Velocity Field Divergence

How it works

Evidence quality

Highlighted claims

• The divergence-compression correlation on the Checkerboard benchmark is verified with Pearson r > 0.94 and p < 10⁻³⁰⁰ for all models tested, and DS-RectFlow achieves a further ~6% reduction in mean absolute divergence beyond vanilla reflow. — Divergence-Suppressing Couplings for Rectified Flow
• The Helmholtz decomposition splits the velocity field into a divergence-free transport component that routes mass between distributions and an irrotational dipole component that carries all the field's compressibility. — Divergence-Suppressing Couplings for Rectified Flow
• The convergent component of divergence (∇·v < 0) drives trajectory crossings by compressing volume; expansion (∇·v > 0) separates particles and actually reduces crossing risk. — Divergence-Suppressing Couplings for Rectified Flow
• Demanding zero divergence everywhere is too restrictive because the continuity equation requires nonzero divergence for any flow transporting a Gaussian to a structured target. — Divergence-Suppressing Couplings for Rectified Flow
• The Hutchinson trace estimator with Rademacher vectors approximates divergence at the cost of one vector-Jacobian product per sample, without requiring second-order computation. — Divergence-Suppressing Couplings for Rectified Flow
• Trajectory bending is localized to the support of the irrotational dipole; where the dipole is negligible, neighbouring trajectories already travel in parallel under the transport component alone. — Divergence-Suppressing Couplings for Rectified Flow