Sprinkle gelatin over milk in a saucepan; let stand 1 minute. Cook over low heat, stirring constantly, until gelatin dissolves. Remove from heat, and add sugar and salt, stirring until sugar dissolves. Stir in yogurt, vanilla, and peaches. Cover and chill.

Pour yogurt mixture into the freezer can of a 4-quart ice cream maker; freeze according to manufacturer's instructions. Serve immediately or store in freezer.