# FMS2: Unified Flow Matching for Segmentation and Synthesis of Thin Structures

arXiv: https://arxiv.org/abs/2603.13659 · HTML: https://mlsanity.com/paper/2603.13659/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [T2I-Adapter: Learning Adapters to Dig out More Controllable Ability for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.08453/) (2023)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [MedSegDiff-V2: Diffusion based Medical Image Segmentation with Transformer](https://mlsanity.com/paper/2301.11798/) (2023)
- [CS2-Net: Deep Learning Segmentation of Curvilinear Structures in Medical Imaging](https://mlsanity.com/paper/2010.07486/) (2020)
- [Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching](https://mlsanity.com/paper/2405.18816/) (2024)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures](https://mlsanity.com/paper/2404.03010/) (2024)
- [DCSAU-Net: A Deeper and More Compact Split-Attention U-Net for Medical Image Segmentation](https://mlsanity.com/paper/2202.00972/) (2022)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [Directional Connectivity-based Segmentation of Medical Images](https://mlsanity.com/paper/2304.00145/) (2023)
- [UniGS: Unified Representation for Image Generation and Segmentation](https://mlsanity.com/paper/2312.01985/) (2023)
- [Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment](https://mlsanity.com/paper/2506.02221/) (2025)
- [FlowSDF: Flow Matching for Medical Image Segmentation Using Distance Transforms](https://mlsanity.com/paper/2405.18087/) (2024)
- [SemFlow: Binding Semantic Segmentation and Image Synthesis via Rectified Flow](https://mlsanity.com/paper/2405.20282/) (2024)
- [A Simple Latent Diffusion Approach for Panoptic Segmentation and Mask Inpainting](https://mlsanity.com/paper/2401.10227/) (2024)
- [Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation](https://mlsanity.com/paper/2411.03228/) (2024)
- [SCSegamba: Lightweight Structure-Aware Vision Mamba for Crack Segmentation in Structures](https://mlsanity.com/paper/2503.01113/) (2025)
- [DeNVeR: Deformable Neural Vessel Representations for Unsupervised Video Vessel Segmentation](https://mlsanity.com/paper/2406.01591/) (2024)
- [Topology-aware Mamba for Crack Segmentation in Structures](https://mlsanity.com/paper/2410.19894/) (2024)
- [Enriching Information and Preserving Semantic Consistency in Expanding Curvilinear Object Segmentation Datasets](https://mlsanity.com/paper/2407.08209/) (2024)

## Built on by (most cited first, 2 of 2)

- [CurvSegFlow: Time-Conditioned Flow Matching for Robust Segmentation of Curvilinear Structures in Noisy Biomedical Images](https://mlsanity.com/paper/2606.21608/) (2026)
- [Flow Matching Meets 3D Curvilinear Structure Segmentation in Medical Imaging](https://mlsanity.com/paper/2608.19965/) (2026)

## Abstract (arXiv)

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 FMS2, 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.