Hierarchy-Guided Topology Latent Flow for Molecular Graph Generation

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.

Modern graph generative models typically operate directly in the discrete graph space, explicitly generating node and edge variables, which can become costly as graphs grow. In this paper, we perform generation explicitly on latent representations of entire graphs obtained from a pretrained Variational Autoencoder with high reconstruction fidelity. The generated representations, obtained through flow matching, are then decoded only at the final step. Across molecular benchmarks of increasing size, our approach achieves strong validity and FCD while offering a favorable quality-efficiency trade-off compared with state-of-the-art explicit graph generative models. One of the main advantages of this formulation is that the graph representation only needs to be learned once, after which the same one can be reused across multiple generative objectives without retraining. We demonstrate generation guided by molecular properties and further introduce validity-aware generation though a classifier learned directly in latent space. All code will be made available upon acceptance.

Latent diffusion is a promising framework for scalable 3D molecular generation, but it requires a latent space that remains smooth, valid, and navigable beyond posterior samples. Existing molecular VAEs, however, are typically learned through reconstruction-based objectives, which do not guarantee such a latent space. We show that this leads to dark areas: regions of latent space that are reachable during diffusion sampling but decode to disconnected or chemically invalid molecules. Unlike in image generation, molecular decoding requires strict structural and chemical precision, so even small latent perturbations can produce catastrophic failures. We therefore propose TopVAE, a topology-optimized VAE that reduces dark areas by making the decoder internalize structural and chemical constraints during training, eliminating the need for test-time chemical correction. TopVAE greatly improves off-posterior robustness, and when paired with a standard DiT, achieves $77\%$ lower FCD-3D on QM9, the highest V&C, $52\%$ lower FCD-3D on GEOM-Drugs, and $1.29{\times}$ more stable and connected molecules on zero-shot scaffold inpainting.