) de novo prop-cond target = 290 100200300400500 MW (Da) 0.00 0.01 0.02 0.03 0.04 density mw 360 (p50) de novo prop-cond target = 360 100200300400500600 MW (Da) 0.000 0.005 0.010 0.015 0.020 0.025 density mw 450 (p90) de novo prop-cond target = 450 100200300400500 MW (Da) 0.000 0.002 0.004 0.006 0.008 0.010 density mw 180 (ood_low) de novo prop-cond target = 180 200400600800 MW (Da) 0.000 0.002 0.004 0.006 0.008 density mw 600 (ood_high) de novo prop-cond target = 600 Figure 9: Property distributions for single-property conditioned generation (MW). Results for in-distribution and out-of-distribution targets are shown. 20406080100120140 MR 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 density mr 76 (p10) de novo prop-cond target = 76 20406080100120140 MR 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 density mr 95 (p50) de novo prop-cond target = 95 255075100125150175200 MR 0.00 0.01 0.02 0.03 0.04 0.05 0.06 density mr 121 (p90) de novo prop-cond target = 121 020406080100120140 MR 0.00 0.01 0.02 0.03 0.04 0.05 density mr 50 (ood_low) de novo prop-cond target = 50 050100150200 MR 0.000 0.005 0.010 0.015 0.020 0.025 0.030 density mr 160 (ood_high) de novo prop-cond target = 160 Figure 10: Property distributions for single-property conditioned generation (MR). Results for in-distribution and out-of-distribution targets are shown. 20246 logP 0.0 0.2 0.4 0.6 0.8 1.0 density logp 0 (p10) de novo prop-cond target = 0 20246 logP 0.0 0.2 0.4 0.6 0.8 1.0 density logp 2.3 (p50) de novo prop-cond target = 2.3 20246 logP 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 density logp 4.4 (p90) de novo prop-cond target = 4.4 420246 logP 0.0 0.2 0.4 0.6 0.8 density logp -2 (ood_low) de novo prop-cond target = -2 2.50.02.55.07.510.012.5 logP 0.0 0.2 0.4 0.6 0.8 density logp 7 (ood_high) de novo prop-cond target = 7 Figure 11: Property distributions for single-property conditioned generation (logP). Results for in-distribution and out-of-distribution targets are shown. 2 1 0 1 2 3 4 5 6 logP 100 150 200 250 300 350 400 450 500 MW (Da) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 QED C1_lipinski hit = 0.76 0.40.60.8 QED 1 2 3 4 5 6 SA C2_leadlike hit = 0.84 210123 PC1 (58%) 2 1 0 1 2 3 PC2 (31%) C3_big_lipo (PCA) hit = 0.52 100200300400500 MW (Da) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 QED C4_tiny_drug hit = 0.44 2 1 0 1 2 3 4 5 6 logP 100 150 200 250 300 350 400 450 500 MW (Da) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 QED C1_lipinski hit = 0.76 0.40.60.8 QED 1 2 3 4 5 6 SA C2_leadlike hit = 0.84 210123 PC1 (58%) 2 1 0 1 2 3 PC2 (31%) C3_big_lipo (PCA) hit = 0.52 100200300400500 MW (Da) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 QED C4_tiny_drug hit = 0.44 Figure 12: Realised property distributions under conditioning (coloured) versus unconditional generation (grey). The prefix shifts the entire probability mass toward each requested target. 1.01.52.03.04.0 CFG scale 0.80 0.85 0.90 0.95 1.00 hit@0.5 / validity Effect of classifier-free guidance scale hit@0.5 MAE/ validity 0.315 0.320 0.325 0.330 0.335 MAE / Figure 13: Hit rate, MAE, and validity versus CFG scaleγ. The near-flat hit curve shows guidance is redundant given the strong prefix. γhit@0.5σMAE/σvalidity 1.00.8050.3150.996 1.50.8080.3200.998 2.00.8020.3180.996 3.00.7980.3340.993 4.00.8070.3320.989 Table 13: Guidance sweep, aggregated over five single- property targets. C.3 Property Prediction and Representation Transfer Setup and dataset. The evaluation subset con- tains 5,000 molecules from the property-annotated SAFE-GPT data, disjoint by a SHA1-based split from the 30,000 molecules used to fit reference regressors. The five RDKit properties supply the targets. CAGenMol-2 directly evaluates its pre- trained scalar head by hiding the property slots and observing the molecule. This head receives property supervision during joint pretraining; no additional regressor is fitted for this evaluation. Referencepredictors. Morganradius- 2, 2048-bit fingerprints are paired with a gradient boosting regressor.Frozen GIN (gin_supervised_contextpred,300-d)is evaluated with GBR or an MLP, and frozen ChemBERTa (Chithrananda et al., 2020) provides a 768-d classification-token representation to an