Magnetic resonance imaging (MRI) is critical for diagnosing neurodegenerative diseases, yet accurately assessing mild cortical atrophy remains a challenge due to its subtlety. Automated cortex reconstruction, paired with healthy reference ranges, aids in pinpointing pathological atrophy, yet their generalization is limited by biases from image acquisition and processing. We introduce the concept of stochastic cortical self-reconstruction (SCSR) that creates a subject-specific healthy reference by taking MRI-derived thicknesses as input and, therefore, implicitly accounting for potential confounders. SCSR randomly corrupts parts of the cortex and self-reconstructs them from the remaining information. Trained exclusively on healthy individuals, repeated self-reconstruction generates a stochastic reference cortex for assessing deviations from the norm. We present three implementations of this concept: XGBoost applied on parcels, and two autoencoders on vertex level -- one based on a multilayer perceptron and the other using a spherical U-Net. These models were trained on healthy subjects from the UK Biobank and subsequently evaluated across four public Alzheimer's datasets. Finally, we deploy the model on clinical in-house data, where deviation maps' high spatial resolution aids in discriminating between four types of dementia.