Can Cubans leave Cuba?

According to Deutsche Welle, reformed travel regulations introduced in early 2013 allow Cubans to travel with only a passport and a visa from the destination country. The source notes, however, that the Cuban Communist Party is able to deny applicants a passport for a wide range of stated reasons.

Prior to 2013, Cubans had to receive an invitation from a foreign country and apply for a "tarjeta blanca," or white card. Deutsche Welle explains that some scholars have expressed skepticism with respect to the reforms, which still allow the Cuban government to deny applicants a passport based on arbitrary, vague criteria such as "the public interest."