MLP. The MLP readouts use a 256-unit hidden layer, GELU, dropout 0.1, AdamW (10 −3 , weight decay10 −4 ), Huber loss, batches of 64, and up to 200 epochs with patience-20 early stopping. These reference models and the native scalar head have different pretraining supervision; the table reports their resulting prediction performance. Full results. Table 14 reports errors separately for each property. CAGenMol-2 achieves macro R 2 = 0.910and the lowest MAE on logP, MW, QED, and MR among the listed predictors. Cross- property summaries use the dimensionlessR 2 and Pearson correlation; raw errors remain in their re- spective property units. Confidence calibration and selective predic- tion. The head emits(value, std, conf). Vari- ance is learned through the Gaussian likelihood term; confidence is a deterministic function of pre- dicted standard deviation. Table 15 reports reli- ability (predicted std vs empirical RMSE in ten equal-population std bins) and selective prediction (rolling MAE when keeping the most confident fractions). The head is over-confident on the ab- solute scale (RMSE/std1.2–3.2×) but its ranking supports selection: retaining the top25%by confi- dence reduces MAE for all five properties, with a reported QED reduction of59.9%. This is the rank- ing signal used by AdaFO-S. Figures 14 and 15 MethodMetriclogPMWQEDSAMRMacro CAGenMol-2 MAE0.2353.890.0360.3640.981— RMSE0.43424.60.0540.4346.11— R 2 0.9660.9630.8960.7550.971 0.910 Pears.0.9870.9860.9510.9590.989 0.974 ChemBERTa+MLP MAE0.75025.80.0810.2687.40— R 2 0.7710.7940.5940.8390.8130.762 Morgan+GBR MAE0.72637.90.0800.25410.2— R 2 0.5410.3180.5980.7980.3670.525 GIN+MLP MAE0.61438.90.0830.31910.3— R 2 0.6190.2310.5460.7160.2740.477 GIN+GBR MAE0.76449.20.0970.37113.1— R 2 0.347 −0.1090.4240.645 −0.2130.219 Table 14: Native property prediction and fitted reference predictors on the same 5,000-molecule evaluation set. MAE and RMSE retain each property’s units; macro averages apply to R 2 and Pearson correlation. Prop RMSE/ std Top-50% (rel. drop) Top-25% (rel. drop) logP2.270.185 (21.3%)0.167 (29.1%) MW1.432.34 (39.8%)2.10 (46.0%) QED1.820.020 (43.5%)0.014 (59.9%) SA3.220.263 (27.8%)0.223 (38.9%) MR1.170.684 (30.2%)0.683 (30.3%) Table 15: Confidence reliability (RMSE/std ratio;> 1over-confident) and selective-prediction MAE with relative reduction versus the full-set MAE. show the reliability and coverage curves. MoleculeNet transfer.We train small MLP read- outs on frozen molecular representations for ten MoleculeNet endpoints (Wu et al., 2018), using Bemis–Murcko scaffold splits (Bemis and Murcko, 1996), three seeds, masked binary cross-entropy for classification, and Huber loss for regression. GenMol is rerun with this readout protocol. Pub- lished prediction-model scores are included as con- text under their original training protocols. Ta- ble 16 reports all tasks. The BBBP ROC-AUC is 0.931± 0.006; results across the remaining end- points characterize the representation’s transfer pro- file. 0.000.250.500.751.00 predicted std 0.0 0.2 0.4 0.6 0.8 1.0 observed RMSE logp (ECE_std = 0.194) ideal y = x 020406080 predicted std 0 20 40 60 80 observed RMSE mw (ECE_std = 6.43) 0.000.020.040.060.08 predicted std 0.00 0.02 0.04 0.06 0.08 observed RMSE qed (ECE_std = 0.0158) 0.00.20.40.6 predicted std 0.0 0.2 0.4 0.6 observed RMSE sa (ECE_std = 0.272) 05101520 predicted std 0 5 10 15 20 observed RMSE mr (ECE_std = 1.82) Reliability observed RMSE vs predicted std 0.000.250.500.751.00 predicted std 0.0 0.2 0.4 0.6 0.8 1.0 observed RMSE logp (ECE_std = 0.194) ideal y = x 020406080 predicted std 0 20 40 60 80 observed RMSE mw (ECE_std = 6.43) 0.000.020.040.060.08 predicted std 0.00 0.02 0.04 0.06 0.08 observed RMSE qed (ECE_std = 0.0158) 0.00.20.40.6 predicted std 0.0 0.2 0.4 0.6 observed RMSE sa (ECE_std = 0.272) 05101520 predicted std 0 5 10 15 20 observed RMSE mr (ECE_std = 1.82) Reliability observed RMSE vs predicted std 0.000.250.500.751.00 predicted std 0.0 0.2 0.4 0.6 0.8 1.0 observed RMSE logp (ECE_std = 0.194) ideal y = x 020406080 predicted std 0 20 40 60 80 observed RMSE mw (ECE_std = 6.43) 0.000.020.040.060.08 predicted std 0.00 0.02 0.04 0.06 0.08 observed RMSE qed (ECE_std = 0.0158) 0.00.20.40.6 predicted std 0.0 0.2 