Physics-aligned Schrödinger bridge

The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in extracting features from data. However, except for the low accuracy on complex physical systems, these models often fail to comply with essential physical constraints, such as governing equations and boundary conditions. To overcome this limitation, we introduce a novel data-driven field reconstruction framework, termed the Physics-aligned Schr\"{o}dinger Bridge (PalSB). This framework leverages a diffusion Schr\"{o}dinger bridge mechanism that is specifically tailored to align with physical constraints. The PalSB approach incorporates a dual-stage training process designed to address both local reconstruction mapping and global physical principles. Additionally, a boundary-aware sampling technique is implemented to ensure adherence to physical boundary conditions. We demonstrate the effectiveness of PalSB through its application to three complex nonlinear systems: cylinder flow from Particle Image Velocimetry experiments, two-dimensional turbulence, and a reaction-diffusion system. The results reveal that PalSB not only achieves higher accuracy but also exhibits enhanced compliance with physical constraints compared to existing methods. This highlights PalSB's capability to generate high-quality representations of intricate physical interactions, showcasing its potential for advancing field reconstruction techniques.

DPoser: Diffusion Model as Robust 3D Human Pose Prior

Modeling human pose is a cornerstone in applications from human-robot interaction to augmented reality, yet crafting a robust human pose prior remains a challenge due to biomechanical constraints and diverse human movements. Traditional priors like VAEs and NDFs often fall short in realism and generalization, especially in extreme conditions such as unseen noisy poses. To address these issues, we introduce DPoser, a robust and versatile human pose prior built upon diffusion models. Designed with optimization frameworks, DPoser seamlessly integrates into various pose-centric applications, including human mesh recovery, pose completion, and motion denoising. Specifically, by formulating these tasks as inverse problems, we employ variational diffusion sampling for efficient solving. Furthermore, acknowledging the disparity between the articulated poses we focus on and structured images in previous research, we propose a truncated timestep scheduling to boost performance on downstream tasks. Our exhaustive experiments demonstrate DPoser's superiority over existing state-of-the-art pose priors across multiple tasks.