The estimation of multi-parametric quantitative maps from Magnetic Resonance Fingerprinting (MRF) compressed sampled acquisitions, albeit successful, remains a challenge due to the high underspampling rate and artifacts naturally occuring during image reconstruction. Whilst state-of-the-art DL methods can successfully address the task, to fully exploit their capabilities they often require training on a paired dataset, in an area where ground truth is seldom available. In this work, we propose a method that combines a deep image prior (DIP) module that, without ground truth and in conjunction with a Bloch consistency enforcing autoencoder, can tackle the problem, resulting in a method faster and of equivalent or better accuracy than DIP-MRF.