Heat oven to 400 degrees. Lightly oil nine standard-size muffin cups, or line them with paper liners.
Combine wheat bran, prune juice, yogurt, currants, molasses, oil, egg, and vanilla in a large mixing bowl. Let stand for 10 minutes.
Whisk together flour, baking powder, baking soda, and salt in a small bowl. Stir dry ingredients into the bran mixture just until dry ingredients are moistened. Do not overmix.
Spoon batter into muffin cups, filling each about three-quarters full. Bake in the center of the oven for 20 minutes.
Turn muffins out of the pan, and let them cool on a rack.