Evaluate alternative exchangeable source laws

Investigate whether alternative exchangeable source distributions, including heavy-tailed edge noise and regime-conditioned mixtures, alter transport difficulty while preserving permutation equivariance.

Background

CorrFlow uses a hollow symmetric matrix with independent standard Gaussian edge noise as its source distribution. The paper notes that permutation equivariance would be preserved under other exchangeable source laws, but the transport implications of such choices may differ. Heavy-tailed edge noise and regime-conditioned mixtures are identified as concrete alternatives whose effects on flow-matching difficulty have not been assessed.

References

Alternative exchangeable source laws, such as heavy-tailed edge noise or a regime-conditioned mixture, could change transport difficulty while preserving equivariance; we have not evaluated them.

— CorrFlow: Exact and Permutation-Equivariant Flow Matching on the Correlation Elliptope  (2610.13606 - Marti, 9 Oct 2026) in Section 5, “What the Guarantees Solve and What They Do Not,” p. 8