STARRY: Spatial-Temporal Action-Centric World Modeling for Robotic Manipulation

Vision-language-action (VLA) models have achieved great success on general robotic tasks, but still face challenges in fine-grained spatiotemporal manipulation. Typically, existing methods mainly embed spatiotemporal knowledge into visual and action representations, and directly perform a cross-modal mapping for step-level action prediction. However, such spatiotemporal reasoning remains largely implicit, making it difficult to handle multiple sequential behaviors with explicit spatiotemporal boundaries. In this work, we propose ST-$π$, a structured spatiotemporal VLA model for robotic manipulation. Our model is guided by two key designs: 1) Spatiotemporal VLM. We encode 4D observations and task instructions into latent spaces, and feed them into the LLM to generate a sequence of causally ordered chunk-level action prompts consisting of sub-tasks, spatial grounding and temporal grounding. 2) Spatiotemporal action expert. Conditioned on chunk-level action prompts, we design a structured dual-generator guidance to jointly model spatial dependencies and temporal causality, thus predicting step-level action parameters. Within this structured framework, the VLM explicitly plans global spatiotemporal behavior, and the action expert further refines local spatiotemporal control. In addition, we propose a real-world robotic dataset with structured spatiotemporal annotations for fine-tuning. Extensive experiments have been conducted to demonstrate the effectiveness of our model. Our code link: https://github.com/chuanhaoma/ST-pi.

Vision-language-action (VLA) models integrate visual observations and language instructions to predict robot actions, demonstrating promising generalization in manipulation tasks. However, most existing approaches primarily rely on direct mappings from 2D visual inputs to action sequences, without explicitly modeling the underlying 3D spatial structure or temporal world dynamics. Such representations may limit spatial reasoning and long-horizon decision-making in dynamic environments. To address this limitation, we propose StemVLA, a novel framework that explicitly incorporates both future-oriented 3D spatial knowledge and historical 4D spatiotemporal representations into action prediction. First, instead of relying solely on observed images, StemVLA forecasts structured 3D future spatial-geometric world knowledge, enabling the model to anticipate upcoming scene geometry and object configurations. Second, to capture temporal consistency and motion dynamics, we feed historical image frames into a pretrained video-geometry transformer backbone to extract implicit 3D world representations, and further aggregate them across time using a temporal attention module, termed VideoFormer [20], forming a unified 4D historical spatiotemporal representation. By jointly modeling 2D observations, predicted 3D future structure, and aggregated 4D temporal dynamics, StemVLA enables more comprehensive world understanding for robot manipulation. Extensive experiments in simulation demonstrate that Stem-VLA achieves an average accuracy of 92.0% across the LIBERO subsets, and 86.0% on the long-horizon LIBERO-Long subset.

Most Vision-Language-Action (VLA) models map observations directly to actions without explicit reasoning, limiting their capacity for reasoning-intensive long-horizon tasks. To address this, existing approaches adopt Chain-of-Thought (CoT) reasoning to enable subgoal decomposition and spatial anticipation. However, those methods lack a unified architecture for effective cross-modal reasoning and fail to explicitly include inverse reasoning ability based on the target state. We argue that manipulation planning naturally decomposes into prediction, anticipating the next visual state, and inverse dynamics, inferring the actions to reach it. Bridging both requires a unified autoregressive architecture that interleaves textual and visual reasoning in a single generation process. We propose \textbf{ThinkingVLA}, a generative model that realizes this decomposition within a unified Mixture-of-Transformers architecture. ThinkingVLA consists of a forward CoT that identifies the immediate subgoal and guides the visual forecasting; the predicted image then serves as the target state, grounding an inverse CoT that reasons about spatial relationships and action intent based on the predicted image; and the final action is generated conditioned on this full reasoning context. Extensive experiments on simulation and real-world benchmarks demonstrate that ThinkingVLA consistently outperforms state-of-the-art baselines, with particularly large gains on long-horizon manipulation tasks.