  The diffusion model has long been plagued by scalability and quadratic
complexity issues, especially within transformer-based structures. In this
study, we aim to leverage the long sequence modeling capability of a
State-Space Model called Mamba to extend its applicability to visual data
generation. Firstly, we identify a critical oversight in most current
Mamba-based vision methods, namely the lack of consideration for spatial
continuity in the scan scheme of Mamba. Secondly, building upon this insight,
we introduce a simple, plug-and-play, zero-parameter method named Zigzag Mamba,
which outperforms Mamba-based baselines and demonstrates improved speed and
memory utilization compared to transformer-based baselines. Lastly, we
integrate Zigzag Mamba with the Stochastic Interpolant framework to investigate
the scalability of the model on large-resolution visual datasets, such as
FacesHQ $1024\times 1024$ and UCF101, MultiModal-CelebA-HQ, and MS COCO
$256\times 256$ . Code will be released at https://taohu.me/zigma/
