Do US REU programs sponsor the student visas (J1 or F1) for international candidates? US REU programs sometimes accept "self-funded" international students. However, do they also sponsor the student visa (J1 or F1) for the selected international candidates? Or do the students have to use a tourist visa? (From what I read so far, using a tourist visa for that purpose would not be legal as REU programs fall in the "internship" or "training" category.)

Edit:

I noticed that the J1 requires that 51% of funding come from either the hosting institute or some external source. So I suppose the J1 wouldn't be applicable for international students. However, as far as I understand, the F1 is only applicable for students enrolled in a degree course in the US. So is there no visa that would be applicable for international students willing to participate in a US REU program? That seems contradictory as many REU programs clearly mention that they are open to international applicants. [Source]
All official participants in NSF REU programs must be US citizens or permanent residents per the NSF REU homepage:


  Undergraduate students supported with NSF funds must be citizens or permanent residents of the United States or its possessions.


A self-funded student or non-NSF REU funded student would simply be an intern or student at the host institution.