Beyond Straightness: Non-Crossing Flow Matching via Quantile AlignTree Coupling

arXiv:2609.03443 · cs.LG · Submitted 2026-09-03 · Read on arXiv

cs.LG

Submitted: 2026-09-03

Updated: 2026-09-03

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

Terminology

• Flow Matching — 25× in this paper · explained in 8 episodes
• Alignment — 16× in this paper · explained in 1 episode
• Generative Model — 6× in this paper · explained in 2 episodes
• Generative Models — 6× in this paper · explained in 3 episodes
• Diffusion Model — 5× in this paper · explained in 8 episodes
• Diffusion Models — 5× in this paper · explained in 6 episodes
• Generative Modeling — 5× in this paper · explained in 3 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Benchmark — 4× in this paper · explained in 2 episodes
• Consistency — 4× in this paper · explained in 3 episodes
• Embeddings — 4× in this paper · explained in 2 episodes
• Optimal Transport — 4× in this paper · explained in 5 episodes
• Rectified Flow — 4× in this paper · explained in 3 episodes
• Ablation — 3× in this paper · explained in 1 episode
• Fidelity — 3× in this paper · explained in 2 episodes
• Latent Space — 3× in this paper · explained in 7 episodes
• Ablation Studies — 2× in this paper · explained in 1 episode
• Conference on Computer Vision and Pattern Recognition — 2× in this paper
• Latent Diffusion Model — 2× in this paper · explained in 2 episodes
• Latent Diffusion Models — 2× in this paper · explained in 2 episodes
• Latent Representation — 2× in this paper · explained in 2 episodes
• Latent Representations — 2× in this paper · explained in 3 episodes
• Transformer — 2× in this paper · explained in 2 episodes
• U-net architecture — 2× in this paper · explained in 3 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Activation Function — 1× in this paper · explained in 1 episode
• Computational overhead — 1× in this paper · explained in 2 episodes
• Exposure Bias — 1× in this paper · explained in 2 episodes
• IEEE International Conference on Computer Vision — 1× in this paper
• Nash Equilibrium — 1× in this paper · explained in 2 episodes
• Normalizing Flow — 1× in this paper · explained in 3 episodes
• Normalizing Flows — 1× in this paper · explained in 4 episodes
• Ordinary Differential Equations (ODEs) — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Semantic Understanding — 1× in this paper · explained in 2 episodes

Sources

• Flow Matching Guide and Code
• Searching for Activation Functions
• SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features
• On Fitting Flow Models with Large Sinkhorn Couplings

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