Flow matching paths hide convergence gaps despite identical objectives
Flow matching, a core generative modeling technique, exhibits hidden optimization fragility: researchers prove that different path parameterizations can produce identical training objectives yet yield vastly different SGD convergence rates. This finding exposes a critical gap between theoretical equivalence and practical training dynamics, forcing practitioners to reconsider path design choices that were previously treated as interchangeable. The work matters because flow matching underpins modern diffusion alternatives, and convergence efficiency directly impacts training cost and model quality at scale.62







