Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin process. However, in the setting where samples from the target are not available, e.g. when this target's density is known up to a normalization constant, the score estimation task is challenging. Previous approaches rely on Monte Carlo estimators that are either computationally heavy to implement or sample-inefficient. In this work, we propose a computationally attractive alternative, relying on the so-called dilation path, that yields score vectors that are available in closed-form. This path interpolates between a Dirac and the target distribution using a convolution. We propose a simple implementation of Langevin dynamics guided by the dilation path, using adaptive step-sizes. We illustrate the results of our sampling method on a range of tasks, and shows it performs better than classical alternatives.

翻译：扩散模型是生成建模领域的前沿方法，当目标概率分布的样本可用时，可通过分数匹配估计引导朗之万过程的分数向量，从而高效采样。然而，在无法获得目标分布样本的情况下（例如当目标分布的密度函数仅知其未归一化形式时），分数估计任务变得极具挑战性。现有方法依赖于蒙特卡洛估计器，这些估计器要么计算实现代价高昂，要么采样效率低下。本文提出一种计算上更具吸引力的替代方案，该方法基于所谓的膨胀路径，能够以闭式形式获得分数向量。该路径通过卷积操作在狄拉克分布与目标分布之间进行插值。我们提出了一种基于膨胀路径的朗之万动力学简单实现方案，采用自适应步长机制。通过在多种任务上展示采样结果，验证了本方法优于经典替代方案。