# CurvSegFlow: Time-Conditioned Flow Matching for Robust Segmentation of Curvilinear Structures in Noisy Biomedical Images

arXiv: https://arxiv.org/abs/2606.21608 · HTML: https://mlsanity.com/paper/2606.21608/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 25 of its 67 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Road Extraction by Deep Residual U-Net](https://mlsanity.com/paper/1711.10684/) (2017)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [UCTransNet: Rethinking the Skip Connections in U-Net from a Channel-wise Perspective with Transformer](https://mlsanity.com/paper/2109.04335/) (2021)
- [Recurrent Residual Convolutional Neural Network based on U-Net (R2U-Net) for Medical Image Segmentation](https://mlsanity.com/paper/1802.06955/) (2018)
- [State of the Art on Diffusion Models for Visual Computing](https://mlsanity.com/paper/2310.07204/) (2023)
- [IterNet: Retinal Image Segmentation Utilizing Structural Redundancy in Vessel Networks](https://mlsanity.com/paper/1912.05763/) (2019)
- [CS2-Net: Deep Learning Segmentation of Curvilinear Structures in Medical Imaging](https://mlsanity.com/paper/2010.07486/) (2020)
- [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)
- [Deep Retinal Image Segmentation with Regularization Under Geometric Priors](https://mlsanity.com/paper/1909.09175/) (2019)
- [Channel Attention Residual U-Net for Retinal Vessel Segmentation](https://mlsanity.com/paper/2004.03702/) (2020)
- [Denoising Diffusion Probabilistic Model for Retinal Image Generation and Segmentation](https://mlsanity.com/paper/2308.08339/) (2023)
- [A Deep Learning Model for Coronary Artery Segmentation and Quantitative Stenosis Detection in Angiographic Images](https://mlsanity.com/paper/2406.00492/) (2024)
- [FMS2: Unified Flow Matching for Segmentation and Synthesis of Thin Structures](https://mlsanity.com/paper/2603.13659/) (2026)
- [MTFlow: Time-Conditioned Flow Matching for Microtubule Segmentation in Noisy Microscopy Images](https://mlsanity.com/paper/2601.14841/) (2026)

## Built on by (most cited first, 1 of 1)

- [Flow Matching Meets 3D Curvilinear Structure Segmentation in Medical Imaging](https://mlsanity.com/paper/2608.19965/) (2026)

## Abstract (arXiv)

Accurate segmentation of curvilinear structures remains challenging in biomedical imaging due to their thin geometry, complex topology, and sensitivity to noise. This is particularly critical for microscopy images of cytoskeletal network, where low signal-to-noise ratios and dense filament crossings often lead to fragmented or inaccurate segmentation. In this work, we propose CurvSegFlow, a segmentation framework based on time-conditioned flow matching. Instead of predicting a segmentation mask in a single pass, the method models segmentation as a dynamic process that progressively refines a noisy initialization into the target structure through a learned velocity field. The proposed model combines a U-Net backbone with triple-term loss function and temporal embeddings to guide the refinement process across reconstruction stages. This formulation enables gradual error correction and improves the continuity of thin structures. CurvSegFlow is evaluated on multiple synthetic and real microtubule datasets, as well as on public benchmarks of retinal vessels, corneal nerves and coronary arteries. Across datasets, the method achieves competitive or superior performance compared to established segmentation models, with consistent improvements in precision and structural continuity, particularly under low signal-to-noise conditions. These results show that flow-based iterative refinement provides a robust and general framework for curvilinear structure segmentation. Overall, the proposed approach improves segmentation quality in challenging imaging conditions and generalizes effectively across modalities without architectural changes.