PiFM extends Flow Matching to multi-parameter settings by enforcing path-independent flows that approximate Wasserstein barycenters under suitable assumptions.
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The shadow projection onto couplings is bi-Hölder continuous in Wasserstein distance, yielding explicit sample complexity rates for its estimation.
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Path-independent Flow Matching for Multi-parameter Generative Dynamics
PiFM extends Flow Matching to multi-parameter settings by enforcing path-independent flows that approximate Wasserstein barycenters under suitable assumptions.
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Quantitative Stability of the Shadow for Wasserstein Projections and Sample Complexity
The shadow projection onto couplings is bi-Hölder continuous in Wasserstein distance, yielding explicit sample complexity rates for its estimation.