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Recent advances in diffusion models have demonstrated their strong capabilities in generating high-fidelity samples from complex distributions through an iterative refinement process. Despite the empirical success of diffusion models in…

In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jacobi equations on the space SE(3)/({0} \times SO(2)) of 3D-positions and orientations naturally embedded in the group SE(3) of 3D-rigid body…

Given a dataset of expert trajectories, standard imitation learning approaches typically learn a direct mapping from observations (e.g., RGB images) to actions. However, such methods often overlook the rich interplay between different…

Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…

We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality…

Modeling 4D scenes requires capturing both spatial structure and temporal motion, which is challenging due to the need for physically consistent representations of complex rigid and non-rigid motions. Existing approaches mainly rely on…

Diffusion model, the state-of-the-art generative machine learning architecture, has shown promising results airfoil inverse designs. In this study, we implemented and trained a series of diffusion models on three different airfoil geometry…

The ability to manipulate objects in a desired configurations is a fundamental requirement for robots to complete various practical applications. While certain goals can be achieved by picking and placing the objects of interest directly,…

Cloth manipulation is challenging due to its highly complex dynamics, near-infinite degrees of freedom, and frequent self-occlusions, which complicate both state estimation and dynamics modeling. Inspired by recent advances in generative…

Generating high-quality whole-body human object interaction motion sequences is becoming increasingly important in various fields such as animation, VR/AR, and robotics. The main challenge of this task lies in determining the level of…

Curved objects pose a fundamental challenge for skill transfer in robotics: unlike planar surfaces, they do not admit a global reference frame. As a result, task-relevant directions such as "toward" or "along" the surface vary with position…

Diffusion policies excel at learning complex action distributions for robotic visuomotor tasks, yet their iterative denoising process poses a major bottleneck for real-time deployment. Existing acceleration methods apply a fixed number of…

As the number of the robot's degrees of freedom increases, the implementation of robot motion becomes more complex and difficult. In this study, we focus on learning 6DOF-grasping motion and consider dividing the grasping motion into…

Nine-degrees-of-freedom (9-DoF) object pose and size estimation is crucial for enabling augmented reality and robotic manipulation. Category-level methods have received extensive research attention due to their potential for generalization…

We propose MonoSE(3)-Diffusion, a monocular SE(3) diffusion framework that formulates markerless, image-based robot pose estimation as a conditional denoising diffusion process. The framework consists of two processes: a…

Robotic manipulation faces critical challenges in understanding spatial affordances--the "where" and "how" of object interactions--essential for complex manipulation tasks like wiping a board or stacking objects. Existing methods, including…

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…

Trajectory generation for mobile robots in unstructured environments faces a critical dilemma: balancing kinematic smoothness for safe execution with terminal precision for fine-grained tasks. Existing generative planners often struggle…

Three-dimensional molecular generators based on diffusion models can now reach near-crystallographic accuracy, yet they remain fragmented across tasks. SMILES-only inputs, two-stage pretrain-finetune pipelines, and one-task-one-model…

Reliable dual-arm grasping is essential for manipulating large and complex objects but remains a challenging problem due to stability, collision, and generalization requirements. Prior methods typically decompose the task into two…