Coarse-to-Fine Autoregression over Hierarchical Discrete Codes for Molecular Graph Generation

Molecular graph generation typically involves a trade-off between two paradigms: diffusion models capture global structure well but require hundreds of denoising steps, while autoregressive (AR) models sample in a single pass yet generate atoms in a flat canonical order with no semantic hierarchy, leaving long-range topology to chance. We introduce the **Hierarchical Graph VQ-Transformer (H-GVT)**, which removes this dichotomy by performing coarse-to-fine AR generation over hierarchical discrete codes. A **Spectrally-Regularized Multi-Scale VQ-VAE** first compresses each molecule into a sequence of discrete tokens at multiple scales, where coarse tokens provide regularized low-resolution structural context and fine tokens encode atom-level details. The compression combines Adaptive Min-Cut Pooling with a novel **Spectral Topology Consistency Loss** that aligns low-frequency normalized Laplacian spectra across scales, adding only 2.8% training overhead. A standard decoder-only Transformer with level embeddings then generates these tokens from coarse to fine, allowing fine-grained atom tokens to condition on coarser structural context. This requires no specialized tree, motif, or scale-causal masking. On QM9 and ZINC250k, H-GVT achieves the best NSPDK among compared baselines ($2\times10^{-4}$ on QM9 and $1\times10^{-4}$ on ZINC250k), while sampling 10K molecules $68\times$ faster than DiGress. On MOSES, H-GVT achieves $4.8\times$ better FCD than a Novelty-thresholded GVT baseline under the same thresholded protocol (0.19 vs. 0.92; 86.4% vs. 80.5% Novelty). Crucially, ablations reveal that the coarse-to-fine ordering itself, not merely multi-scale tokenization, is what enables global structural planning: randomizing the order while keeping the same tokens, codebook, and level embeddings degrades NSPDK by $29\times$.