0.4 0.6 observed RMSE sa (ECE_std = 0.272) 05101520 predicted std 0 5 10 15 20 observed RMSE mr (ECE_std = 1.82) Reliability observed RMSE vs predicted std 0.000.250.500.751.00 predicted std 0.0 0.2 0.4 0.6 0.8 1.0 observed RMSE logp (ECE_std = 0.194) ideal y = x 020406080 predicted std 0 20 40 60 80 observed RMSE mw (ECE_std = 6.43) 0.000.020.040.060.08 predicted std 0.00 0.02 0.04 0.06 0.08 observed RMSE qed (ECE_std = 0.0158) 0.00.20.40.6 predicted std 0.0 0.2 0.4 0.6 observed RMSE sa (ECE_std = 0.272) 05101520 predicted std 0 5 10 15 20 observed RMSE mr (ECE_std = 1.82) Reliability observed RMSE vs predicted std 0.000.250.500.751.00 predicted std 0.0 0.2 0.4 0.6 0.8 1.0 observed RMSE logp (ECE_std = 0.194) ideal y = x 020406080 predicted std 0 20 40 60 80 observed RMSE mw (ECE_std = 6.43) 0.000.020.040.060.08 predicted std 0.00 0.02 0.04 0.06 0.08 observed RMSE qed (ECE_std = 0.0158) 0.00.20.40.6 predicted std 0.0 0.2 0.4 0.6 observed RMSE sa (ECE_std = 0.272) 05101520 predicted std 0 5 10 15 20 observed RMSE mr (ECE_std = 1.82) Reliability observed RMSE vs predicted std Figure 14: Reliability: predicted std versus empirical RMSE per bin. Points above the diagonal indicate over- confidence. 0.000.250.500.751.00 coverage (top-confidence fraction) 0.05 0.10 0.15 0.20 rolling MAE logp 21.3% MAE @ 50% coverage full MAE = 0.235 rolling MAE 0.000.250.500.751.00 coverage (top-confidence fraction) 1 2 3 4 rolling MAE mw 39.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.01 0.02 0.03 rolling MAE qed 43.5% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.1 0.2 0.3 rolling MAE sa 27.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.2 0.4 0.6 0.8 1.0 rolling MAE mr 30.2% MAE @ 50% coverage Selective prediction does confidence let us trade coverage for accuracy? 0.000.250.500.751.00 coverage (top-confidence fraction) 0.05 0.10 0.15 0.20 rolling MAE logp 21.3% MAE @ 50% coverage full MAE = 0.235 rolling MAE 0.000.250.500.751.00 coverage (top-confidence fraction) 1 2 3 4 rolling MAE mw 39.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.01 0.02 0.03 rolling MAE qed 43.5% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.1 0.2 0.3 rolling MAE sa 27.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.2 0.4 0.6 0.8 1.0 rolling MAE mr 30.2% MAE @ 50% coverage Selective prediction does confidence let us trade coverage for accuracy? 0.000.250.500.751.00 coverage (top-confidence fraction) 0.05 0.10 0.15 0.20 rolling MAE logp 21.3% MAE @ 50% coverage full MAE = 0.235 rolling MAE 0.000.250.500.751.00 coverage (top-confidence fraction) 1 2 3 4 rolling MAE mw 39.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.01 0.02 0.03 rolling MAE qed 43.5% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.1 0.2 0.3 rolling MAE sa 27.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.2 0.4 0.6 0.8 1.0 rolling MAE mr 30.2% MAE @ 50% coverage Selective prediction does confidence let us trade coverage for accuracy? 0.000.250.500.751.00 coverage (top-confidence fraction) 0.05 0.10 0.15 0.20 rolling MAE logp 21.3% MAE @ 50% coverage full MAE = 0.235 rolling MAE 0.000.250.500.751.00 coverage (top-confidence fraction) 1 2 3 4 rolling MAE mw 39.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.01 0.02 0.03 rolling MAE qed 43.5% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.1 0.2 0.3 rolling MAE sa 27.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.2 0.4 0.6 0.8 1.0 rolling MAE mr 30.2% MAE @ 50% coverage Selective prediction does confidence let us trade coverage for accuracy? 0.000.250.500.751.00 coverage (top-confidence fraction) 0.05 0.10 0.15 0.20 rolling MAE logp 21.3% MAE @ 50% coverage full MAE = 0.235 rolling MAE 0.000.250.500.751.00 coverage (top-confidence fraction) 1 2 3 4 rolling MAE mw 39.