Leveraging multi-view diffusion models as priors for 3D optimization have alleviated the problem of 3D consistency eg the Janus face problem or the content drift problem in zero-shot text-to-3D models. However the 3D geometric fidelity of the output remains an unresolved issue; albeit the rendered 2D views are realistic the underlying geometry may contain errors such as unreasonable concavities. In this work we propose CorrespondentDream an effective method to leverage annotation-free cross-view correspondences yielded from the diffusion U-Net to provide additional 3D prior to the NeRF optimization process. We find that these correspondences are strongly consistent with human perception and by adopting it in our loss design we are able to produce NeRF models with geometries that are more coherent with common sense eg more smoothed object surface yielding higher 3D fidelity. We demonstrate the efficacy of our approach through various comparative qualitative results and a solid user study.