Sparse2Act: Learning Action-Aligned Sparse 3D Representations for Cross-Domain Robot Manipulation

World models that capture how actions induce physical change enable scalable robot learning without reliance on embodiment-specific action labels. Pixel-space video models provide broad visual priors but expend model capacity on dense appearance reconstruction, while direct action models require embodiment-specific labels that hinder scalability. We present $μ_0$, a scalable world model based on 3D traces. Rather than predicting dense pixels or directly modeling actions, $μ_0$ forecasts smooth 3D trajectories for salient interaction points such as objects, tools, hands, and contact regions, yielding a compact, embodiment-agnostic motion interface. To enable training from diverse video sources, our TraceExtract system automatically extracts 3D supervision by selecting keypoints, constructing globally aligned traces, and associating motion segments with hierarchical language captions. This TraceExtract supervision pretrains $μ_0$ by combining a pretrained vision-language backbone with a modular trace expert, which represents each query via B-spline control points and predicts future traces. Experiments show that $μ_0$ outperforms baselines in both 2D and 3D trace prediction, including trace prediction models and tokenized VLM methods. Because $μ_0$ is frozen and reusable, it can be paired with action experts for downstream robot embodiments. Despite action-free pretraining, the resulting trace-conditioned policies achieve performance competitive with VLA models pretrained with action supervision, such as $π_0$. These results establish 3D traces as a scalable and transferable representation for cross-embodiment manipulation.

Vision-Language-Action (VLA) models have shown strong potential for general-purpose robotic manipulation by leveraging large pretrained vision-language backbones. However, most existing VLAs rely primarily on 2D visual representations, which limit their ability to reason about fine-grained geometry and spatial grounding - capabilities that are essential for precise and robust manipulation in 3D environments. In this paper, we propose PointACT, a dual-system 3D-aware VLA policy that integrates hierarchical 3D point cloud representations directly into the action decoding process. PointACT employs a multi-scale point-action interaction mechanism with efficient bottleneck window self-attention, enabling evolving action tokens to densely attend to both local geometric detail and global scene structure. We evaluate PointACT on the LIBERO and RLBench benchmarks and systematically compare it against monolithic and dual-system VLA baselines, including variants augmented with point cloud inputs. PointACT achieves consistent improvements across both benchmarks, increasing success rates by 10% on the challenging RLBench-10Tasks suite over state-of-the-art pretrained VLAs, with even larger gains when the vision-language backbone is frozen and the action expert is trained from scratch. Extensive ablation studies demonstrate that tightly coupling hierarchical 3D geometry with pretrained 2D semantic representations is critical for robust and spatially grounded robot control. Our results also highlight the promise of pretrained 3D representations for 3D-aware VLA policies.

Video-Action Models (VAMs) leverage the broad visual dynamics captured by pre-trained video diffusion models, offering a promising path toward generalizable robot manipulation. However, RGB-only video rollouts are not directly actionable: they leave metric 3D motion, contact geometry, and fine-grained spatial constraints under-specified, making action grounding ambiguous. Meanwhile, scaling action supervision across diverse tasks and embodiments remains costly. We present PointAction, a framework that bridges video predictions to robot actions through explicit point-based 4D modeling. PointAction fine-tunes a foundation video generation model to jointly predict future RGB frames and dynamic 3D pointmaps, producing temporally consistent 3D motion of task-relevant scene geometry. These point dynamics serve as a structured, embodiment-agnostic action interface, which a diffusion-based action decoder maps to executable robot actions. By using metric 3D point dynamics as the interface between video prediction and control, PointAction reduces the ambiguity of RGB-only action grounding and supports transfer across tasks and embodiments with limited action supervision. Experiments show that PointAction achieves state-of-the-art 4D generation quality on robot scenes, outperforms existing baselines in simulation, and generalizes to two real robot arms unseen during pretraining.