  Deep model-based architectures (DMBAs) are widely used in imaging inverse
problems to integrate physical measurement models and learned image priors.
Plug-and-play priors (PnP) and deep equilibrium models (DEQ) are two DMBA
frameworks that have received significant attention. The key difference between
the two is that the image prior in DEQ is trained by using a specific
measurement model, while that in PnP is trained as a general image denoiser.
This difference is behind a common assumption that PnP is more robust to
changes in the measurement models compared to DEQ. This paper investigates the
robustness of DEQ priors to changes in the measurement models. Our results on
two imaging inverse problems suggest that DEQ priors trained under mismatched
measurement models outperform image denoisers.
