mlsanityData to 7 Oct 2026

Transport, Don't Generate: Deterministic Geometric Flows for Combinatorial Optimization

arXiv 2602.10794 ↗First posted 11 Feb 2026cs.LG cs.AIcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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 × 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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 19 of its 27 references that are in the map. First posted on arXiv 11 Feb 2026.

Builds on

19 of 27 references.

Closest ancestors · 5

Same direction, newest first

  1. 2025Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimization5 Feb
  2. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization16 Feb
  3. 2022Diffusion models as plug-and-play priors17 Jun
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 14

  1. 2022Flow Matching for Generative Modelingcited by 5,426
  2. 2021E(n) Equivariant Graph Neural Networkscited by 951
  3. 2018Attention, Learn to Solve Routing Problems!cited by 646
  4. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
  5. 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 341
  6. 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 265
  7. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  8. 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
  9. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
  10. 2020Learning the Travelling Salesperson Problem Requires Rethinking Generalizationcited by 96
  11. 2023Stochastic interpolants with data-dependent couplingscited by 94
  12. 2021The Transformer Network for the Traveling Salesman Problemcited by 59
2 more
  1. 2024DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problemscited by 10
  2. 2025CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysiscited by 2

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  3. 2024A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization
  4. 2026CADO: From Imitation to Cost Minimization for Heatmap-based Solvers in Combinatorial Optimization
  5. 2024Unsupervised Training of Diffusion Models for Feasible Solution Generation in Neural Combinatorial Optimization
  6. 2023Accelerating Diffusion-based Combinatorial Optimization Solvers by Progressive Distillation
  7. 2025Boosting Cross-problem Generalization in Diffusion-Based Neural Combinatorial Solver via Inference Time Adaptation
  8. 2026EDISCO: Equivariant DIScrete Diffusion for Euclidean Combinatorial Optimization