Accurately modeling multi-class cell topology is crucial in digital pathology, as it provides critical insights into tissue structure and pathology. The synthetic generation of cell topology enables realistic simulations of complex tissue environments, enhances downstream tasks by augmenting training data, aligns more closely with pathologists' domain knowledge, and offers new opportunities for controlling and generalizing the tumor microenvironment. In this paper, we propose a novel approach that integrates topological constraints into a diffusion model to improve the generation of realistic, contextually accurate cell topologies. Our method refines the simulation of cell distributions and interactions, increasing the precision and interpretability of results in downstream tasks such as cell detection and classification. To assess the topological fidelity of generated layouts, we introduce a new metric, Topological Fréchet Distance (TopoFD), which overcomes the limitations of traditional metrics like FID in evaluating topological structure. Experimental results demonstrate the effectiveness of our approach in generating multi-class cell layouts that capture intricate topological relationships. Code is available at https://github.com/Melon-Xu/TopoCellGen.

In semi-supervised segmentation, capturing meaningful semantic structures from unlabeled data is essential. This is particularly challenging in histopathology image analysis, where objects are densely distributed. To address this issue, we propose a semi-supervised segmentation framework designed to robustly identify and preserve relevant topological features. Our method leverages multiple perturbed predictions obtained through stochastic dropouts and temporal training snapshots, enforcing topological consistency across these varied outputs. This consistency mechanism helps distinguish biologically meaningful structures from transient and noisy artifacts. A key challenge in this process is to accurately match the corresponding topological features across the predictions in the absence of ground truth. To overcome this, we introduce a novel matching strategy that integrates spatial overlap with global structural alignment, minimizing discrepancies among predictions. Extensive experiments demonstrate that our approach effectively reduces topological errors, resulting in more robust and accurate segmentations essential for reliable downstream analysis. Code is available at https://github.com/Melon-Xu/MATCH.