Face Recognition Systems (FRS) are vulnerable to morph attacks. A face morph is created by combining multiple identities with the intention to fool FRS and making it match the morph with multiple identities. Current Morph Attack Detection (MAD) can detect the morph but are unable to recover the identities used to create the morph with satisfactory outcomes. Existing work in de-morphing is mostly reference-based, i.e. they require the availability of one identity to recover the other. Sudipta et al. \cite{ref9} proposed a reference-free de-morphing technique but the visual realism of outputs produced were feeble. In this work, we propose SDeMorph (Stably Diffused De-morpher), a novel de-morphing method that is reference-free and recovers the identities of bona fides. Our method produces feature-rich outputs that are of significantly high quality in terms of definition and facial fidelity. Our method utilizes Denoising Diffusion Probabilistic Models (DDPM) by destroying the input morphed signal and then reconstructing it back using a branched-UNet. Experiments on ASML, FRLL-FaceMorph, FRLL-MorDIFF, and SMDD datasets support the effectiveness of the proposed method.