The purpose of this work was to develop and evaluate a model-guided self-supervised deep learning MRI reconstruction framework called REference-free LAtent map eXtraction (RELAX) for rapid quantitative relaxometry of the whole knee joint. This approach incorporated end-to-end CNN mapping to perform image-to-parameter domain transform. A concept of cyclic loss was utilized to enforce data fidelity and eliminate the explicit need for full-sampled training references. This approach was demonstrated in accelerated T1/T2 mapping of the whole knee joint and proven to outperform state-of-the-art reconstruction methods. The result suggests that RELAX allows accelerated relaxometry without training with reference data.