What Does a Stream Model Buy You in Flow Matching?

Stream-level flow matching (gpcfm) replaces the linear interpolant of conditional flow matching (CFM) by a Gaussian-process (GP) stream connecting each source–target pair, and reports lower sample error than I-CFM on 2-Gaussian, MNIST and CIFAR-10 benchmarks. We ask what such a stream model actually contributes. Three results answer the question. (i)Reduction. The stream-level CFM objective depends on the stream law only through the per-time joint law of $(s_t,sdo{t}_t)$; for Gaussian streams the continuity equation forces $Cov(s_t,sdo{t}_t)=\frac{1}{2}vdo{t}_t$, so the reachable set of conditional paths is exactly the Gaussian conditional paths already covered by CFM, parametrised by two scalar curves $(m_t,v_t)$; cross-time covariance affects only estimator variance. (ii)The GP is a constrained chart of that space. One kernel sets both $m_t$ and $v_t$, so the paper's own recipe for widening coverage—shrinking the SE length-scale—destroys the interpolant (the midpoint mean weight falls from $1.03$ to $0.00$). On the 2-Gaussian benchmark the GP chart diverges on $15/200$ runs at high coverage while a decoupled $(m_t,v_t)$ chart diverges on $0/200$ ($p=6.6\times 10^{-5}$), at identical median quality and $2$–$5\times$ lower cost; two independent implementations of the GP chart agree ($p=0.51$). (iii)Audit. The released code does not implement the mechanism it describes: state and velocity are drawn independently ($\mathrm{corr}=0.00\pm 0.01$ against an intended $\pm 0.83$–$0.99$), with variances taken from misindexed covariance entries. Independently of the bug, the flagship 2-Gaussian table has no power (the reported $0.03$ $W_2$ gap needs $\approx 7,600$ seeds; $100$ were run) and in the reported configuration the GP contributes $0.4\%$ state spread and $0.12\%$ velocity noise. On MNIST the released method is worse than I-cfm by $2.6$ FID (paired, $p<10^{-3}$) and on CIFAR-10 by $1.6$ FID on every seed; correct implementations of the intended law are indistinguishable from I-cfm on both, and fixing the bug recovers $2.2$–$2.3$ FID on MNIST. The design space of stream-level flow matching is two curves; a GP is a worse way to write them down.