© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the ''https://creativecommons.org/licenses/by/4.0/''Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.We introduce a new family of generalized parton distribution models able to fulfill by construction all the theoretical properties imposed by QCD. These models are built on standard parton distribution functions and extended to off-forward kinematics through a well-defined procedure. We apply this strategy on the pion, first handling a simple but insightful algebraic model, and then exploiting state-of-the-art computations obtained in continuum QCD. We compare these models with a more standard one relying on an xFitter extraction of the pion parton distribution functions. The results for both quark and gluon generalized parton distributions are presented and exploited for calculation of electromagnetic, gravitational, and Compton form factors. Results on the latter highlight the relevance of next-to-leading-order corrections, even in the so-called valence region.