Context. Low surface brightness galaxies (LSBGs) represent a significant percentage of local galaxies but their formation and evolution remain elusive. They may hold crucial information for our understanding of many key issues (i.e., census of baryonic and dark matter, star formation in the low density regime, mass function). The most massive examples - the so called giant LSBGs - can be as massive as the Milky Way, but with this mass being distributed in a much larger disk. Aims: Malin 1 is an iconic giant LSBG - perhaps the largest disk galaxy known. We attempt to bring new insights on its structure and evolution on the basis of new images covering a wide range in wavelength. Methods: We have computed surface brightness profiles (and average surface brightnesses in 16 regions of interest), in six photometric bands (FUV, NUV, u, g, i, z). We compared these data to various models, testing a variety of assumptions concerning the formation and evolution of Malin 1. Results: We find that the surface brightness and color profiles can be reproduced by a long and quiet star-formation history due to the low surface density; no significant event, such as a collision, is necessary. Such quiet star formation across the giant disk is obtained in a disk model calibrated for the Milky Way, but with an angular momentum approximately 20 times larger. Signs of small variations of the star-formation history are indicated by the diversity of ages found when different regions within the galaxy are intercompared. Conclusions: For the first time, panchromatic images of Malin 1 are used to constrain the stellar populations and the history of this iconic example among giant LSBGs. Based on our model, the extreme disk of Malin 1 is found to have a long history of relatively low star formation (about 2 M_⊙ yr^-1). Our model allows us to make predictions on its stellar mass and metallicity. The Appendix images (FITS files) are available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/593/A126