Came across your question just now...my answer may be way too late; anyway, here it is:
1. Audi has a significant track record of corrosion of the cooling pipes. If this is the case, you should see vapor coming out of the engine. If this is not the case, then the pipes are not responsible for the leak;
2. Do a breather test (check if there are exhaust gases in the coolant tank). If this is the case, then the head gaskets are in question. To make sure this is the reason, check if the oil is contaminated with water. If these two checks lead to...positive results, then you will need to replace the head gaskets. This is a complex job (http://wiki.answers.com/Q/How_do_you_replace_a_head_gasket) so I suggest you take your car to a specialist (BUT BY NO MEANS TO AN AUDI GARAGE, unless you want to pay 3 x the money).
Good luck...
Paul (London, UK)