In nanofluidic devices, nonuniform confinement induces an entropic force that automatically drives biopolymers toward less-confined regions to gain entropy. To understand this phenomenon, we first analyze the diffusion of an entropy-driven particle system. The derived Fokker-Planck equation reveals an effective driving force as the negative gradient of the free energy. The derivation also shows that both the diffusion constant and drag coefficient are location dependent on an arbitrary free-energy landscape. As an application, DNA motion and deformation in nonuniform channels are investigated. Typical solutions reveal large gradients of stress on the polymer where the channel width changes rapidly. Migration of DNA in several nonuniform channels is discussed.