Hierarchy-Guided Topology Latent Flow for Molecular Graph Generation

Urvi Awasthi; Alexander Arjun Lobo; Leonid Zhukov

cs.LGMar 28, 2026

Hierarchy-Guided Topology Latent Flow for Molecular Graph Generation

Authors: Urvi Awasthi, Alexander Arjun Lobo, Leonid Zhukov

Organizations: BCG X AI Science Institute

Abstract

Generating chemically valid 3D molecules is hindered by discrete bond topology: small local bond errors can cause global failures (valence violations, disconnections, implausible rings), especially for drug-like molecules with long-range constraints. Many unconditional 3D generators emphasize coordinates and then infer bonds or rely on post-processing, leaving topology feasibility weakly controlled. We propose Hierarchy-Guided Latent Topology Flow (HLTF), a planner-executor model that generates bond graphs with 3D coordinates, using a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures. On QM9, HLTF achieves 98.8% atom stability and 92.9% valid-and-unique, improving PoseBusters validity to 94.0% (+0.9 over the strongest reported baseline). On GEOM-DRUGS, HLTF attains 85.5%/85.0% validity/valid-unique-novel without post-processing and 92.2%/91.2% after standardized relaxation, within 0.9 points of the best post-processed baseline. Explicit topology generation also reduces "false-valid" samples that pass RDKit sanitization but fail stricter checks.

Figures & tables

Figure 1: HLTF: Planner–Executor–Geometry Pipeline.

Figure 2: Leaf-anchored hierarchy conditioning.

Table 1: QM9 results. (a) Unconditional generation; (b) novelty and PoseBusters validity. Baselines reproduced from GCDM Table 1 Morehead and Cheng (2023) . Arrows

\uparrow/\downarrow

indicate whether higher/lower is better. Asterisk * denotes best; underline denotes second best.

Method	Valid (%)	V&U (%)	V&U&N (%)
EQGAT-diff	59.7	59.7	59.5
+PP	84.2	84.2	84.0
FlowMol	59.8	59.8	59.7
+PP	84.2	84.2	84.1
GCDM	0.2	0.2	0.2
+PP	95.2	95.2	95.2

Table 2: GEOM-DRUGS success rates. “PP” denotes standardized post-processing Buttenschoen et al. (2025) . Asterisk * denotes the best value in the category and underline denotes the second best.

Variant	QM9 V&U	QM9 PB	GEOM V&U&N	GEOM V&U&N+PP
Post-hoc geometry (graph then coords)	92.4	91.9	82.0	90.6
Joint geometry (default)	93.2	92.4	85.0	91.2
Probability-space + projection	91.6	90.9	77.0	88.2
Logit-space (default)	93.2	92.4	85.0	91.2
No planning (null plan)	90.8	91.0	76.0	88.5
Teacher-only plan (train-time only)	91.4	91.5	78.5	89.2

Table 3: Ablations (HLTF only).

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Sweep	$\eta_{\text{chem},0}$	$\eta_{\text{cons},0}$	$\eta_{\text{geom},0}$	V&U&N (%)	V&U&N+PP (%)
Default	1.0	0.5	0.2	85.0	91.2
$\eta_{\text{chem},0}$ sweep	0.5	0.5	0.2	83.2	90.8
$\eta_{\text{chem},0}$ sweep	2.0	0.5	0.2	85.7	91.3
$\eta_{\text{cons},0}$ sweep	1.0	0.2	0.2	84.4	91.1
$\eta_{\text{cons},0}$ sweep	1.0	1.0	0.2	84.8	91.0
$\eta_{\text{geom},0}$ sweep	1.0	0.5	0.1	84.5	91.1

Appendix

Table 4: Sensitivity to guidance amplitudes. One-at-a-time sweeps of base amplitudes (schedule shape fixed).

Variant	Valence (%)	Disconn. (%)	Ring/arom. (%)	Geometry (%)
No energy guidance	40	35	15	10
+ $E_{\text{chem}}$	18	20	10	52
+ $E_{\text{chem}}+E_{\text{cons}}$	14	12	8	66

Appendix

Table 5: Invalidity cause breakdown. Percentages among invalid samples.

Molecular Graph Generation

Molecular graph generation creates new chemically plausible molecules as graphs of atoms and bonds, often guided by desired properties or structures.

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3D Molecular Generation Molecular Generation Flow-Based Generative Modeling

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Molecular size is intrinsically linked to composition, structure, and properties, but most 3D molecular generators treat size as a predefined input rather than a quantity to be generated. We introduce Equivariant-Free Transformer-Autoencoded Latent Flow Matching, a two-stage framework that samples a fixed-dimensional latent vector using flow matching and employs an autoregressive Transformer to determine molecular size, atom types, coordinates, and chemical attributes. Canonical atom ordering and rigid-pose alignment enable Transformers without equivariant layers, while decoded attributes guide bond reconstruction. On PCQM4Mv2, unconditional generation yields 87.9% unique and novel molecules passing sanitization and PoseBusters checks, exceeding baselines with lower end-to-end training and sampling time and higher end-to-end throughput. Across ten target HOMO-LUMO gaps, internal ranking retains 30% of the screened candidates and increases the density functional theory-verified hit rate within 0.1 eV of the target from 25.0% to 52.4%, while largely preserving novelty and diversity. These results demonstrate fixed-dimensional latent generation with autoregressive decoding as a practical approach to molecular design without prespecifying size.

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