  Image super-resolution (SR) has attracted increasing attention due to its
wide applications. However, current SR methods generally suffer from
over-smoothing and artifacts, and most work only with fixed magnifications.
This paper introduces an Implicit Diffusion Model (IDM) for high-fidelity
continuous image super-resolution. IDM integrates an implicit neural
representation and a denoising diffusion model in a unified end-to-end
framework, where the implicit neural representation is adopted in the decoding
process to learn continuous-resolution representation. Furthermore, we design a
scale-controllable conditioning mechanism that consists of a low-resolution
(LR) conditioning network and a scaling factor. The scaling factor regulates
the resolution and accordingly modulates the proportion of the LR information
and generated features in the final output, which enables the model to
accommodate the continuous-resolution requirement. Extensive experiments
validate the effectiveness of our IDM and demonstrate its superior performance
over prior arts.
