Absolutely nothing. But you are comparing bio-diesel with TDP; which are two totally and completely seperate processes. They literally have nothing in common, other than they can produce a fuel source.
Thermal De-Polymerization is a process in which just about any long hydrocarbon molecule is broken down into smaller molecules. Like in nature, the components are time, pressure and heat.
Biodiesels, on the other hand are usually fancy names for refined french fry oil. These are typically vegetable oil derivatives, which contain various ingredients for flavoring, preservatives and color. What these various 'ingredients' do, when used as a combustable fuel is something I cannot comment on; because I simply do not know.
However, chemically speaking, TDP uses the SAME ingredients that mother nature uses. The process is just sped up a few billion-fold.