Recent advancements in diffusion models have set new benchmarks in image and video generation, enabling realistic visual synthesis across single- and multi-frame contexts. However, these models still struggle with efficiently and explicitly generating 3D-consistent content. To address this, we propose World-consistent Video Diffusion (WVD), a novel framework that incorporates explicit 3D supervision using XYZ images, which encode global 3D coordinates for each image pixel. More specifically, we train a diffusion transformer to learn the joint distribution of RGB and XYZ frames. This approach supports multi-task adaptability via a flexible inpainting strategy. For example, WVD can estimate XYZ frames from ground-truth RGB or generate novel RGB frames using XYZ projections along a specified camera trajectory. In doing so, WVD unifies tasks like single-image-to-3D generation, multi-view stereo, and camera-controlled video generation. Our approach demonstrates competitive performance across multiple benchmarks, providing a scalable solution for 3D-consistent video and image generation with a single pretrained model.