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Abstract Neutron interferometry uniquely combines neutron imaging and scattering methods to enable characterization of multiple length scales from 1 nm to 10 µm. However, building, operating, and using such neutron imaging instruments poses constraints on the acquisition time and on the number of measured images per sample. Experiment time-constraints yield small quantities of measured images that are insufficient for automating image analyses using supervised artificial intelligence (AI) models. One approach alleviates this problem by supplementing annotated measured images with synthetic images. To this end, we create a data-driven simulation framework that supplements training data beyond typical data-driven augmentations by leveraging statistical intensity models, such as the Johnson family of probability density functions (PDFs). We follow the simulation framework steps for an image segmentation task including Estimate PDFs $$\,\rightarrow \,$$ → Validate PDFs $$\,\rightarrow \,$$ → Design Image Masks $$\,\rightarrow \,$$ → Generate Intensities $$\,\rightarrow \,$$ → Train AI Model for Segmentation. Our goal is to minimize the manual labor needed to execute the steps and maximize our confidence in simulations and segmentation accuracy. We report results for a set of nine known materials (calibration phantoms) that were imaged using a neutron interferometer acquiring four-dimensional images and segmented by AI models trained with synthetic and measured images and their masks.