Self-pulsating lasers based on cascaded reshaping and reamplification (2R) are capable of initiating ultrashort pulses despite the accumulation of large amounts of nonlinearities in all-fiber resonators. The spectral properties of pulses in self-similar propagation are compatible with cascaded 2R regeneration by offset filtering, making parabolic pulses suitable for the design of a laser of this recently introduced class. A new type of regenerative laser giving birth to similaritons is numerically investigated and shows that this laser is the analog of regenerative sources based solely on self-phase modulation and offset filtering. The regenerative similariton laser does not suffer from instabilities due to excessive nonlinearities and enables ultrashort pulse generation in a simple cavity configuration. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).