This paper considers the problem of sampling from non-logconcave
distribution, based on queries of its unnormalized density. It first describes
a framework, Diffusion Monte Carlo (DMC), based on the simulation of a
denoising diffusion process with its score function approximated by a generic
Monte Carlo estimator. DMC is an oracle-based meta-algorithm, where its oracle
is the assumed access to samples that generate a Monte Carlo score estimator.
Then we provide an implementation of this oracle, based on rejection sampling,
and this turns DMC into a true algorithm, termed Zeroth-Order Diffusion Monte
Carlo (ZOD-MC). We provide convergence analyses by first constructing a general
framework, i.e. a performance guarantee for DMC, without assuming the target
distribution to be log-concave or satisfying any isoperimetric inequality. Then
we prove that ZOD-MC admits an inverse polynomial dependence on the desired
sampling accuracy, albeit still suffering from the curse of dimensionality.
Consequently, for low dimensional distributions, ZOD-MC is a very efficient
sampler, with performance exceeding latest samplers, including
also-denoising-diffusion-based RDMC and RS-DMC. Last, we experimentally
demonstrate the insensitivity of ZOD-MC to increasingly higher barriers between
modes or discontinuity in non-convex potential.

非对数凹分布下的采样问题中，提出了一种基于非归一化密度查询的采样方法，通过模拟去噪扩散过程以及用通用蒙特卡罗估计器逼近其评分函数，构建了 Diffusion Monte Carlo (DMC) 框架。进一步，通过拒绝采样实现 DMC 的 oracle，形成真正的算法 Zeroth-Order Diffusion Monte Carlo (ZOD-MC)。在不假设目标分布为对数凹或满足任何等面积不等式的情况下，提供了 DMC 的收敛性分析。证明了 ZOD-MC 具有与所需采样精度的反多项式依赖关系，但仍然受到维度诅咒的影响。因此，在低维度分布中，ZOD-MC 是一种高效的采样器，其性能超越了最新的采样器，包括基于去噪扩散的 RDMC 和 RS-DMC。最后，实验证明 ZOD-MC 对于模态之间的高屏障或非凸势能的不连续性具有不敏感性。