<p>Tracing paper made of cellulose fibres exhibit intriguing bending behaviour upon water absorption due to differential swelling across the paper layers, making them suitable candidates for water-induced actuators in paper-based microfluidic devices. However, the bending of tracing paper as a result of water absorption has not been successfully modelled. Here, a unified equation for water diffusion in cellulose papers is derived from Onsager’s principle to take into account both Fickian diffusion driven by water entropy and non-Fickian diffusion driven by osmotic strain energy of the fibres, against dissipation forces comprising friction of water transport and rheological losses of the fibre deformation. The results indicate that the bending dynamics of tracing papers with dense and uniform cellulose fibres is dominated by non-Fickian diffusion. This research advances the understanding of water transport and deformation in cellulose-based materials and provides a theoretical framework for their bending actuation driven by water diffusion.</p>