Generative modeling of crystal data distribution is an important yet challenging task due to the unique periodic physical symmetry of crystals. Diffusion-based methods have shown early promise in modeling crystal distribution. More recently, Bayesian Flow Networks were introduced to aggregate noisy latent variables, resulting in a variance-reduced parameter space that has been shown to be advantageous for modeling Euclidean data distributions with structural constraints (Song et al., 2023). Inspired by this, we seek to unlock its potential for modeling variables located in non-Euclidean manifolds e.g. those within crystal structures, by overcoming challenging theoretical issues. We introduce CrysBFN, a novel crystal generation method by proposing a periodic Bayesian flow, which essentially differs from the original Gaussian-based BFN by exhibiting non-monotonic entropy dynamics. To successfully realize the concept of periodic Bayesian flow, CrysBFN integrates a new entropy conditioning mechanism and empirically demonstrates its significance compared to time-conditioning. Extensive experiments over both crystal ab initio generation and crystal structure prediction tasks demonstrate the superiority of CrysBFN, which consistently achieves new state-of-the-art on all benchmarks. Surprisingly, we found that CrysBFN enjoys a significant improvement in sampling efficiency, e.g., ~100x speedup 10 v.s. 2000 steps network forwards) compared with previous diffusion-based methods on MP-20 dataset. Code is available at https://github.com/wu-han-lin/CrysBFN.

Generative models for structure-based drug design (SBDD) have shown promising results in recent years. Existing works mainly focus on how to generate molecules with higher binding affinity, ignoring the feasibility prerequisites for generated 3D poses and resulting in false positives. We conduct thorough studies on key factors of ill-conformational problems when applying autoregressive methods and diffusion to SBDD, including mode collapse and hybrid continuous-discrete space. In this paper, we introduce MolCRAFT, the first SBDD model that operates in the continuous parameter space, together with a novel noise reduced sampling strategy. Empirical results show that our model consistently achieves superior performance in binding affinity with more stable 3D structure, demonstrating our ability to accurately model interatomic interactions. To our best knowledge, MolCRAFT is the first to achieve reference-level Vina Scores (-6.59 kcal/mol) with comparable molecular size, outperforming other strong baselines by a wide margin (-0.84 kcal/mol). Code is available at https://github.com/AlgoMole/MolCRAFT.

Advanced generative model (e.g., diffusion model) derived from simplified continuity assumptions of data distribution, though showing promising progress, has been difficult to apply directly to geometry generation applications due to the multimodality and noise-sensitive nature of molecule geometry. This work introduces Geometric Bayesian Flow Networks (GeoBFN), which naturally fits molecule geometry by modeling diverse modalities in the differentiable parameter space of distributions. GeoBFN maintains the SE-(3) invariant density modeling property by incorporating equivariant inter-dependency modeling on parameters of distributions and unifying the probabilistic modeling of different modalities. Through optimized training and sampling techniques, we demonstrate that GeoBFN achieves state-ofthe-art performance on multiple 3D molecule generation benchmarks in terms of generation quality (90.87% molecule stability in QM9 and 85.6% atom stability in GEOM-DRUG For example, proteins can be represented as proximity spatial graphs (Jing et al., 2021) and molecules as atomic graphs in 3D (Schütt et al., 2017). Most recently, inspired by the huge success of diffusion model (DM) in image generation Figure 1: The framework of GeoBFN Meng et al. (2022); Ho et al. (2020) However, two major challenges remain in directly applying DM to molecule geometry: multi-modality and noise sensitivity. The multi-modality issue refers to the dependency on diverse data forms to effectively depict the atomic-level geometry of a molecule.

The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in generating feature-rich geometries. However, existing DMs typically suffer from unstable probability dynamics with inefficient sampling speed. In this paper, we introduce geometric flow matching, which enjoys the advantages of both equivariant modeling and stabilized probability dynamics. More specifically, we propose a hybrid probability path where the coordinates probability path is regularized by an equivariant optimal transport, and the information between different modalities is aligned. Experimentally, the proposed method could consistently achieve better performance on multiple molecule generation benchmarks with 4.75$\times$ speed up of sampling on average.

Generating desirable molecular structures in 3D is a fundamental problem for drug discovery. Despite the considerable progress we have achieved, existing methods usually generate molecules in atom resolution and ignore intrinsic local structures such as rings, which leads to poor quality in generated structures, especially when generating large molecules. Fragment-based molecule generation is a promising strategy, however, it is nontrivial to be adapted for 3D non-autoregressive generations because of the combinational optimization problems. In this paper, we utilize a coarse-to-fine strategy to tackle this problem, in which a Hierarchical Diffusion-based model (i.e.~HierDiff) is proposed to preserve the validity of local segments without relying on autoregressive modeling. Specifically, HierDiff first generates coarse-grained molecule geometries via an equivariant diffusion process, where each coarse-grained node reflects a fragment in a molecule. Then the coarse-grained nodes are decoded into fine-grained fragments by a message-passing process and a newly designed iterative refined sampling module. Lastly, the fine-grained fragments are then assembled to derive a complete atomic molecular structure. Extensive experiments demonstrate that HierDiff consistently improves the quality of molecule generation over existing methods

A lot of natural language processing problems need to encode the text sequence as a fix-length vector, which usually involves aggregation process of combining the representations of all the words, such as pooling or self-attention. However, these widely used aggregation approaches did not take higher-order relationship among the words into consideration. Hence we propose a new way of obtaining aggregation weights, called eigen-centrality self-attention. More specifically, we build a fully-connected graph for all the words in a sentence, then compute the eigen-centrality as the attention score of each word. The explicit modeling of relationships as a graph is able to capture some higher-order dependency among words, which helps us achieve better results in 5 text classification tasks and one SNLI task than baseline models such as pooling, self-attention and dynamic routing. Besides, in order to compute the dominant eigenvector of the graph, we adopt power method algorithm to get the eigen-centrality measure. Moreover, we also derive an iterative approach to get the gradient for the power method process to reduce both memory consumption and computation requirement.}