We present a microfluidic device for selective separation and extraction of molecules based on their diffusivity. The separation relies on electroosmotically driven bidirectional flows in which high-diffusivity species experience a net-zero velocity and lower diffusivity species are advected to a collection reservoir. The device can operate continuously and is suitable for processing low sample volumes. Using several model systems, we show that the extraction efficiency of the system is maintained at more than 90% over tens of minutes with a purity of more than 99%. We demonstrate the applicability of the device to the extraction of genomic DNA from short DNA fragments.