FMS$^2$: Unified Flow Matching for Segmentation and Synthesis of Thin Structures

Segmenting thin structures like infrastructure cracks and anatomical vessels is a task hampered by topology-sensitive geometry, high annotation costs, and poor generalization across domains. Existing methods address these challenges in isolation. We propose FMS$^2$, a flow-matching framework with two modules. (1) SegFlow is a 2.96M-parameter segmentation model built on a standard encoder-decoder backbone that recasts prediction as continuous image $\rightarrow$ mask transport. It learns a time-indexed velocity field with a flow-matching regression loss and outputs the mask via ODE integration, rather than supervising only end-state logits. This trajectory-level supervision improves thin-structure continuity and sharpness, compared with tuned topology-aware loss baselines, without auxiliary topology heads, post-processing, or multi-term loss engineering. (2) SynFlow is a mask-conditioned mask $\rightarrow$ image generator that produces pixel-aligned synthetic image-mask pairs. It injects mask geometry at multiple scales and emphasizes boundary bands via edge-aware gating, while a controllable mask generator expands sparsity, width, and branching regimes. On five crack and vessel benchmarks, SegFlow alone outperforms strong CNN, Transformer, Mamba, and generative baselines, improving the volumetric metric (mean IoU) from 0.511 to 0.599 (+17.2%) and reducing the topological metric (Betti matching error) from 82.145 to 51.524 (-37.3%). When training with limited labels, augmenting SegFlow with SynFlow-generated pairs recovers near-full performance using 25% of real annotations and improves cross-domain IoU by 0.11 on average. Unlike classical data augmentation that promotes invariance via label-preserving transforms, SynFlow provides pixel-aligned paired supervision with controllable structural shifts (e.g., sparsity, width, branching), which is particularly effective under domain shift.

CrackSegFlow: Controllable Flow Matching Synthesis for Generalizable Crack Segmentation with a 50K Image-Mask Benchmark

Automated crack segmentation is essential for condition assessment, yet deployment is limited by scarce pixel-level labels and domain shift. We present CrackSegFlow, a controllable flow-matching synthesis framework that generates crack images conditioned on binary masks with mask-image alignment. The renderer combines topology-preserving mask injection with edge gating to maintain thin-structure continuity and suppress false positives. A class-conditional flow-matching mask model synthesizes masks with control over crack coverage, enabling balanced, topology-diverse data without manual annotation. We inject masks into crack-free backgrounds to diversify illumination and reduce false positives. On five datasets with a CNN-Transformer backbone, incorporating synthesized pairs improves in-domain performance by 5.37 mIoU and 5.13 F1, and target-guided cross-domain synthesis yields gains of 13.12 mIoU and 14.82 F1 using target mask statistics. We also release CSF-50K, 50,000 image-mask pairs for benchmarking.