Segmentation of curvilinear anatomical structures in 3D medical images remains challenging due to complex topology, severe class imbalance, weak contrast, and large variations in structure morphology. While deep learning approaches for 3D curvilinear segmentation have been proposed, they are often tailored to specific anatomies or modalities, limiting generalization across clinical settings and leaving room for improvement. Recent generative models have shown the benefits of iterative prediction for structured segmentation tasks, yet diffusion-based methods suffer from computationally expensive sampling, hindering their use on high-resolution 3D volumes. We present 3D-CurvSegFlow, a flow matching-based model for 3D curvilinear structure segmentation. The model learns a continuous transformation from a simple source distribution to the target vascular representation, enabling progressive refinement of complex curvilinear geometries with efficient inference. We evaluate our method on Three public challenging datasets covering distinct anatomies and modalities: portal vein, cerebral vessel, and coronary arteries. Using a common architecture and training strategy across all tasks, our method outperforms general-purpose and vessel-specific approaches, with strong preservation of thin branches and vascular continuity. This work not only advances the state-of-the-art in 3D curvilinear segmentation but also opens new avenues for efficient, generalizable, and clinically applicable methods in medical image analysis.
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