The structure of topology underpins much of the research on performance and robustness, yet available topology data are typically scarce, necessitating the generation of synthetic graphs with desired properties for testing or release. Prior diffusion-based approaches either embed conditions into the diffusion model, requiring retraining for each attribute and hindering real-time applicability, or use classifier-based guidance post-training, which does not account for topology scale and practical constraints. In this paper, we show from a discrete perspective that gradients from a pre-trained graph?level classifier can be incorporated into the discrete reverse diffusion posterior to steer generation toward specified structural properties. Based on this insight, we propose Classifier-guided Conditional Topology Generation with Persistent Homology (CoPHo), which builds a persistent homology filtration over intermediate graphs and interprets features as guidance signals that steer generation toward the desired properties at each denoising step. Experiments on four generic/network datasets demonstrate that CoPHo outperforms existing methods at matching target metrics, and we further validate its transferability on the QM9 molecular dataset. The code is available at https://github.com/Lrbomchz/CoPHo.

Contouring prostate tumor in magnetic resonance images is a prerequisite for diagnosis. Automatically segmenting blurred lesion regions is challenging and requires fully leveraging multi-parameter MR images. This paper proposes MFSL-Net, an end-to-end network that cascades two novel sub-networks: 1) a modality fusion network that selectively fuses information of two MRI modalities by expanding a dual-stream CNN with spatial and channel attention modules; 2) a shape learning network that integrates shape learning and context learning to recognize the shape and edge information while preserving high-resolution semantic information. We justify MFSL-Net’s design by ablation experiments and compare its performance with the state-of-the-art approaches. Experimental results show a 3.6% improvement in Dice Similarity Coefficient, which confirms the effectiveness of MFSL-Net.