CyFM: Cylindrical Optimal Transport for Few-Step Complex-Valued Flow Matching

arXiv:2609.14171 · cs.LG · Submitted 2026-09-12 · Read on arXiv

cs.LG

Submitted: 2026-09-12

Updated: 2026-09-24

Comments: 16 pages, 1 figure, 5 tables

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Flow Matching — 28× in this paper · explained in 8 episodes
• Optimal Transport — 13× in this paper · explained in 5 episodes
• Magnetic Resonance Imaging — 5× in this paper
• Adaptation — 4× in this paper · explained in 1 episode
• Copula — 4× in this paper · explained in 2 episodes
• Distillation — 4× in this paper · explained in 2 episodes
• Generative Modeling — 4× in this paper · explained in 3 episodes
• Normalizing Flow — 4× in this paper · explained in 3 episodes
• Normalizing Flows — 4× in this paper · explained in 4 episodes
• In International Conference on Learning Representations — 3× in this paper
• Optimal Transport (OT) — 3× in this paper · explained in 4 episodes
• Alignment — 2× in this paper · explained in 1 episode
• Diffusion Model — 2× in this paper · explained in 8 episodes
• Diffusion Models — 2× in this paper · explained in 6 episodes
• Domain Adaptation — 2× in this paper · explained in 5 episodes
• Generative Model — 2× in this paper · explained in 2 episodes
• Generative Models — 2× in this paper · explained in 2 episodes
• Representation Learning — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Geometric Mismatch — 1× in this paper · explained in 2 episodes
• In International Conference on Machine Learning — 1× in this paper
• Latent Space — 1× in this paper · explained in 7 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Rectified Flow — 1× in this paper · explained in 3 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• U-net architecture — 1× in this paper · explained in 3 episodes

Sources

• Expected Batch Optimal Transport Plans and Consequences for Flow Matching
• Direct Product Flow Matching: Decoupling Radial and Angular Dynamics for Few-Shot Adaptation
• UniverSR: Unified and Versatile Audio Super-Resolution via Vocoder-Free Flow Matching
• One-Sided Quantile Coupling for Flow Matching
• PhaseGen: A Diffusion-Based Approach for Complex-Valued MRI Data Generation
• Generative Modeling of Complex-Valued Brain MRI Data
• DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation
• fastMRI: An Open Dataset and Benchmarks for Accelerated MRI

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