Coarse-grained molecular models of proteins permit access to length and time scales unattainable by all-atom models and the simulation of processes that occur on long-time scales such as aggregation and folding. The reduced resolution realizes computational accelerations but an atomistic representation can be vital for a complete understanding of mechanistic details. Backmapping is the process of restoring all-atom resolution to coarse-grained molecular models. In this work, we report DiAMoNDBack (Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping) as an autoregressive denoising diffusion probability model to restore all-atom details to coarse-grained protein representations retaining only Cα coordinates. The autoregressive generation process proceeds from the protein N-terminus to C-terminus in a residue-by-residue fashion conditioned on the Cα trace and previously backmapped backbone and side chain atoms within the local neighborhood. The local and autoregressive nature of our model makes it transferable between proteins. The stochastic nature of the denoising diffusion process means that the model generates a realistic ensemble of backbone and side chain all-atom configurations consistent with the coarse-grained Cα trace. We train DiAMoNDBack over 65k+ structures from Protein Data Bank (PDB) and validate it in applications to a hold-out PDB test set, intrinsically-disordered protein structures from the Protein Ensemble Database (PED), molecular dynamics simulations of fast-folding mini-proteins from DE Shaw Research, and coarse-grained simulation data. We achieve state-of-the-art reconstruction performance in terms of correct bond formation, avoidance of side chain clashes, and diversity of the generated side chain configurational states. We make DiAMoNDBack model publicly available as a free and open source Python package.