Moving an object in a single image requires geometry-consistent spatial rearrangement, including handling occlusions, revealing previously unseen regions, and maintaining coherent shadows and reflections. Existing approaches are not well suited to this setting and often fail to preserve such scene-level consistency. We address this problem by introducing a geometry-aware object motion method that operates directly on the positional representations of diffusion transformers. Our key insight is that rotary positional embeddings (RoPE) define a structured spatial field that can be explicitly manipulated to induce controlled motion. We extend 2D RoPE into a depth-aware formulation that encodes 3D spatial structure, enabling consistent object displacement and scene-aware updates. Our model is trained using synthetic data combined with a small set of real images via parameter-efficient fine-tuning. Despite minimal real supervision, it preserves object identity under large spatial displacements, generates plausible content in newly revealed regions, and consistently updates scene-dependent effects such as shadows and illumination. Experimental results on standard object motion benchmarks demonstrate state-of-the-art performance across all evaluation metrics.
Relative position embedding has become a standard mechanism for encoding positional information in Transformers. However, existing formulations are typically limited to a fixed geometric space, namely 1D sequences or regular 2D/3D grids, which restricts their applicability to many computer vision tasks that require geometric reasoning across camera views or between 2D and 3D spaces. To address this limitation, we propose URoPE, a universal extension of Rotary Position Embedding (RoPE) to cross-view or cross-dimensional geometric spaces. For each key/value image patch, URoPE samples 3D points along the corresponding camera ray at predefined depth anchors and projects them into the query image plane. Standard 2D RoPE can then be applied using the projected pixel coordinates. URoPE is a parameter-free and intrinsics-aware relative position embedding that is invariant to the choice of global coordinate systems, while remaining fully compatible with existing RoPE-optimized attention kernels. We evaluate URoPE as a plug-in positional encoding for transformer architectures across a diverse set of tasks, including novel view synthesis, 3D object detection, object tracking, and depth estimation, covering 2D-2D, 2D-3D, and temporal scenarios. Experiments show that URoPE consistently improves the performance of transformer-based models across all tasks, demonstrating its effectiveness and generality for geometric reasoning. Our code is available on our project website: https://urope-pe.github.io/.
We study positional encodings for multi-view transformers that process tokens from a set of posed input images, and seek a mechanism that encodes patches uniquely, allows SE(3)-invariant attention with multi-frequency similarity, and can adapt to the geometry of the underlying 3D scene. We find that prior (absolute or relative) encoding schemes for multi-view attention do not meet these desiderata, and present RayRoPE to address this gap. RayRoPE represents patch positions based on associated rays and computes query-frame projective coordinates to ensure SE(3) invariance. To adapt to scene geometry, RayRoPE predicts (without direct supervision) a per-token depth to obtain its position along the corresponding ray, while also modeling uncertainty and analytically computing the expected positional encoding. We validate our method on the tasks of novel-view synthesis, stereo depth estimation, and feed-forward 3DGS reconstruction. While remaining efficient, RayRoPE consistently improves over alternate position encoding schemes (e.g., 24% relative improvement on LPIPS in RE10K).
Video depth estimation extends monocular prediction into the temporal domain to ensure coherence. However, existing methods often suffer from spatial blurring in fine-detail regions and temporal inconsistencies. We argue that current approaches, which primarily rely on temporal smoothing via Transformers, struggle to maintain strict 3D geometric consistency-particularly under rotations or drastic view changes. To address this, we propose GemDepth, a framework built on the insight that an explicit awareness of camera motion and global 3D structure is a prerequisite for 3D consistency. Distinctively, GemDepth introduces a Geometry-Embedding Module (GEM) that predicts inter-frame camera poses to generate implicit geometric embeddings. This injection of motion priors equips the network with intrinsic 3D perception and alignment capabilities. Guided by these geometric cues, our Alternating Spatio-Temporal Transformer (ASTT) captures latent point-level correspondences to simultaneously enhance spatial precision for sharp details and enforce rigorous temporal consistency. Furthermore, GemDepth employs a data-efficient training strategy, effectively bridging the gap between high efficiency and robust geometric consistency. As shown in Fig.2, comprehensive evaluations demonstrate that GemDepth achieves state-of-the-art performance across multiple datasets, particularly in complex dynamic scenarios. The code is publicly available at: https://github.com/Yuecheng919/GemDepth.