# Parallel Sampling of Diffusion Models on SO(3)

arXiv: https://arxiv.org/abs/2507.10347 · HTML: https://mlsanity.com/paper/2507.10347/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Pix2Pose: Pixel-Wise Coordinate Regression of Objects for 6D Pose Estimation](https://mlsanity.com/paper/1908.07433/) (2019)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [Explaining the Ambiguity of Object Detection and 6D Pose From Visual Data](https://mlsanity.com/paper/1812.00287/) (2018)
- [Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold](https://mlsanity.com/paper/2106.05965/) (2021)
- [6D-Diff: A Keypoint Diffusion Framework for 6D Object Pose Estimation](https://mlsanity.com/paper/2401.00029/) (2023)
- [Confronting Ambiguity in 6D Object Pose Estimation via Score-Based Diffusion on SE(3)](https://mlsanity.com/paper/2305.15873/) (2023)
- [Object Pose Estimation via the Aggregation of Diffusion Features](https://mlsanity.com/paper/2403.18791/) (2024)
- [COPE: End-to-end trainable Constant Runtime Object Pose Estimation](https://mlsanity.com/paper/2208.08807/) (2022)

## Built on by (most cited first, 1 of 1)

- [The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space](https://mlsanity.com/paper/2606.01847/) (2026)

## Abstract (arXiv)

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×, significantly reducing the latency for generating a single sample.