Over the past decade, the field of holography has gained significant ground due to advances in computational imaging. However, the utilization of computational tools is hampered by the mismatch between experimental setups and the conceptual model. Differentiable holography ($$\bm{\partial }\mathbf {H}$$), a novel framework for automatically self-calibrating experimental imperfections in inverse holographic imaging, is presented here. The technique is demonstrated on auto-focused complex field imaging from a single intensity-only inline hologram.