arXiv:2607.04113v1 Announce Type: new Abstract: Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $\sigma_{\min}$, at which the score is stiff and the flow develops a boundary layer. We treat $\sigma_{\min}$ as a singular-perturbation parameter and determine which fixed-step samplers are asymptotic-preserving (AP), that is, stable and uniformly accurate as $\sigma_{\min}\to0$, casting the criteria as an a posteriori audit: residual functionals with $\sigma_{\min}$-uniform coefficients, computable on a pretraine
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