Quantitative MRI (qMRI) of the heart has become an important clinical tool for examining myocardial tissue properties. Because heart is a moving object, it is usually imaged with electrocardiogram and respiratory gating during acquisition, to “freeze” its motion. In reality, gating is more-often-than-not imperfect given the heart rate variability and nonideal breath-hold. qMRI of the heart, consequently, is characteristic of varying image contrast as well as residual motion, the latter compromising the quality of quantitative mapping. Motion correction is an important step prior to parametric mapping, however, a long-standing difficulty for registering the dynamic sequence is that the contrast across frames varies wildly: depending on the acquisition scheme some frames can have extremely poor contrast, which fails both traditional optimization-based and modern learning-based registration methods. In this work, we propose a novel framework named DisQ, which Disentangles Quantitative mapping sequences into the latent space of contrast and anatomy, fully unsupervised. The disentangled latent spaces serve for the purpose of generating a series of images with identical contrast, which enables easy and accurate registration of all frames. We applied our DisQ method to the modified Look-Locker inversion recovery (MOLLI) sequence, and demonstrated improved performance of T₁ mapping. In addition, we showed the possibility of generating a dynamic series of baseline images with exactly the same shape, strictly registered and perfectly “frozen". Our proposed DisQ methodology readily extends to other types of cardiac qMRI such as T₂ mapping and perfusion.