Joint source-channel coding schemes based on deep neural networks (DeepJSCC) have recently achieved remarkable performance for wireless image transmission. However, these methods usually focus only on the distortion of the reconstructed signal at the receiver side with respect to the source at the transmitter side, rather than the perceptual quality of the reconstruction which carries more semantic information. As a result, severe perceptual distortion can be introduced under extreme conditions such as low bandwidth and low signal-to-noise ratio. In this work, we propose CommIN, which views the recovery of high-quality source images from degraded reconstructions as an inverse problem. To address this, CommIN combines Invertible Neural Networks (INN) with diffusion models, aiming for superior perceptual quality. Through experiments, we show that our CommIN significantly improves the perceptual quality compared to DeepJSCC under extreme conditions and outperforms other inverse problem approaches used in DeepJSCC.