The latest advances in artificial intelligence (AI) present many unprecedented opportunities to achieve much improved bandwidth saving in communications. Unlike conventional communication systems focusing on packet transport, rich datasets and AI makes it possible to efficiently transfer only the information most critical to the goals of message recipients. One of the most exciting advances in generative AI known as diffusion model presents a unique opportunity for designing ultra-fast communication systems well beyond language-based messages. This work presents an ultra-efficient communication design by utilizing generative AI-based on diffusion models as a specific example of the general goal-oriented communication framework. To better control the regenerated message at the receiver output, our diffusion system design includes a local regeneration module with finite dimensional noise latent. The critical significance of noise latent control and sharing residing on our Diff-GO is the ability to introduce the concept of "local generative feedback" (Local-GF), which enables the transmitter to monitor the quality and gauge the quality or accuracy of the message recovery at the semantic system receiver. To this end, we propose a new low-dimensional noise space for the training of diffusion models, which significantly reduces the communication overhead and achieves satisfactory message recovery performance. Our experimental results demonstrate that the proposed noise space and the diffusion-based generative model achieve ultra-high spectrum efficiency and accurate recovery of transmitted image signals. By trading off computation for bandwidth efficiency (C4BE), this new framework provides an important avenue to achieve exceptional computation-bandwidth tradeoff.