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.01 0.02 0.03 rolling MAE qed 43.5% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.1 0.2 0.3 rolling MAE sa 27.8% MAE @ 50% coverage 0.000.250.500.751.00 coverage (top-confidence fraction) 0.2 0.4 0.6 0.8 1.0 rolling MAE mr 30.2% MAE @ 50% coverage Selective prediction does confidence let us trade coverage for accuracy? Figure 15: Selective prediction: rolling MAE as a function of retained coverage (sorted by confidence). The curves show the accuracy–coverage trade-off as low-confidence molecules are dropped. Classification (ROC-AUC↑) MethodBACE↑BBBP↑ClinTox↑SIDER↑Tox21↑HIV↑MUV↑ D-MPNN0.8090.7100.9060.5700.7590.7710.786 AttentiveFP0.7840.6630.8470.6060.7810.7570.786 GROVER base 0.8210.7000.8120.6480.7430.6250.673 MolCLR0.8240.7220.9120.5890.7500.7810.796 GEM0.8560.7240.9010.6720.7810.8060.817 Uni-Mol0.8570.7290.9190.6590.7960.8080.821 KA-GCN 0.8900.7870.9890.8420.7990.821 0.834 KA-GAT0.8840.785 0.991 0.847 0.800 0.823 0.834 ChemBERTa30.7810.7000.9790.6110.7180.740— GenMol (re-run)0.7680.8970.6590.5880.7530.7680.693 CAGenMol-20.802 0.9310.8820.6310.7890.7920.671 Regression (RMSE↓) MethodESOL↓FreeSolv↓Lipo↓ D-MPNN— AttentiveFP— GROVER base — MolCLR— GEM0.7981.8770.660 Uni-Mol0.7881.480 0.603 KA-GCN— KA-GAT— ChemBERTa30.920 0.5360.758 GenMol (re-run) 0.7251.7440.948 CAGenMol-20.7891.8400.790 Table 16: MoleculeNet transfer and published reference scores. Ours and the GenMol re-run use frozen representa- tions with trained MLP readouts; published models follow their own training protocols. Classification: ROC-AUC (↑); regression: RMSE (↓). Baseline numbers transcribed from the KA-GNN and ChemBERTa3 papers and a Uni-Mol survey; GenMol is our own re-run under the identical protocol. Bold = best per column. C.4 Structure-Based Drug Design Setup and dataset. The CrossDocked2020 100- pocket test split (Francoeur et al., 2020) follow- ing the CAGenMol protocol (Li et al., 2026). For each pocket we generate100molecules under the pocket-conditional layout at(τ,r) = (0.5, 0.5) and dock each with QuickVina 2 (Alhossary et al., 2015) at exhaustiveness8in a25 3 Å 3 box on the reference-ligand centroid. Metrics: Vina Dock, High Affinity (fraction at least as good as the refer- ence ligand), QED, normalised SA(10− SA raw )/9, Diversity, and Success Rate (Vina < −8.18 ∧ QED > 0.25∧ SA > 0.59). The pretrained base- line and AdaFO are zero-shot; the reinforcement baseline is the only trained variant. Reinforcement-learning baseline. A step-wise PPO (Schulman et al., 2017, 2015) fine-tune of the pretrained checkpoint with four accelerators: a reference-ligand advantage baseline, a failed-dock penalty, advantage clipping at±3σ, and a layer- wise freeze that trains only the top six Transformer layers plus the prefix and pocket adapter. Reward is dock-primary (w q =w a =0.1). Training runs150 PPO steps per pocket at batch32on four A6000 ac- celerators — about one hour of training plus twenty minutes of final evaluation per pocket, against eight minutes of inference for AdaFO. 100-pocket aggregate. Table 17 gives the baseline-to-AdaFO change with per-pocket stan- dard deviations. Mean Success Rate increases by 40.6 percentage points, and mean Vina improves by 1.40 kcal/mol. Figure 16 shows the paired pocket results, and Figure 17 shows their distributions. QED, normalized SA, and Diversity change by −0.03,−0.01, and−0.02, respectively. AdaFOablations. Onapilotpocket (BSD_ASPTE_1_130_0),Table18disables each of the three innovations. Removing mask annealing is most damaging (−1.2kcal/mol Vina,−8.4p SR): a fixed radius cannot both escape and settle. Removing MMR costs diversity without moving Vina; removing the elite filter roughly doubles run variance. Table 19 sweeps the reward weights:w q =w a =0.7is the smallest value that stops the refinement trading drug-likeness for affinity (QED rises+0.02instead of falling −0.04). Figure 18 shows the progress curve. MetricBaselineAdaFO∆ Vina (kcal/mol)↓ −7.36±1.14 −8.76±1.26 −1.40 High Affinity (%)↑53.5±37.485.1±31.7+31.6 Success Rate (%)↑30.2±31.070.8±40.7+40.6 QED↑0.734±0.0080.705±0.026 −0.029 SA (norm)↑0.844±0.0040.833±0.013 −0.011 Diversity↑0.838±0.0080.818±0.017 −0.020 Table 17: SBDD 100-pocket aggregate, mean±std across pockets, pretrained baseline versus five AdaFO iterations. 020406080100 Baseline pretrained SR (%) 0 20 40 60 80 100 EFO refined SR (%) Per-pocket SR uplift (n=100, mean = +40.6 p) Figure 16: Per-pocket Success Rate under AdaFO (y) versus the pretrained baseline (x). Each point represents one of the 100 evaluation pockets; the diagonal denotes equal success rates. 