Predicting single-cell perturbation outcomes directly advances gene function analysis and facilitates drug candidate selection, making it a key driver of both basic and translational biomedical research. However, a major bottleneck in this task is the unpaired nature of single-cell data, as the same cell cannot be observed both before and after perturbation due to the destructive nature of sequencing. Although some neural generative transport models attempt to tackle unpaired single-cell perturbation data, they either lack explicit conditioning or depend on prior spaces for indirect distribution alignment, limiting precise perturbation modeling. In this work, we approximate Schrödinger Bridge (SB), which defines stochastic dynamic mappings recovering the entropy-regularized optimal transport (OT), to directly align the distributions of control and perturbed single-cell populations across different perturbation conditions. Unlike prior SB approximations that rely on bidirectional modeling to infer optimal source-target sample coupling, we leverage Minibatch-OT based pairing to avoid such bidirectional inference and the associated ill-posedness of defining the reverse process. This pairing directly guides bridge learning, yielding a scalable approximation to the SB. We approximate two SB models, one modeling discrete gene activation states and the other continuous expression distributions. Joint training enables accurate perturbation modeling and captures single-cell heterogeneity. Experiments on public genetic and drug perturbation datasets show that our model effectively captures heterogeneous single-cell responses and achieves state-of-the-art performance.

Graph Transformer has demonstrated impressive capabilities in the field of graph representation learning. However, existing approaches face two critical challenges: (1) most models suffer from exponentially increasing computational complexity, making it difficult to scale to large graphs; (2) attention mechanisms based on node-level operations limit the flexibility of the model and result in poor generalization performance in out-of-distribution (OOD) scenarios. To address these issues, we propose VecFormer (the Vec tor Quantized Graph Transformer ), an efficient and highly generalizable model for node classification, particularly under OOD settings. VecFormer adopts a two-stage training paradigm. In the first stage, two codebooks are used to reconstruct the node features and the graph structure, aiming to learn the rich semantic Graph Codes. In the second stage, attention mechanisms are performed at the Graph Token level based on the transformed cross codebook, reducing computational complexity while enhancing the model's generalization capability. Extensive experiments on datasets of various sizes demonstrate that VecFormer outperforms the existing Graph Transformer in both performance and speed.

Antibodies are Y-shaped proteins that protect the host by binding to specific antigens, and their binding is mainly determined by the Complementary Determining Regions (CDRs) in the antibody. Despite the great progress made in CDR design, existing computational methods still encounter several challenges: 1) poor capability of modeling complex CDRs with long sequences due to insufficient contextual information; 2) conditioned on pre-given antigenic epitopes and their static interaction with the target antibody; 3) neglect of specificity during antibody optimization leads to non-specific antibodies. In this paper, we take into account a variety of node features, edge features, and edge relations to include more contextual and geometric information. We propose a novel Relation-Aware Antibody Design (RAAD) framework, which dynamically models antigen-antibody interactions for co-designing the sequences and structures of antigen-specific CDRs. Furthermore, we propose a new evaluation metric to better measure antibody specificity and develop a contrasting specificity-enhancing constraint to optimize the specificity of antibodies. Extensive experiments have demonstrated the superior capability of RAAD in terms of antibody modeling, generation, and optimization across different CDR types, sequence lengths, pre-training strategies, and input contexts.

Score Distillation Sampling (SDS) has been successfully extended to text-driven 3D scene editing with 2D pretrained diffusion models. However, SDS-based editing methods suffer from lengthy optimization processes with slow inference and low quality. We attribute the issue of lengthy optimization to the stochastic optimization scheme used in SDS-based editing, where many steps may conflict with each other (e.g., the inherent trade-off between editing and preservation). To reduce this internal conflict and speed up the editing process, we propose to separate editing and preservation in time with a diffusion time schedule and frame the 3D editing optimization process as a diffusion bridge sampling process. Motivated by the analysis above, we introduce DaCapo, a fast diffusion sampling-like 3D editing method that incorporates a novel stacked bridge framework, which estimates a direct diffusion bridge between source and target distribution with only a pretrained 2D diffusion model. Specifically, It models the editing process as a combination of inversion and generation, where both processes happen simultaneously as a stack of Diffusion Bridges. DaCapo shows a 15× speed-up with comparable results to the state-of-the-art SDS-based method. It completes the process in just 2,500 steps on a single GPU and accommodates a variety of 3D representation methods.

