Structure-Based Drug Design (SBDD) has emerged as a popular approach in drug discovery, leveraging three-dimensional protein structures to generate drug ligands. However, existing generative models encounter several key challenges: (1) Incorporating boundary condition constraints, (2) Integrating hierarchical structural conditions and (3) Ensuring spatial modeling fidelity. To overcome these limitations, we propose SculptDrug, a spatial condition-aware generative model based on Bayesian Flow Networks (BFNs). First, SculptDrug follows a BFNs-based framework and employs a progressive denoising strategy to ensure spatial modeling fidelity, iteratively refining atom positions while enhancing local interactions for precise spatial alignment. Second, we introduce the Boundary Awareness Block, which incorporates protein surface constraints into the generative process to ensure that the generated ligands are geometrically compatible with the target protein. Finally, we design a Hierarchical Encoder that captures global structural context while preserving fine-grained molecular interactions, ensuring overall consistency and accurate ligand-protein conformations. We evaluate SculptDrug on the CrossDocked dataset, and experimental results demonstrate that SculptDrug outperforms state-of-the-art baselines, proving the efficacy of spatial condition-aware modeling.

In real-world web applications, especially those involving sensor networks and Internet of Things (IoT) devices, time series data are often incomplete due to network delays, device failures or logging constraints. Such missing data can severely affect downstream tasks including anomaly detection, recommendation, and A/B testing, making imputation a critical step for reliable web analytics. Diffusion models have recently achieved strong performance for time series imputation. As relevant research progresses, the spectral nature of time series has received increasing attention. However, most ''frequency-aware'' diffusion variants modify either the input or network architecture, but the variance schedule in the forward process remains unchanged, injecting noise with the same variance into every frequency bin. This limitation prevents diffusion from adapting to real data, where spectral energy varies irregularly across frequencies rather than following a simple high–low split. To address these issues, we propose Frequency-Shaped Diffusion (FSDI), which replaces the uniform variance schedule with a data-driven schedule in the frequency domain. Frequency bin variances are estimated from the spectral energy distribution of the data, allocated as inverses of that energy, and then Parseval-calibrated so the total noise energy exactly matches standard diffusion, preserving training stability and ensuring fair comparison. Experiments on real-world datasets demonstrate that FSDI achieves state-of-the-art performance. All code have been made publicly at https://github.com/decisionintelligence/FSDI.

Probabilistic time series imputation has been widely applied in real-world scenarios due to its ability for uncertainty estimation and denoising diffusion probabilistic models (DDPMs) have achieved great success in probabilistic time series imputation tasks with its power to model complex distributions. However, current DDPM-based probabilistic time series imputation methodologies are confronted with two types of challenges: 1) The backbone modules of the denoising parts are not capable of achieving sequence modeling with low time complexity. 2) The architecture of denoising modules can not handle the dependencies in the time series data effectively. To address the first challenge, we explore the potential of state space model, namely Mamba, as the backbone denoising module for DDPMs. To tackle the second challenge, we carefully devise several SSM-based blocks for time series data modeling. Experimental results demonstrate that our approach can achieve state-of-the-art time series imputation results on multiple real-world datasets. Our datasets and code are available at https://github.com/decisionintelligence/SSD-TS/