Masked autoregressive models (MAR) have emerged as a powerful paradigm for image and video generation, combining the flexibility of masked modeling with the expressiveness of continuous tokenizers. However, when sampling individual frames, video MAR models often produce highly distorted outputs due to the lack of a structured global prior, especially when using only a few sampling steps. To address this, we propose CanvasMAR, a novel autoregressive video prediction model that predicts high-fidelity frames with few sampling steps by introducing a canvas--a blurred, global one-step prediction of the next frame that serves as a non-uniform mask during masked generation. The canvas supplies global structure early in sampling, enabling faster and more coherent frame synthesis. To further stabilize autoregressive sampling, we propose an easy-to-hard curriculum via a motion-aware sampling order that synthesizes relatively stationary regions before attending to highly dynamic ones. We also integrate compositional classifier-free guidance that jointly strengthens the canvas and temporal conditioning to improve generation fidelity. Experiments on the BAIR, UCF-101, and Kinetics-600 benchmarks demonstrate that CanvasMAR produces higher-quality videos with fewer autoregressive steps. On the challenging Kinetics-600 dataset, CanvasMAR achieves remarkable performance among autoregressive models and rivals advanced diffusion-based methods.