# Matching the Optimal Denoiser in Point Cloud Diffusion with (Improved) Rotational Alignment

arXiv: https://arxiv.org/abs/2510.03335 · HTML: https://mlsanity.com/paper/2510.03335/

## 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 2 Oct 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)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [On the Generalization Properties of Diffusion Models](https://mlsanity.com/paper/2311.01797/) (2023)
- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [Improved motif-scaffolding with SE(3) flow matching](https://mlsanity.com/paper/2401.04082/) (2024)
- [Probabilistic orientation estimation with matrix Fisher distributions](https://mlsanity.com/paper/2006.09740/) (2020)
- [Generalization through variance: how noise shapes inductive biases in diffusion models](https://mlsanity.com/paper/2504.12532/) (2025)
- [FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation](https://mlsanity.com/paper/2508.12629/) (2025)
- [Bayesian Attitude Estimation with the Matrix Fisher Distribution on SO(3)](https://mlsanity.com/paper/1710.03746/) (2017)
- [Nearest Neighbour Score Estimators for Diffusion Generative Models](https://mlsanity.com/paper/2402.08018/) (2024)
- [JAMUN: Bridging Smoothed Molecular Dynamics and Score-Based Learning for Conformational Ensembles](https://mlsanity.com/paper/2410.14621/) (2024)

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

- [AnchorPose for Geometry-Aware MOF Assembly through Meso-Grained Pose Generation](https://mlsanity.com/paper/2610.05843/) (2026)

## Abstract (arXiv)

Diffusion models are a popular class of generative models trained to reverse a noising process starting from a target data distribution. Training a diffusion model consists of learning how to denoise noisy samples at different noise levels. When training diffusion models for point clouds such as molecules and proteins, there is often no canonical orientation that can be assigned. To capture this symmetry, the true data samples are often augmented by transforming them with random rotations sampled uniformly over SO(3). Then, the denoised predictions are often rotationally aligned via the Kabsch-Umeyama algorithm to the ground truth samples before computing the loss. However, the effect of this alignment step has not been well studied. Here, we show that the optimal denoiser can be expressed in terms of a matrix Fisher distribution over SO(3). Alignment corresponds to sampling the mode of this distribution, and turns out to be the zeroth order approximation for small noise levels, explaining its effectiveness. We build on this perspective to derive better approximators to the optimal denoiser in the limit of small noise. Our experiments highlight that alignment is often a `good enough' approximation for the noise levels that matter most for training diffusion models.