The red robe is the default robe that the player wears in Journey. At the beginning of the game the robe is plain and has no scarf - as the player collects glowing symbols scattered throughout the game a scarf will be added and the robe will become more extravagant. If the player finds all the symbols in the game by the end, an option is given to wear the White Robe, which can be acessed from the chapter selection screen or in the sunken city found in The Beginning.
You can obtain the white robe by obtaining the Transcendence trophy, which is to acquire all Scarf upgrades hidden in the game. You can do this over multiple playthroughs.
Once you acquire the trophy, head to the start of the game via "Chapter Select". From the center of the area, look to the right and you will see three large cloths sticking out from the ground. Go over to them and simply walk into them. Your cloak will now be white and the scarf you start off with will be longer. Unlike the red scarf, the white scarf will automatically regenerate scarf power once you land after jumping. [Source: wikia]
You can download the papercraft models here: Journey - Red and White Robe Free Papercrafts Download