World models allow agents to simulate the consequences of actions in imagined environments for planning, control, and long-horizon decision-making. However, existing autoregressive world models struggle with visually coherent predictions due to disrupted spatial structure, inefficient decoding, and inadequate motion modeling. In response, we propose \textbf{S}cale-wise \textbf{A}utoregression with \textbf{M}otion \textbf{P}r\textbf{O}mpt (\textbf{SAMPO}), a hybrid framework that combines visual autoregressive modeling for intra-frame generation with causal modeling for next-frame generation. Specifically, SAMPO integrates temporal causal decoding with bidirectional spatial attention, which preserves spatial locality and supports parallel decoding within each scale. This design significantly enhances both temporal consistency and rollout efficiency. To further improve dynamic scene understanding, we devise an asymmetric multi-scale tokenizer that preserves spatial details in observed frames and extracts compact dynamic representations for future frames, optimizing both memory usage and model performance. Additionally, we introduce a trajectory-aware motion prompt module that injects spatiotemporal cues about object and robot trajectories, focusing attention on dynamic regions and improving temporal consistency and physical realism. Extensive experiments show that SAMPO achieves competitive performance in action-conditioned video prediction and model-based control, improving generation quality with 4.4$\times$ faster inference. We also evaluate SAMPO's zero-shot generalization and scaling behavior, demonstrating its ability to generalize to unseen tasks and benefit from larger model sizes.

Learning from demonstration allows robots to acquire complex skills from human demonstrations, but conventional approaches often require large datasets and fail to generalize across coordinate transformations. In this paper, we propose Prompt2Auto, a geometry-invariant one-shot Gaussian process (GeoGP) learning framework that enables robots to perform human-guided automated control from a single motion prompt. A dataset-construction strategy based on coordinate transformations is introduced that enforces invariance to translation, rotation, and scaling, while supporting multi-step predictions. Moreover, GeoGP is robust to variations in the user's motion prompt and supports multi-skill autonomy. We validate the proposed approach through numerical simulations with the designed user graphical interface and two real-world robotic experiments, which demonstrate that the proposed method is effective, generalizes across tasks, and significantly reduces the demonstration burden. Project page is available at: https://prompt2auto.github.io

Videos contain rich spatio-temporal information. Traditional methods for extracting motion, used in tasks such as action recognition, often rely on visual contents rather than precise motion features. This phenomenon is referred to as 'blind motion extraction' behavior, which proves inefficient in capturing motions of interest due to a lack of motion-guided cues. Recently, attention mechanisms have enhanced many computer vision tasks by effectively highlighting salient visual areas. Inspired by this, we propose using a modified Sigmoid function with learnable slope and shift parameters as an attention mechanism to activate and modulate motion signals derived from frame differencing maps. This approach generates a sequence of attention maps that enhance the processing of motion-related video content. To ensure temporally continuity and smoothness of the attention maps, we apply pair-wise temporal attention variation regularization to remove unwanted motions (e.g., noise) while preserving important ones. We then perform Hadamard product between each pair of attention maps and the original video frames to highlight the evolving motions of interest over time. These highlighted motions, termed video motion prompts, are subsequently used as inputs to the model instead of the original video frames. We formalize this process as a motion prompt layer and incorporate the regularization term into the loss function to learn better motion prompts. This layer serves as an adapter between the model and the video data, bridging the gap between traditional 'blind motion extraction' and the extraction of relevant motions of interest.