发表机构
UW-Madison; WashU（威斯康星大学麦迪逊分校; 圣路易斯华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
SNaP 提出测量自适应高斯源，实现含噪线性逆问题的单步后验采样，一次网络评估生成高质量样本，速度提升 30-2250 倍。
AI 中文摘要
扩散模型和流匹配模型能够为逆问题生成高质量的后验样本，但通常每次采样需要数十到数千次网络评估。MeanFlow 实现了单步生成，然而将其应用于逆问题时，没有中间步骤来强制执行测量一致性。我们提出了 SNaP，一种用于含高斯噪声的线性逆问题的单步 MeanFlow 后验采样器。其核心创新在于一种测量自适应的源分布：一个均值和各向异性协方差由测量算子、观测和噪声水平决定的高斯分布。该源在测量良好的方向上锚定，同时在测量较弱或无信息的方向上保留变化。我们证明，精确的条件流将该源传输到真实后验。在自然图像恢复和多线圈 MRI 中，SNaP 每次采样仅需一次网络评估，即可生成多样、高质量的样本，比迭代采样器快 30 至 2250 倍。
英文摘要
Diffusion and flow-matching models can produce high-quality posterior samples for inverse problems, but typically require tens to thousands of network evaluations per draw. MeanFlow enables one-step generation, yet applying it to inverse problems leaves no intermediate steps at which to enforce measurement consistency. We introduce SNaP, a one-step MeanFlow posterior sampler for linear inverse problems with Gaussian noise. Its central innovation is a measurement-adapted source: a Gaussian distribution whose mean and anisotropic covariance are determined by the measurement operator, observation, and noise level. The source anchors well-measured directions while preserving variation where the measurements are weak or uninformative. We show that the exact conditional flow transports this source to the true posterior. Across natural-image restoration and multi-coil MRI, SNaP produces diverse, high-quality samples with one network evaluation per draw, 30 to 2250 $\times$ faster than iterative samplers.
