The controls can be remapped, but not in-game yet unfortunately. The control mappings can be found in the content directory under the Input folder.
If you want to edit an existing mapping, then open the file and change any of the values under the Binding section.
Keyboard
Each value in the binding section corresponds to a windows 'Virtual Key' code. Look up (here for example) the code you want and just change the value in the file.
Controllers
For controllers, any value with + or - in front of it indicates a controller axis to check, with the sign indicating which direction to look in. A value without a sign means to check a button.
Let's say we want to change the controls so that the Xbox 360 d-pad controls the direction. We'll find the move controls and update them to use the d-pad buttons instead:
Left=13
Right=11
Down=12
Up=10
Unsupported Controllers
If you have a controller that doesn't already have bindings then you can add your own!
We've just updated the game to attempt to generate a default control mapping for any controllers that it doesn't recognize. When this happens, the game will use the driver default mappings to try to make a good guess at what the control scheme should be. When you exit the game, you will see a new control scheme that has been saved out in the Input directory. You can now edit this control scheme to suit your needs!