1110987654 Vina (kcal/mol) 0 2 4 6 8 10 12 14 # pockets baseline (mean=-7.36) EFO (mean=-8.76) 020406080100 High-Affinity fraction 0 10 20 30 40 50 60 70 baseline (mean=53.48) EFO (mean=85.09) 020406080100 Success Rate 0 10 20 30 40 50 baseline (mean=30.22) EFO (mean=70.77) 0.640.660.680.700.720.740.76 QED 0 5 10 15 20 25 baseline (mean=0.73) EFO (mean=0.70) 0.780.790.800.810.820.830.840.850.86 SA (norm) 0 5 10 15 20 25 30 baseline (mean=0.84) EFO (mean=0.83) 0.780.800.820.84 Diversity 0 5 10 15 20 baseline (mean=0.84) EFO (mean=0.82) CAGenMolv2 SBDD per-pocket distributions across 100 pockets 1110987654 Vina (kcal/mol) 0 2 4 6 8 10 12 14 # pockets baseline (mean=-7.36) EFO (mean=-8.76) 020406080100 High-Affinity fraction 0 10 20 30 40 50 60 70 baseline (mean=53.48) EFO (mean=85.09) 020406080100 Success Rate 0 10 20 30 40 50 baseline (mean=30.22) EFO (mean=70.77) 0.640.660.680.700.720.740.76 QED 0 5 10 15 20 25 baseline (mean=0.73) EFO (mean=0.70) 0.780.790.800.810.820.830.840.850.86 SA (norm) 0 5 10 15 20 25 30 baseline (mean=0.84) EFO (mean=0.83) 0.780.800.820.84 Diversity 0 5 10 15 20 baseline (mean=0.84) EFO (mean=0.82) CAGenMolv2 SBDD per-pocket distributions across 100 pockets 1110987654 Vina (kcal/mol) 0 2 4 6 8 10 12 14 # pockets baseline (mean=-7.36) EFO (mean=-8.76) 020406080100 High-Affinity fraction 0 10 20 30 40 50 60 70 baseline (mean=53.48) EFO (mean=85.09) 020406080100 Success Rate 0 10 20 30 40 50 baseline (mean=30.22) EFO (mean=70.77) 0.640.660.680.700.720.740.76 QED 0 5 10 15 20 25 baseline (mean=0.73) EFO (mean=0.70) 0.780.790.800.810.820.830.840.850.86 SA (norm) 0 5 10 15 20 25 30 baseline (mean=0.84) EFO (mean=0.83) 0.780.800.820.84 Diversity 0 5 10 15 20 baseline (mean=0.84) EFO (mean=0.82) CAGenMolv2 SBDD per-pocket distributions across 100 pockets 1110987654 Vina (kcal/mol) 0 2 4 6 8 10 12 14 # pockets baseline (mean=-7.36) EFO (mean=-8.76) 020406080100 High-Affinity fraction 0 10 20 30 40 50 60 70 baseline (mean=53.48) EFO (mean=85.09) 020406080100 Success Rate 0 10 20 30 40 50 baseline (mean=30.22) EFO (mean=70.77) 0.640.660.680.700.720.740.76 QED 0 5 10 15 20 25 baseline (mean=0.73) EFO (mean=0.70) 0.780.790.800.810.820.830.840.850.86 SA (norm) 0 5 10 15 20 25 30 baseline (mean=0.84) EFO (mean=0.83) 0.780.800.820.84 Diversity 0 5 10 15 20 baseline (mean=0.84) EFO (mean=0.82) CAGenMolv2 SBDD per-pocket distributions across 100 pockets 1110987654 Vina (kcal/mol) 0 2 4 6 8 10 12 14 # pockets baseline (mean=-7.36) EFO (mean=-8.76) 020406080100 High-Affinity fraction 0 10 20 30 40 50 60 70 baseline (mean=53.48) EFO (mean=85.09) 020406080100 Success Rate 0 10 20 30 40 50 baseline (mean=30.22) EFO (mean=70.77) 0.640.660.680.700.720.740.76 QED 0 5 10 15 20 25 baseline (mean=0.73) EFO (mean=0.70) 0.780.790.800.810.820.830.840.850.86 SA (norm) 0 5 10 15 20 25 30 baseline (mean=0.84) EFO (mean=0.83) 0.780.800.820.84 Diversity 0 5 10 15 20 baseline (mean=0.84) EFO (mean=0.82) CAGenMolv2 SBDD per-pocket distributions across 100 pockets 1110987654 Vina (kcal/mol) 0 2 4 6 8 10 12 14 # pockets baseline (mean=-7.36) EFO (mean=-8.76) 020406080100 High-Affinity fraction 0 10 20 30 40 50 60 70 baseline (mean=53.48) EFO (mean=85.09) 020406080100 Success Rate 0 10 20 30 40 50 baseline (mean=30.22) EFO (mean=70.77) 0.640.660.680.700.720.740.76 QED 0 5 10 15 20 25 baseline (mean=0.73) EFO (mean=0.70) 0.780.790.800.810.820.830.840.850.86 SA (norm) 0 5 10 15 20 25 30 baseline (mean=0.84) EFO (mean=0.83) 0.780.800.820.84 Diversity 0 5 10 15 20 baseline (mean=0.84) EFO (mean=0.82) CAGenMolv2 SBDD per-pocket distributions across 100 pockets Figure 17: Per-pocket metric distributions (grey: baseline; green: AdaFO). The Vina and Success-Rate distributions shift one-sidedly. 