Multigrid Training for Molecular Generation using Graph Neural Networks

Molecular graph generation (MGG) is essentially a multi-class generative task, aimed at predicting categories of atoms and bonds under strict chemical and structural constraints. However, many prevailing diffusion paradigms learn to regress numerical embeddings and rely on a hard discretization rule during sampling to recover discrete labels. This introduces a fundamental discrepancy between training and sampling. While models are trained for point-wise numerical fidelity, the sampling process fundamentally relies on crossing categorical decision boundaries. This discrepancy forces the model to expend efforts on intra-class variations that become irrelevant after discretization, ultimately compromising diversity, structural statistics, and generalization performance. Therefore, we propose TopBF, a unified framework that (i) performs MGG directly in continuous parameter distributions, (ii) learns graph-topological understanding through a Quasi-Wasserstein optimal-transport coupling under geodesic costs, and (iii) supports controllable, property-conditioned generation during sampling without retraining the base model. TopBF innovatively employs cumulative distribution function (CDF) to compute category probabilities induced by the Gaussian channel, thereby unifying the training objective with the sampling discretization operation. Experiments on QM9 and ZINC250k demonstrate superior structural fidelity and efficient generation with improved performance.

Three-dimensional (3D) molecule generation has been dominated by diffusion models, which achieve strong generation quality but typically require the molecular size to be specified a priori. Recent autoregressive approaches have substantially narrowed the performance gap while naturally supporting variable-length generation and conditioning on partial molecular context. However, balancing unconditional and context-conditioned generation remains challenging. We introduce KRONOS, a latent autoregressive diffusion framework that generates molecules in the latent space of a pre-trained autoencoder, jointly modeling molecular graph topology and geometry, while retaining the flexibility of autoregressive generation. We further introduce a mixed training strategy inspired by Fill-in-the Middle (FIM) paradigm, enabling both unconditional and fragment-conditioned molecular generation within a single left-to-right autoregressive model. Experiments on QM9 and GEOM-Drugs demonstrate that KRONOS achieves leading unconditional generation performance among autoregressive methods, while remaining competitive with diffusion models. Moreover, fragment-conditioned generation is achieved with negligible impact on unconditional generation performance, demonstrating that both generation paradigms can be supported within a single architecture.

De novo molecular generation from tandem mass spectra is a challenging inverse problem whose core difficulty lies in the circular dependency between atom-level and bond-level reasoning: determining a bond's type requires knowing its endpoint atoms' chemical environment, yet an atom's environment is in turn defined by its incident bonds. Existing graph diffusion methods process atoms and bonds within a single computation stream, where atom-bond information synchronization can only occur implicitly across layers. We argue that this single-stream paradigm, rather than the choice of any particular aggregation kernel, is a key architectural bottleneck. We propose DualLGD (Dual-stream Line Graph Diffusion), which reformulates molecular graph denoising as the alternating solution of two coupled subproblems: atom-level reasoning and bond-level reasoning, each operating in its own dedicated representation space. The line graph provides a natural mathematical construction for the bond space, in which bond angles, dihedrals, conjugation chains, and rings correspond to local topological motifs between bonds. Incidence-constrained bidirectional cross-attention synchronizes the two streams at every layer, ensuring that each atom attends only to its incident bonds and vice versa, respecting the fundamental chemical principle that an atom's environment is determined by its bonding context. On the NPLIB1 and MassSpecGym benchmarks, DualLGD achieves top-1 accuracy of 34.37% and 23.89%, approximately $3\times$ the previous state of the art. Ablation studies confirm the architecture as the primary source of improvement: DualLGD without any pre-training already surpasses the previous best fully pretrained model.