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

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$\times$, significantly reducing the latency for generating a single sample.