012345 EFO iteration 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Score ( -Vina + reg. ) EFO progress pilot pocket 0 (BSD_ASPTE_1_130_0 / 2z3h_A) best score in Top-K mean(Top-K) Figure 18: AdaFO score trajectory over iterations on the pilot pocket: best-in-pool climbs and mean-of-Top-K improves as the mask anneals. SettingVinaSR (%)Diversity Full AdaFO −8.5280.20.84 − annealing −7.3471.80.83 − MMR −8.4679.60.78 − elite −8.4876.40.82 Table 18: AdaFO innovation ablation on the pilot pocket, five iterations. w q =w a VinaSR (%)∆QED∆SA 0.0 −8.6282.4 −0.04 −0.02 0.3 −8.5583.1 −0.03 −0.01 0.7 −8.5280.2+0.02+0.00 Table 19: Reward-weight sweep on the pilot pocket;∆ relative to the pretrained baseline. C.5 Directional Property Editing Setup.50de-novo seeds per configuration are drawn at(τ,r) = (0.5, 0.5)and evaluated with RDKit for ground truth. For each of the twelve con- figurationsQED, SA, logP×+,−×0.5σ,σ we run AdaFO-S for three iterations with small, scaffold-preserving masksα ∈ [0.06, 0.20]. A directional success requires the realised value to move at least0.5∆in the requested direction; a scaffold-preserving success additionally requires Tanimoto to the seed≥ 0.20. The reward is the model’s own prediction; no external oracle is queried. The random-span baseline (confidence radius, random location) is the ablation. Sample efficiency (single edit).Table 21 isolates the effect of localisation: each seed takes exactly one forced edit and we ask only whether the prop- erty moved in the requested direction. A single saliency-guided edit succeeds 76.3% of the time versus 41.1% for random-span editing (mean over six axes, 60 seeds), winning all six, and produces a larger mean property change per step (|∆|=0.58σ vs0.28σ). Mean per-edit similarity is0.64for saliency guidance and0.79for random spans, char- acterizing the associated edit size. Full per-configuration results.Table 20 lists all twelve configurations under the full constrained protocol. The identity baseline scores0%every- where. Saliency guidance attains mean success of 61.2%versus57.8%, at mean similarities of0.67 and0.69, and matches or improves success in nine of twelve configurations. Figure 23 visualises the saliency signal; Figures 22 and 19 show worked examples and a trajectory. Figure 19: A three-iteration AdaFO-S trajectory decreasing logP from3.45to1.77while preserving the scaffold. Red marks the atoms changed at each step. qed up d0.5 qed up d1.0 qed down d0.5 qed down d1.0 sa up d0.5 sa up d1.0 sa down d0.5 sa down d1.0 logp up d0.5 logp up d1.0 logp down d0.5 logp down d1.0 0 20 40 60 80 100 SR_dir+sim (%) moved right direction Tan 0.20 46 40 49 76 7 63 61 50 98 92 67 97 57 41 52 66 9 54 69 50 98 93 73 99 PropOpt v2 single-property directional optimisation (N=100 seeds/config) propopt_random propopt_conf Figure 20: Auxiliary random-span experiment (100 seeds per configuration): confidence-guided versus uniform mask fractions. Saliency-guided small-mask results are reported separately in Table 20. Config Random-span SR/Sim AdaFO-S SR/Sim QED↑ 0.5σ34 / 0.8140 / 0.78 QED↑ 1.0σ28 / 0.7624 / 0.79 QED↓ 0.5σ44 / 0.7842 / 0.75 QED↓ 1.0σ66 / 0.6472 / 0.60 SA↑ 0.5σ8 / 0.9210 / 0.91 SA↑ 1.0σ56 / 0.7362 / 0.70 SA↓ 0.5σ56 / 0.5956 / 0.55 SA↓ 1.0σ48 / 0.5254 / 0.53 logP↑ 0.5σ98 / 0.60100 / 0.61 logP↑ 1.0σ86 / 0.5198 / 0.47 logP↓ 0.5σ70 / 0.7478 / 0.72 logP↓ 1.0σ100 / 0.6398 / 0.60 Mean57.8 / 0.6961.2 / 0.67 Table 20: Directional editing, all twelve configurations, small-mask regime (α ∈ [0.06, 0.20], 50 seeds). SR is the scaffold-preserving directional success rate (%); Sim is mean Tanimoto to the seed. Random-span is the former AdaFO-D (confidence radius, random location). DIR-only %|∆|/σSim AxisRandAdaFO-SRandAdaFO-SRandAdaFO-S QED↑12.533.30.210.500.820.65 QED↓32.781.20.270.740.810.64 SA↑51.191.40.330.440.790.67 SA↓29.859.10.310.670.760.58 logP↑47.9100.00.160.520.810.63 logP↓72.592.70.400.600.720.66 Mean41.176.30.280.580.790.64 Table 21: Single forced edit, direction-only success (60 seeds). One saliency-guided edit moves the property the correct way about twice as often as a random-span edit, and twice as far, at a modest similarity cost. 0.30.40.50.60.70.80.9 Sim(seed) mean Tanimoto to seed 20 40 60 80 100 SR_dir+sim (%) successful scaffold-preserving move PropOpt v2 Pareto view. Upper-right is the win region. qed sa logp =0.5 =1.0 propopt_random propopt_conf Figure 21: Auxiliary random-span experiment (100 seeds): success versus seed similarity for confidence-guided and uniform mask fractions. The saliency-guided results are reported separately in Table 20. Figure 22: Worked directional edits (QED up, SA down, logP up/down). Red marks the atoms changed relative to the seed; each is a local, chemically interpretable single-group modification that achieves the requested shift at high similarity. Figure 23: The model localises