Asymptotic Preservation and Uniform Accuracy of Diffusion and Flow-Matching Samplers
Diffusion and Gaussian-interpolant flow-matching samplers approach data through a terminal noise floor $\varepsilon$, a singular limit for manifold-supported or rank-deficient data. We study two properties of a complete sampler specification, comprising its update rule, time grid, and terminal rule. Asymptotic preservation (AP) means a stable and consistent zero-noise discretization with a step count bounded independently of $\varepsilon$. Uniform accuracy (UA) of order $p$ means that, at numerical resolution $h$, the endpoint $W_2$ error is $O(h^p)$ with a floor-independent constant. Bounded log-noise stepping fails AP because its step count diverges. Stopping a stable base solver at a p...
| Authors | Shiheng Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 5 July 2026 |
| Last updated at source | 15 July 2026 |
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