Parallel Sampling of Diffusion Models on $SO(3)$

2025-07-14

AI Summary

To address the high latency in sampling diffusion models on the SO(3) manifold—caused by sequential denoising—this work introduces, for the first time, numerical Picard iteration onto the SO(3) space, proposing a parallelized denoising algorithm. By breaking the sequential dependency inherent in conventional iterative solvers, our method enables concurrent multi-step denoising while preserving pose estimation accuracy and downstream task performance. Experiments demonstrate up to a 4.9× speedup over state-of-the-art SO(3) diffusion approaches, significantly reducing per-sample generation latency without compromising task reward. The core contribution lies in adapting Picard iteration to Lie group manifolds—specifically SO(3)—thereby establishing an efficient, scalable, and geometry-aware parallel sampling paradigm for generative models operating on rotational spaces.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation, we proposed to adapt the numerical Picard iteration for the $SO(3)$ space. We demonstrate our algorithm on an existing method that employs diffusion models to address the pose ambiguity problem. Moreover, we show that this acceleration advantage occurs without any measurable degradation in task reward. The experiments reveal that our algorithm achieves a speed-up of up to 4.9$ imes$, significantly reducing the latency for generating a single sample.

Problem

• Accelerate diffusion process on SO(3) manifold
• Reduce time for denoising perturbed data
• Maintain task reward without degradation

Innovation

• Parallel sampling accelerates diffusion on SO(3)
• Picard iteration adapted for SO(3) manifold
• 4.9x speed-up without task reward loss