倾斜扩散采样器的直接中间初始化
Direct Intermediate Initialization for Tilted Diffusion Samplers
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中文总结 AI 辅助
该研究提出直接中间初始化方法，利用高斯桥将后验拉回至较弱条件空间，以有限粒子性能换取渐近一致性，显著提升MCGDiff采样器的切片Wasserstein距离，尤其在罕见模式问题上效果显著。
中文摘要 AI 辅助
一些扩散后验采样器在逆过程中构造了高斯倾斜的中间分布。我们观察到，这些目标可以拉回到具有较弱条件作用的干净空间后验，并通过高斯桥将样本解析地传输到相应的噪声空间目标。对于序贯蒙特卡洛（SMC）采样器MCGDiff，该拉回问题的有效观测方差高达扩散噪声方差的两倍。我们利用这一结构直接在中间时间初始化MCGDiff：一个近似求解器对软化的干净空间后验进行采样，高斯桥将这些样本映射到倾斜目标，然后仅运行剩余的SMC后缀。这以渐近一致性换取有限粒子性能。以矩匹配后验采样（MMPS）作为求解器，该混合方法在结构化高斯混合反问题中，在匹配粒子数下将切片Wasserstein距离改善了约2倍；当后验相关模式在先验下罕见时，改善超过一个数量级。一个保留桥但放弃干净空间条件作用的先验初始化对照表明，在MCGDiff的标准高斯混合基准上，大部分改善对条件作用不敏感。对初始化施加条件作用在结构化问题上带来进一步的一致增益，并在罕见模式问题上成为决定性因素，因为重采样无法重新填充初始群体中不存在的模式。
英文摘要
Some diffusion posterior samplers construct Gaussian-tilted intermediate distributions along the reverse process. We observe that these targets can be pulled back to clean-space posteriors with weaker conditioning, with samples transported analytically to the corresponding noisy-space target through a Gaussian bridge. For the sequential Monte Carlo (SMC) sampler MCGDiff, the effective observation variance of this pulled-back problem is up to twice the diffusion-noise variance. We exploit this structure to initialize MCGDiff directly at an intermediate time: an approximate solver samples the softened clean-space posterior, the Gaussian bridge maps these samples to the tilted target, and only the remaining SMC suffix is run. This trades asymptotic consistency for finite-particle performance. With moment-matching posterior sampling (MMPS) as the solver, the hybrid improves sliced Wasserstein distance by roughly $2\times$ at matched particle count on a structured Gaussian-mixture inverse problem, and by more than an order of magnitude when the posterior-relevant mode is rare under the prior. A prior-initialization control, which retains the bridge but drops the clean-space conditioning, shows that on MCGDiff's standard Gaussian-mixture benchmark most of the improvement is insensitive to the conditioning. Conditioning the initialization gives a further consistent gain on the structured problem, and becomes decisive on a rare-mode problem, where resampling cannot repopulate a mode absent from the initial population.
发表机构
- PhysicsX Ltd.（PhysicsX有限公司）
机构由 AI 辅助整理，请以论文原文为准。
