We describe and demonstrate an optimization-based X-ray image reconstruction framework called Adorym. Our framework provides a generic forward model, allowing one code framework to be used for a wide range of imaging methods ranging from near-field holography to fly-scan ptychographic tomography. By using automatic differentiation for optimization, Adorym has the flexibility to refine experimental parameters including probe positions, multiple hologram alignment, and object tilts. It is written with strong support for parallel processing, allowing large datasets to be processed on high-performance computing systems. We demonstrate its use on several experimental datasets to show improved image quality through parameter refinement.