Sounding Video Generation (SVG) is an audio-video joint generation task challenged by high-dimensional signal spaces, distinct data formats, and different patterns of content information. To address these issues, we introduce a novel multi-modal latent diffusion model (MM-LDM) for the SVG task. We first unify the representation of audio and video data by converting them into a single or a couple of images. Then, we introduce a hierarchical multi-modal autoencoder that constructs a low-level perceptual latent space for each modality and a shared high-level semantic feature space. The former space is perceptually equivalent to the raw signal space of each modality but drastically reduces signal dimensions. The latter space serves to bridge the information gap between modalities and provides more insightful cross-modal guidance. Our proposed method achieves new state-of-the-art results with significant quality and efficiency gains. Specifically, our method achieves a comprehensive improvement on all evaluation metrics and a faster training and sampling speed on Landscape and AIST++ datasets. Moreover, we explore its performance on open-domain sounding video generation, long sounding video generation, audio continuation, video continuation, and conditional single-modal generation tasks for a comprehensive evaluation, where our MM-LDM demonstrates exciting adaptability and generalization ability.