We introduce the Binary Diffusion Probabilistic Model (BDPM), a novelgenerative model optimized for binary data representations. While denoisingdiffusion probabilistic models (DDPMs) have demonstrated notable success intasks like image synthesis and restoration, traditional DDPMs rely oncontinuous data representations and mean squared error (MSE) loss for training,applying Gaussian noise models that may not be optimal for discrete or binarydata structures. BDPM addresses this by decomposing images into bitplanes andemploying XOR-based noise transformations, with a denoising model trained usingbinary cross-entropy loss. This approach enables precise noise control andcomputationally efficient inference, significantly lowering computational costsand improving model convergence. When evaluated on image restoration tasks suchas image super-resolution, inpainting, and blind image restoration, BDPMoutperforms state-of-the-art methods on the FFHQ, CelebA, and CelebA-HQdatasets. Notably, BDPM requires fewer inference steps than traditional DDPMmodels to reach optimal results, showcasing enhanced inference efficiency.