On the Role of Strain and Vorticity in Numerical Integration Error for Flow Matching
Flow matching generates data by integrating a learned velocity field, where the number of integration steps (NFE) directly determines inference cost. We analyze which properties of the velocity field govern integration error by decomposing the velocity Jacobian into its symmetric part S (strain rate) and antisymmetric part Omega (vorticity). We prove that strain and vorticity play different roles: strain controls exponential error amplification through the logarithmic norm, while vorticity contributes only linearly to the local truncation error. We further show that the optimal transport velocity field is irrotational and has zero material derivative, implying second-order Euler accuracy;...
| Authors | Chenxi Tao, Seung-Kyum Choi |
|---|---|
| Primary category | cs.LG |
| Published | 22 April 2026 |
| Last updated at source | 22 April 2026 |
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