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Research questionHow can Flow Matching avoid crossing paths and velocity ambiguity without costly optimal-transport coupling?Independent source–target pairings can make interpolation paths cross, creating ambiguous local velocities. Optimal-transport couplings can reduce this ambiguity but are expensive to construct at scale.
AI
Machine Learning
Research Paper
Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Beyond Straightness: Non-Crossing Flow Matching via Quantile AlignTree CouplingThe problem concerns coupling a Gaussian prior with target data distributions for large-scale, high-dimensional generative tasks. The source also considers conditional generation and provides theoretical and benchmark evidence for construction cost, path separation, and generative performance.research paper · Sep 3, 2026
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