Predicting disease progression always involves a high degree of uncertainty. White matter hyperintensities (WMHs) are the main neuroradiological feature of small vessel disease and a common finding in brain scans of dementia patients and older adults. In predicting their progression previous studies have identified two main challenges: 1) uncertainty in predicting the areas/boundaries of shrinking and growing WMHs and 2) uncertainty in the estimation of future WMHs volume. This study proposes the use of a probabilistic deep learning model called Probabilistic U-Net trained with adversarial loss for capturing and modelling spatial uncertainty in brain MR images. This study also proposes an evaluation procedure named volume interval estimation (VIE) for improving the interpretation of and confidence in the predictive deep learning model. Our experiments show that the Probabilistic U-Net with adversarial training improved the performance of non-probabilistic U-Net in Dice similarity coefficient for predicting the areas of shrinking WMHs, growing WMHs, stable WMHs, and their average by up to 3.35%, 2.94%, 0.47%, and 1.03% respectively. It also improved the volume estimation by 11.84% in the “Correct Prediction in Estimated Volume Interval” metric as per the newly proposed VIE evaluation procedure.