Title: SeKron: A Decomposition Method Supporting Many Factorization Structures. Abstract: While convolutional neural networks (CNNs) have become the de facto standard for most image processing and computer vision applications, their deployment on edge devices remains challenging. Tensor decomposition methods provide a means of compressing CNNs to meet the wide range of device constraints by imposing certain factorization structures on their convolution tensors. However, being limited to the small set of factorization structures presented by state-of-the-art decomposition approaches can lead to sub-optimal performance. We propose SeKron, a novel tensor decomposition method that offers a wide variety of factorization structures, using sequences of Kronecker products. By recursively finding approximating Kronecker factors, we arrive at optimal decompositions for each of the factorization structures. We show that SeKron is a flexible decomposition that generalizes widely used methods, such as Tensor-Train (TT), Tensor-Ring (TR), Canonical Polyadic (CP) and Tucker decompositions. Crucially, we derive an efficient convolution projection algorithm shared by all SeKron structures, leading to seamless compression of CNN models. We validate SeKron for model compression on both high-level and low-level computer vision tasks and find that it outperforms state-of-the-art decomposition methods.