TendiffPure: a convolutional tensor-train denoising diffusion model for purification

Diffusion models are effective purification methods, where the noises or adversarial attacks are removed using generative approaches before pre-existing classifiers conducting classification tasks. However, the efficiency of diffusion models is still a concern, and existing solutions are based on knowledge distillation which can jeopardize the generation quality because of the small number of generation steps. Hence, we propose TendiffPure as a tensorized and compressed diffusion model for purification. Unlike the knowledge distillation methods, we directly compress U-Nets as backbones of diffusion models using tensor-train decomposition, which reduces the number of parameters and captures more spatial information in multi-dimensional data such as images. The space complexity is reduced from O ( N 2 ) to O ( NR 2 ) with R ≤ 4 as the tensor-train rank and N as the number of channels. Experimental results show that TendiffPure can more efficiently obtain high-quality purification results and outperforms the baseline purification methods on CIFAR-10, Fashion-MNIST, and MNIST datasets for two noises and one adversarial attack.