  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.
