Apparatus, systems, and methods for percutaneous valve replacement and/or augmentation are provided. The apparatus includes a valve having a valve frame, a valve leaflet coupled to the valve frame, and a leaflet transition member coupled to the valve leaflet. The valve leaflet and leaflet transition member can transition from a first position where the valve leaflet and leaflet frame are at least partially outside a lumen of the valve frame to a second position where the valve leaflet and the leaflet transition member are within the lumen of the valve frame.