QC-FM constructs flow-matching source samples by mapping projected data ranks to Gaussian quantiles, without solving a batch assignment, and reports FID improvements up to 12.9% over the independent-coupling baseline.
The three terms are the projectionv ij =u ⊤ j xi, theksorts ofBvalues, and the one-off QR orthogonalization ofU, respectively
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One-Sided Quantile Coupling for Flow Matching
QC-FM constructs flow-matching source samples by mapping projected data ranks to Gaussian quantiles, without solving a batch assignment, and reports FID improvements up to 12.9% over the independent-coupling baseline.