its own edit. Top: contrastive token saliencys i for a “raise logP” target; the model flags both protonated amines ([NH + ]) highest. Bottom: masking the flagged window and refilling under the target removes one amine, raising logP−0.83→ 2.07 at Tanimoto 0.69. C.6CRBN and VHL Candidate Prioritization Targets and generation. The two targets are cereblon (CRBN; PDB 4CI1, the DDB1–CRBN complex with thalidomide) and VHL (PDB 6GFZ, the VHL–Elongin B/C complex with ligand EXE) (Fischer et al., 2014; Testa et al., 2018). Three AdaFO iterations produce 200 candidates per target. The crystal ligands EF2 and EXE are reference compounds for the subsequent calcula- tions. The CRBN structure contains chicken CRBN and human DDB1; the VHL complex is human. Docking and structural filters. Candidates are screened for PAINS and reactive-group alerts. QED, raw SA, molecular weight, and logP are re- ported as descriptors. The raw SA scale runs from 1 (easier) to 10 (harder), whereas the CrossDocked ta- bles use normalized SA with the opposite direction. ECFP Tanimoto similarity is computed against the corresponding crystal ligand; Bemis–Murcko scaf- folds (Bemis and Murcko, 1996) identify repeated chemotypes. Docking uses QuickVina 2 (Alhossary et al., 2015), smina with the Vinardo scoring func- tion (Koes et al., 2013; Quiroga and Villarreal, 2016), and GNINA (McNutt et al., 2021). The recorded outputs comprise QuickVina and Vinardo energies, GNINA pose score and predicted affinity, and a standardized consensus score. The top 50 candidates per target by this consensus enter MD. Docking scores characterize the starting conforma- tions; the subsequent screening criteria measure trajectory-based contact retention and estimated binding energy. MD and M-GBSA protocol. Each selected candidate is simulated from its best docking pose with one 10-ns production trajectory. The supplied protocol uses amber99sb-ildn, TIP3P water, a do- decahedral box with 1.2-nm padding, 0.15-M NaCl, 310 K, and a V-rescale thermostat. M-GBSA usesigb = 5and samples every fifth frame. Com- plete free-energy results are available for 95 of the 100 candidates. Each crystal ligand is processed with the same protocol, yielding reference M- GBSA energies of−29.72kcal/mol for EF2 and −30.58 kcal/mol for EXE. Screening definitions.Buried-surface-area reten- tion is the mean BSA over the second half of the trajectory divided by the initial BSA. Polar-contact occupancy is the fraction of frames containing at least one protein N/O–ligand N/O distance≤ 3.5Å. This distance criterion uses no angular constraint, so it measures polar contacts rather than geometri- cally defined hydrogen bonds. Ligand heavy-atom RMSD is measured relative to the initial docking pose and averaged over the second half of the tra- jectory; it is reported as a descriptor rather than a selection threshold. Four binary criteria define the screening score: (1) BSA retention> 0.8; (2) polar-contact occu- pancy≥ 0.5; (3) M-GBSA∆G < 0; and (4) ∆G − ∆G ref ≤ 0. The source protocol names scores 4, 3, 2, and below 2 as strong, promising, weak, and poor. These labels denote computational screening categories. All 46 shortlisted candidates satisfy the first three criteria. Their reference- relative energy gaps are positive, so all belong to the promising category and none to strong. Shortlist characterization. The shortlist con- tains 25/50 MD-selected CRBN candidates and 21/50 VHL candidates, spanning 22 and 18 distinct scaffold strings. Every shortlisted molecule passes the recorded structural-alert filters. Median QED values are 0.706 and 0.607, with median raw SA values of 3.20 and 3.03. Their median reference similarities are 0.141 and 0.116, indicating chem- ical distance from the two reference compounds. This is a reference-relative comparison, not a nov- elty assessment against all known ligands. The best CRBN and VHL M-GBSA values are −26.73and−27.01kcal/mol, respectively; their gaps to the reference energies are+2.99and+3.57 kcal/mol. Across the shortlist, median energies are −20.48and−19.50kcal/mol. Median BSA reten- tions of 0.947 and 0.901 and polar-contact occu- pancies of 0.82 and 0.80 summarize the retained intermolecular contacts. These observations sup- port