The dynamics of polymer decompression from a compact state to swollen conformation can be formally described as nonlinear diffusion. We discuss two basic examples: (i) the expansion, or unfolding from a compact state, and (ii) the ejection of a compressed polymer through a pore. The problem can be solved exactly for case (i), but not for case (ii). Even in such situations, a scheme called uniform approximation is shown to be useful to get a physical insight involved. Its application to case (ii) is able to account for conflicting numerical data in a consistent way.