Camera direction and `view_frame()` - How to calculate the direction vectors that describe the corners of the camera frame

Question

The camera origin is:

scene = bpy.data.scenes["Scene"]
camera_origin = scene.camera.location

The camera direction is calculated with

camera_direction = scene.camera.matrix_world.to_quaternion() @ Vector((0.0,0.0,-1.0))

The view_frame i.e. camera_corners are:

camera_corners = scene.camera.data.view_frame(scene=scene)  # camera corners

At this point camera_corners contains 4 vectors.

Question: From the camera_origin, how do I calculate the direction of the view_frame/camera_corners similar to the camera_direction?