Late Start: Skipping the Single-Attractor Phase of a Flow

Early in a flow-matching trajectory the velocity field has a single attractor, sitting at the \emph{mean} of the target distribution; mode-specific attractors appear only after a time we bound below. Until the mode attractors appear, the drift is common to every trajectory, so the early segment can be replaced rather than integrated. The replacement is available in closed form: a linear interpolant has explicit marginal moments, and the only target-dependent moment, the data mean $\mu_1$, is recoverable from a \emph{single} network evaluation. \emph{Late start} spends that one evaluation, jumps to a moment-matched Gaussian at a chosen $t^\star$, and integrates only $[t^\star,1]$. The sampler is training-free and reduces to ordinary few-step sampling at $t^\star=0$. On a learned 2D flow the replacement beats ordinary sampling at every training budget and step count when the moments of the Gaussian at $t^\star$ is computed from data. On two disjoint held-out suites of 256 prompts each --- one adversarial, one ordinary --- discarding the first $14\%$ of an AuraFlow trajectory is never worse than spending the same budget on the base sampler at any of three step counts, and is better on human preference at all six suite--budget combinations. A 16-prompt development set had chosen $t^\star=0.2$. Our claim is that below the bifurcation the skipped segment can be replaced rather than integrated, essentially for free.