To address the longstanding questions of whether the blind-frombirth 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. This 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 the blind and sighted groups. The five-day two-hour training taught participants to haptically explore, recognize, memorize raised-line images, and draw them free-hand from memory, in detail, including the fine facial characteristics of the face stimuli. Such drawings represent an externalization of the formed memory. Functional MRI 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 nonvisual 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, but absent for the control nonface categories of small objects and houses. The unexpected inversed-sign training effect in CB vs LB 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 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 providing deeper insights into non-visual learning, including emergence of perceptual categories. A rebound learning model and a neuroBayesian economy principle are proposed to explain the multidimensional learning effects. The results provide new insights into the Nature-vs-Nurture interplay in rapid brain plasticity and neurorehabilitation.