Recent advances in Neural Combinatorial Optimization (NCO) have been dominated by diffusion models that treat the Euclidean Traveling Salesman Problem (TSP) as a stochastic $N \times N$ heatmap generation task. In this paper, we propose CycFlow, a framework that replaces iterative edge denoising with deterministic point transport. CycFlow learns an instance-conditioned vector field that continuously transports input 2D coordinates to a canonical circular arrangement, where the optimal tour is recovered from this $2N$ dimensional representation via angular sorting. By leveraging data-dependent flow matching, we bypass the quadratic bottleneck of edge scoring in favor of linear coordinate dynamics. This paradigm shift accelerates solving speed by up to three orders of magnitude compared to state-of-the-art diffusion baselines, while maintaining competitive optimality gaps.

翻译：近期神经组合优化（NCO）领域的进展主要由扩散模型主导，这些模型将欧几里得旅行商问题（TSP）视为一个随机的 $N \times N$ 热图生成任务。本文提出CycFlow框架，该框架用确定性点运输替代迭代的边缘去噪过程。CycFlow学习一个实例条件化的向量场，该向量场将输入的二维坐标连续运输至一个规范的圆形排列，并通过角度排序从这个 $2N$ 维表示中恢复出最优路径。通过利用数据依赖的流匹配，我们绕过了边缘评分的二次复杂度瓶颈，转而采用线性的坐标动力学。这一范式转变使得求解速度相比最先进的扩散基线模型提升了高达三个数量级，同时保持了有竞争力的最优性差距。