  Diffusion models have emerged as powerful tools for solving inverse problems
due to their exceptional ability to model complex prior distributions. However,
existing methods predominantly assume known forward operators (i.e.,
non-blind), limiting their applicability in practical settings where acquiring
such operators is costly. Additionally, many current approaches rely on
pixel-space diffusion models, leaving the potential of more powerful latent
diffusion models (LDMs) underexplored. In this paper, we introduce LatentDEM,
an innovative technique that addresses more challenging blind inverse problems
using latent diffusion priors. At the core of our method is solving blind
inverse problems within an iterative Expectation-Maximization (EM) framework:
(1) the E-step recovers clean images from corrupted observations using LDM
priors and a known forward model, and (2) the M-step estimates the forward
operator based on the recovered images. Additionally, we propose two novel
optimization techniques tailored for LDM priors and EM frameworks, yielding
more accurate and efficient blind inversion results. As a general framework,
LatentDEM supports both linear and non-linear inverse problems. Beyond common
2D image restoration tasks, it enables new capabilities in non-linear 3D
inverse rendering problems. We validate LatentDEM's performance on
representative 2D blind deblurring and 3D sparse-view reconstruction tasks,
demonstrating its superior efficacy over prior arts.
