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We have investigated the bleaching dynamics that occur in opto-fluidic dye lasers, where the liquid laser dye in a channel is locally bleached due to optical pumping. Our studies suggest that for micro-fluidic devices, the dye bleaching may be compensated through diffusion of dye molecules alone. By relying on diffusion rather than convection to generate the necessary dye replenishment, our observation potentially allows for a significant simplification of opto-fluidic dye laser device layouts, omitting the need for cumbersome and costly external fluidic handling or on-chip micro-fluidic pumping devices.