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3D semantic scene completion is critical for multiple downstream tasks in autonomous systems. It estimates missing geometric and semantic information in the acquired scene data. Due to the challenging real-world conditions, this task usually demands complex models processing multi-modal data to achieve acceptable performance. We proposes a unique neural model leveraging advances from the state space and diffusion generative modeling to achieve remarkable 3D semantic scene completion performance with monocular image input. Our technique processes the data in a conditioned latent space of a variational autoencoder where diffusion modeling is carried out with an innovative state space technique. Key component of our neural network is the proposed Skimba (Skimba) denoiser, which is adept at efficient processing of long-sequence data. Meticulously designed using concepts such as triple Mamba structure, dimensional decomposition residuals and varying dilations along three directions, Skimba diffusion model forms an integral part of our 3D scene completion network. We also adopt a variant of this network for the subsequent semantic segmentation stage of our technique. Extensive evaluation on the standard SemanticKITTI and SSCBench-KITTI360 datasets show that our approach not only outperforms other monocular techniques by a large margin, it also achieves competitive performance against stereo methods. We will release our model and code.