Explaining the origin of the orbits of 2000 CR₁₀₅ (a = 230 AU, q = 44 AU) and 2003 VB₁₂ (a = 531 AU, q = 74 AU, unofficially known as Sedna) is a major test for our understanding of the primordial evolution of the outer solar system. Gladman et al. have shown that 2000 CR₁₀₅ could not have been a normal member of the scattered disk that had its perihelion distance increased by chaotic diffusion. The same conclusion also clearly applies to 2003 VB₁₂. In this paper, we explore five seemingly promising mechanisms to explain the origin of the orbits of these peculiar objects: (1) the passage of Neptune through a high-eccentricity phase, (2) the past existence of massive planetary embryos in the Kuiper belt or the scattered disk, (3) the presence of a massive trans-Neptunian disk at early epochs that perturbed highly inclined scattered-disk objects, (4) encounters with other stars that perturbed the orbits of some of the solar system's trans-Neptunian planetesimals, and (5) the capture of extrasolar planetesimals from low-mass stars or brown dwarfs encountering the Sun. Of all these mechanisms, the ones giving the most satisfactory results are those related to the passage of stars (4 and 5). An important advantage of both stellar-passage scenarios is that all the resulting objects with large perihelion distances also have large semimajor axes. This is in good agreement with the fact that 2000 CR₁₀₅ and 2003 VB₁₂ have semimajor axes larger than 200 AU and no other bodies with similar perihelion distances but smaller semimajor axes have yet been discovered. We favor mechanism 4, since it produces an orbital element distribution that is more consistent with the observations, unless 2000 CR₁₀₅ and 2003 VB₁₂ represent a population more massive than a few tenths of an Earth mass, in which case this mechanism is not viable.