发表机构
Duke University; University of Copenhagen（杜克大学; 哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多模态分布采样难题，提出沿扩散路径插值的方法，通过变分估计中间得分，引入MAD - Path采样器消除偏差，经谱隙分析明确路径特性，量化误差影响，实验表明其在全局探索和模式权重估计上优于其他方法。
AI 中文摘要
从多模态分布中采样是经典局部马尔可夫链蒙特卡罗（MCMC）方法长期面临的挑战。一种常见补救方法是引入一系列在目标分布和更简单参考分布之间插值的中间分布。经典的回火方法将密度提升到幂次，但会扭曲非对称模式的相对权重并可能导致混合不佳。我们提出沿扩散路径插值，即一个将目标带向高斯分布的噪声扩散过程的边缘分布。此路径保留模式的相对权重并具有良好的混合特性，我们通过对相应理想转移核的谱隙分析来明确这一点。沿路径采样需要中间得分，可通过变分方法从未归一化目标中估计，这仅产生近似采样器。为消除由此产生的偏差，我们引入了 metropolis 调整扩散路径（MAD - Path）采样器，它在增强路径空间中校正扩散路径提议，且无论学习得分的准确性或离散化误差如何，都使目标不变。我们进一步量化这两个误差如何影响接受概率，为实际调整提供指导。在一系列贝叶斯后验上的实验表明，相对于基于回火的 MCMC 方法和未调整的扩散采样器，MAD - Path 改善了全局探索和模式权重估计。
英文摘要
Sampling from multimodal distributions is a longstanding challenge for classical local Markov chain Monte Carlo (MCMC) methods. A popular remedy is to introduce a sequence of intermediate distributions that interpolate between the target and a simpler reference. The classical choice, tempering, raises the density to a power, but distorts the relative weights of asymmetric modes and can lead to poor mixing. We instead propose interpolating along the diffusion path, the marginals of a noising diffusion process that carries the target toward a Gaussian. This path preserves the relative weights of the modes and enjoys favorable mixing properties, which we make precise through a spectral-gap analysis of the corresponding ideal transition kernel. Sampling along the path requires its intermediate scores, which can be estimated from the unnormalized target through variational approaches, yielding only an approximate sampler. To remove the resulting bias, we introduce the Metropolis-adjusted diffusion path (MAD-Path) sampler, which corrects the diffusion-path proposal in an augmented path space and leaves the target invariant regardless of the accuracy of the learned score or the discretization error. We further quantify how these two errors affect the acceptance probability, providing guidance for practical tuning. Experiments on a range of Bayesian posteriors show that MAD-Path improves global exploration and mode-weight estimation relative to tempering-based MCMC methods and unadjusted diffusion samplers.
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