Understanding water absorption dynamics in porous materials is crucial for the preservation of cultural heritage artifacts, particularly in assessing the risk of deterioration due to moisture. In this work, we propose a Bayesian framework for parameter estimation of differential models describing imbibition curves---\ie, the amount of water absorbed over time by a material. Due to the complexity of the forward models and the intractability of the likelihood function, we employ the Approximate Bayesian Computation methodology to infer the model parameters based on experimental data. The proposed approach enables a probabilistic characterization of parameter uncertainty. We validate the method using synthetic and real experimental data collected from materials commonly found in historical buildings and artworks. Results show that the inference method accurately captures the underlying absorption dynamics and can serve as a reliable tool to support preventive conservation strategies.