Digital fabrication machines such as 3D printers and laser-cutters allow users to produce physical objects based on virtual models. The creation process is currently unidirectional: once an object is fabricated it is separated from its originating virtual model. Consequently, users are tied into digital modeling tools, the virtual design must be completed before fabrication, and once fabricated, re-shaping the physical object no longer influences the digital model. To provide a more flexible design process that allows objects to iteratively evolve through both digital and physical input, we introduce bidirectional fabrication. To demonstrate the concept, we built ReForm, a system that integrates digital modeling with shape input, shape output, annotation for machine commands, and visual output. By continually synchronizing the physical object and digital model it supports object versioning to allow physical changes to be undone. Through application examples, we demonstrate the benefits of ReForm to the digital fabrication process.