Flow-based super-resolution (SR) models have demonstrated astonishing capabilities in generating high-quality images. However, these methods encounter several challenges during image generation, such as grid artifacts, exploding inverses, and suboptimal results due to a fixed sampling temperature. To overcome these issues, this work introduces a conditional learned prior to the inference phase of a flow-based SR model. This prior is a latent code predicted by our proposed latent module conditioned on the low-resolution image, which is then transformed by the flow model into an SR image. Our framework is designed to seamlessly integrate with any contemporary flow-based SR model without modifying its architecture or pre-trained weights. We evaluate the effectiveness of our proposed framework through extensive experiments and ablation analyses. The proposed framework successfully addresses all the inherent issues in flow-based SR models and enhances their performance in various SR scenarios. Our code is available at: https://github.com/liyuantsao/FlowSR-LP