To address the longstanding questions of whether the blind-from-birth have an innate face-schema, what plasticity mechanisms underlie non-visual face learning, and whether there are interhemispheric face processing differences in face processing in the blind, we used a unique non-visual drawing-based training in congenitally blind (CB), late-blind (LB) and blindfolded-sighted (BF) groups of adults. The unique Cognitive-Kinesthetic Drawing approach previously developed by Likova (e.g., 2010, 2012, 2013) enabled us to rapidly train and study training-driven neuroplasticity in both blind and sighted people. The five-day one-hour training thought participants to haptically explore, recognize and memorize raised-line images, and draw them free-hand from memory, in detail, including the fine facial characteristics in the face stimuli. Such reproduction represents an externalization of the formed memory. FMRI (Siemens 3T scanner) was run before and after the training. Tactile-face perception activated the occipito-temporal cortex in all groups. However, the training led to a strong, predominantly left-hemispheric reorganization in the two blind groups, in contrast to right-hemispheric in blindfolded-sighted, i.e., the post-training response-change was stronger in the left hemisphere in the blind, but in the right in the blindfolded. This is the first study to discover interhemispheric differences in non-visual face processing. Remarkably, for face perception, this learning-based change was positive in the CB and BF groups, but negative in the LB-group. Both the lateralization and inversed-sign learning effects were specific to face perception only, but absent for the control nonface categories of small objects and houses. The unexpected inversed-sign training effect for faces in congenital vs late blindness suggests different stages of brain plasticity in the ventral pathway specific to the face category. Importantly, the fact that only after a very few days of our training, the totally blind from birth CB manifested a very good (haptic) face perception and even developed strong empathy to the explored faces, implies that there is a preexisting face schema that can be “unmasked” and “tuned up” by a proper learning procedure. The Likova Cognitive-Kinesthetic Training is a powerful tool for driving brain plasticity, and gaining deeper insights into non-visual learning, including development of perceptual categories. A rebound learning model and a neuro-Bayesian economy principle are proposed to explain multidimensional learning effects. The results provide new insights into the Nature-vs-Nurture interplay in rapid brain plasticity and neurorehabilitation.