Motif-scaffolding is a fundamental component of protein design, which aims to construct the scaffold structure that stabilizes motifs conferring desired functions. Recent advances in generative models are promising for designing scaffolds, with two main approaches: training-based and sampling-based methods. Training-based methods are resource-heavy and slow, while training-free sampling-based methods are flexible but require numerous sampling steps and costly, unstable guidance. To speed up and improve sampling-based methods, we analyzed failure cases and found that errors stem from the trade-off between generation and guidance. Thus we proposed to exploit the spatial context and adjust the generative direction to be consistent with guidance to overcome this trade-off. Motivated by this, we formulate motif-scaffolding as a Geometric Inverse Design task inspired by the image inverse problem, and present Evolution-ViA-reconstruction (EVA), a novel sampling-based coupled flow framework on geometric manifolds, which starts with a pretrained flow-based generative model. EVA uses motif-coupled priors to leverage spatial contexts, guiding the generative process along a straighter probability path, with generative directions aligned with guidance in the early sampling steps. EVA is 70× faster than SOTA model RFDiffusion with competitive and even better performance on benchmark tests. Further experiments on real-world cases including vaccine design, multi-motif scaffolding and motif optimal placement searching demonstrate EVA's superior efficiency and effectiveness.

To bridge the gaps between powerful Graph Neural Networks (GNNs) and lightweight Multi-Layer Perceptron (MLPs), GNN-to-MLP Knowledge Distillation (KD) proposes to distill knowledge from a well-trained teacher GNN into a student MLP. In this paper, we revisit the knowledge samples (nodes) in teacher GNNs from the perspective of hardness, and identify that hard sample distillation may be a major performance bottleneck of existing graph KD algorithms. The GNN-to-MLP KD involves two different types of hardness, one student-free knowledge hardness describing the inherent complexity of GNN knowledge, and the other student-dependent distillation hardness describing the difficulty of teacher-to-student distillation. However, most of the existing work focuses on only one of these aspects or regards them as one thing. This paper proposes a simple yet effective Hardness-aware GNN-to-MLP Distillation (HGMD) framework, which decouples the two hardnesses and estimates them using a non-parametric approach. Finally, two hardness-aware distillation schemes (i.e., HGMD-weight and HGMD-mixup) are further proposed to distill hardness-aware knowledge from teacher GNNs into the corresponding nodes of student MLPs. As non-parametric distillation, HGMD does not involve any additional learnable parameters beyond the student MLPs, but it still outperforms most of the state-of-the-art competitors. HGMD-mixup improves over the vanilla MLPs by 12.95% and outperforms its teacher GNNs by 2.48% averaged over seven real-world datasets. Codes will be made public at https://github.com/LirongWu/HGMD.

To mitigate the computational complexity in the self-attention mechanism on long sequences, linear attention utilizes computation tricks to achieve linear complexity, while state space models (SSMs) popularize a favourable practice of using non-data-dependent memory pattern, i.e., emphasize the near and neglect the distant, to processing sequences. Recent studies have shown the priorities by combining them as one. However, the efficiency of linear attention remains only at the theoretical level in a causal setting, and SSMs require various designed constraints to operate effectively on specific data. Therefore, in order to unveil the true power of the hybrid design, the following two issues need to be addressed: (1) hardware-efficient implementation for linear attention and (2) stabilization of SSMs. To achieve this, we leverage the thought of tiling and hierarchy to propose CHELA (short-long Convolutions with Hardware-Efficient Linear Attention), which replaces SSMs with short-long convolutions and implements linear attention in a divide-and-conquer manner. This approach enjoys global abstraction and data-dependent selection from stable SSM and linear attention while maintaining real linear complexity. Our comprehensive experiments on the Long Range Arena benchmark and language modeling tasks demonstrate the effectiveness of the proposed method.

Increasing works for antibody design are emerging to generate sequences and structures in Complementarity Determining Regions (CDRs), but problems still exist. We focus on two of them: (i) authenticity of the generated structure and (ii) rationality of the affinity maturation, and propose GeoAB as a solution. In specific, GeoAB-Designergenerates CDR structures with realistic internal geometries, composed of a generative geometry initializer (Geo-Initializer) and a position refiner (Geo-Refiner); GeoAB-Optimizer achieves affinity maturation by accurately predicting both the mutation effects and structures of mutant antibodies with the same network architecture as Geo-Refiner. Experiments show that GeoAB achieves state-of-the-art performance in CDR co-design and mutation effect predictions, and fulfills the discussed tasks effectively.

In recent years, AI-assisted drug design methods have been proposed to generate molecules given the pockets' structures of target proteins. Most of them are {\em atom-level-based} methods, which consider atoms as basic components and generate atom positions and types. In this way, however, it is hard to generate realistic fragments with complicated structures. To solve this, we propose \textsc{D3FG}, a {\em functional-group-based} diffusion model for pocket-specific molecule generation and elaboration. \textsc{D3FG} decomposes molecules into two categories of components: functional groups defined as rigid bodies and linkers as mass points. And the two kinds of components can together form complicated fragments that enhance ligand-protein interactions. To be specific, in the diffusion process, \textsc{D3FG} diffuses the data distribution of the positions, orientations, and types of the components into a prior distribution; In the generative process, the noise is gradually removed from the three variables by denoisers parameterized with designed equivariant graph neural networks. In the experiments, our method can generate molecules with more realistic 3D structures, competitive affinities toward the protein targets, and better drug properties. Besides, \textsc{D3FG} as a solution to a new task of molecule elaboration, could generate molecules with high affinities based on existing ligands and the hotspots of target proteins.