prioritizing chemically distinct candidates for follow-up characterization. The short simulations and single replicas define an initial screening stage. Candidate-level data. Tables 22 and 23 retain the candidate identifiers from the supplied result table. The accompanyingdata/candidates.csv includes molecular and scaffold SMILES, docking scores, all descriptors, structural-alert flags, and MD metrics. RMSD is available for 13/25 short- listed CRBN candidates and all 21 VHL candidates; missing entries are kept missing. All shortlist medi- ans are computed from the 46 supplied rows. The counts of 200 generated and 50 selected per target, and 95 completed free-energy calculations overall, describe earlier stages of the supplied protocol. ID∆G∆G− ∆G ref BSAPolar contactRMSDRef. sim.QEDRaw SA 11-26.732.990.9920.958.10.1430.6483.89 2-24.135.591.040.9611.180.1430.7542.67 10-24.125.60.9870.8913.480.1450.7633.24 22-22.527.20.970.699.020.150.7483.19 25-22.527.20.9960.91—0.1290.9222.92 29-21.787.940.8730.82—0.1430.8263.46 9-21.628.11.0430.9911.940.090.5342.68 19-21.288.440.9010.787.610.1180.8713.82 34-218.721.0080.83—0.1320.9073.2 49-20.968.760.9070.63.560.080.4393.89 17-20.948.780.9210.8312.960.1510.573.67 20-20.758.970.9790.956.990.1270.6813.48 5-20.489.240.8840.739.840.1490.6682.94 37-20.389.340.9010.73—0.0810.6783.83 44-19.2110.510.9570.74—0.1410.7893.6 3-18.611.120.9780.97.380.1250.8793.56 26-18.611.120.9470.71—0.1450.7293.45 38-18.2311.490.8450.7—0.1310.5342.56 28-17.7112.010.9060.61—0.1410.6733.57 27-17.6212.10.8211—0.1410.5353.09 1-17.4112.310.9220.7410.640.0940.7462.31 41-14.415.320.8180.8717.120.1690.8382.98 42-13.6516.070.9940.85—0.1290.682.71 36-13.516.220.8460.75—0.1450.3832.93 15-13.1616.561.0060.8—0.1290.7063.13 Table 22: CRBN shortlist. Energies are in kcal/mol; RMSD is in Å. BSA is retained fraction, polar contact is frame occupancy, and reference similarity is ECFP Tanimoto. Missing RMSD entries are denoted by dashes. ID∆G∆G− ∆G ref BSAPolar contactRMSDRef. sim.QEDRaw SA 35-27.013.570.9340.993.410.1050.5583.09 13-26.693.890.9530.944.260.1330.7293.17 6-25.155.430.8890.983.380.1020.7712.92 4-24.36.280.87614.370.1240.5033.04 40-23.896.690.9010.993.890.1080.7452.23 23-22.568.021.0430.794.440.1190.4394.12 5-22.488.10.9140.973.490.0980.4372.6 27-22.478.110.9220.555.580.1050.5153.13 19-21.628.960.950.982.870.0970.6073.01 43-19.9110.670.8430.585.840.1160.7573.78 29-19.511.080.8120.646.570.1390.5573.56 24-18.5612.020.820.744.740.1490.7922.75 3-18.2312.350.91614.830.080.7343.08 18-17.4513.130.8470.78130.1410.82.96 17-16.9113.670.870.5812.390.1190.3553.03 20-16.6413.940.9130.86.630.0970.6073.02 9-14.416.180.8730.545.750.0910.4862.44 8-14.2916.290.8130.727.220.1350.5583.41 11-10.7119.870.890.914.980.1190.5292.97 10-9.8720.710.97314.980.0910.7032.36 26-7.9922.591.030.723.040.1370.7383.15 Table 23: VHL shortlist. Energies are in kcal/mol; RMSD is in Å. BSA is retained fraction, polar contact is frame occupancy, and reference similarity is ECFP Tanimoto. Missing RMSD entries are denoted by dashes. Figure 24: Six CRBN candidates selected by ascending M-GBSA energy while retaining distinct scaffold strings. Structures are rendered directly from the supplied SMILES. Each label gives the original candidate ID, M-GBSA energy (kcal/mol), and ECFP similarity to EF2. All 25 shortlisted candidates are listed in Table 22 and the accompanying CSV. Figure 25: Six VHL candidates selected by ascending M-GBSA energy with distinct scaffold strings, rendered from the supplied SMILES. Labels give the original ID, M-GBSA energy (kcal/mol), and ECFP similarity to EXE. All 21 shortlisted candidates are listed in Table 23 and the accompanying CSV. C.7 Compute and Environmental Cost The reported pretraining run uses four A6000 GPUs for approximately 350 device-hours. Gen- eration and editing evaluations use a single RTX 4070 Ti; representative timings are about nine min- utes for a batch of 100 de-novo molecules and eight minutes for one AdaFO pocket pass. These timings describe the model and docking workflow. The new case study additionally selects 100 candidates for 10-ns production MD each; its simulation cost is separate from the model evaluation timings.

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