Obtaining truly representative pore-scale images that match bulk formation properties remains a fundamental challenge in subsurface characterization, as natural spatial heterogeneity causes extracted sub-images to deviate significantly from core-measured values. This challenge is compounded by data scarcity, where physical samples are only available at sparse well locations. This study presents a multi-conditional Generative Adversarial Network (cGAN) framework that generates representative pore-scale images with precisely controlled properties, addressing both the representativeness challenge and data availability constraints. The framework was trained on thin section samples from four depths (1879.50-1943.50 m) of a carbonate formation, simultaneously conditioning on porosity values and depth parameters within a single unified model. This approach captures both universal pore network principles and depth-specific geological characteristics, from grainstone fabrics with interparticle-intercrystalline porosity to crystalline textures with anhydrite inclusions. The model achieved exceptional porosity control (R^2=0.95) across all formations with mean absolute errors of 0.0099-0.0197. Morphological validation confirmed preservation of critical pore network characteristics including average pore radius, specific surface area, and tortuosity, with statistical differences remaining within acceptable geological tolerances. Most significantly, generated images demonstrated superior representativeness with dual-constraint errors of 1.9-11.3% compared to 36.4-578% for randomly extracted real sub-images. This capability provides transformative tools for subsurface characterization, particularly valuable for carbon storage, geothermal energy, and groundwater management applications where knowing the representative morphology of the pore space is critical for implementing digital rock physics.