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Estimating a patient‐specific computational model's parameters relies on data that is often unreliable and ill‐suited for a deterministic approach. We develop an optimization‐based uncertainty quantification framework for probabilistic model tuning that discovers model inputs distributions that generate target output distributions. Probabilistic sampling is performed using a surrogate model for computational efficiency, and a general distribution parameterization is used to describe each input. The approach is tested on seven patient‐specific modeling examples using CircAdapt, a cardiovascular circulatory model. Six examples are synthetic, aiming to match the output distributions generated using known reference input data distributions, while the seventh example uses real‐world patient data for the output distributions. Our results demonstrate the accurate reproduction of the target output distributions, with a correct recreation of the reference inputs for the six synthetic examples. Our proposed approach is suitable for determining the parameter distributions of patient‐specific models with uncertain data and can be used to gain insights into the sensitivity of the model parameters to the measured data.