There are general limitations in 14 CFR 61.89. What are the minimum visibility requirements for a student?

On an international flight, only a student pilot can make solo training flights from Haines, Gustavus, or Juneau, Alaska, to White Horse, Yukon, Canada, and return over the province of British Columbia.

There is a flight or surface visibility of less than 3 statute miles during daylight hours.

In a way that is contrary to any limitations placed in the pilot's logbook by an authorized instructor.

A student pilot may not act as a required pilot flight crewmember on any aircraft for which more than one pilot is required by the type certificate of the aircraft or regulations under which the flight is conducted, except when receiving flight training from an authorized instructor on board an airship.

A student pilot seeking a sport pilot certificate must comply with the provisions of paragraphs (a) and (b) of this section and may not act as pilot in command.