We consider the problem of inferring high-dimensional data $\mathbf{x}$ in a
model that consists of a prior $p(\mathbf{x})$ and an auxiliary differentiable
constraint $c(\mathbf{x},\mathbf{y})$ on $x$ given some additional information
$\mathbf{y}$. In this paper, the prior is an independently trained denoising
diffusion generative model. The auxiliary constraint is expected to have a
differentiable form, but can come from diverse sources. The possibility of such
inference turns diffusion models into plug-and-play modules, thereby allowing a
range of potential applications in adapting models to new domains and tasks,
such as conditional generation or image segmentation. The structure of
diffusion models allows us to perform approximate inference by iterating
differentiation through the fixed denoising network enriched with different
amounts of noise at each step. Considering many noised versions of $\mathbf{x}$
in evaluation of its fitness is a novel search mechanism that may lead to new
algorithms for solving combinatorial optimization problems.

该论文探讨了在先验概率和一个基于 $x$ 和 $y$ 的不等式约束条件下利用高维数据推断潜在结果。通过使用一个独立训练的去噪扩散生成模型和不同的不等式约束，该方法能应用于各种不同领域的任务，例如条件生成、图像分割以及求解组合优化问题等。