Pre-trained generators have been frequently adopted in compressed sensing (CS) owing to their ability to effectively estimate signals with the prior of NNs. To further refine the NN-based prior, we propose a framework that allows the generator to utilize additional information from given measurements of training samples for prior learning, thereby yielding more accurate reconstruction for signals. As our framework has a simple form, it can be easily applied to existing CS methods using pre-trained generators. Through extensive experiments, we demonstrate that our framework consistently outperforms these works by a large margin and can reduce the reconstruction error up to an order of magnitude for the presented target applications. We also explain the experimental success theoretically by showing that our framework can slightly relax the stringent signal presence condition, which is required to guarantee the success of signal recovery.