  Diffusion models have become a successful approach for solving various image
inverse problems by providing a powerful diffusion prior. Many studies tried to
combine the measurement into diffusion by score function replacement, matrix
decomposition, or optimization algorithms, but it is hard to balance the data
consistency and realness. The slow sampling speed is also a main obstacle to
its wide application. To address the challenges, we propose Deep Data
Consistency (DDC) to update the data consistency step with a deep learning
model when solving inverse problems with diffusion models. By analyzing
existing methods, the variational bound training objective is used to maximize
the conditional posterior and reduce its impact on the diffusion process. In
comparison with state-of-the-art methods in linear and non-linear tasks, DDC
demonstrates its outstanding performance of both similarity and realness
metrics in generating high-quality solutions with only 5 inference steps in
0.77 seconds on average. In addition, the robustness of DDC is well illustrated
in the experiments across datasets, with large noise and the capacity to solve
multiple tasks in only one pre-trained model.
