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

• URL: http://arxiv.org/abs/2510.03335v1
• Date: Thu, 02 Oct 2025 05:55:22 GMT
• Title: Matching the Optimal Denoiser in Point Cloud Diffusion with (Improved) Rotational Alignment
• Authors: Ameya Daigavane, YuQing Xie, Bodhi P. Vani, Saeed Saremi, Joseph Kleinhenz, Tess Smidt,
• Abstract summary: Training a diffusion model consists of learning how to denoise noisy samples at different noise levels.<n>We show that the optimal denoiser can be expressed in terms of a matrix Fisher distribution over $SO(3)$.<n>We build on this perspective to derive better approximators to the optimal denoiser in the limit of small noise.
• Score: 5.8069334875117775
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Diffusion Model-Based Posterior Sampling in Full Waveform Inversion [3.2800968305157205]
  posterior sampling directly on observed seismic shot records is rarely practical at the field scale.<n>Our approach couples diffusion-based posterior sampling with simultaneous-source waveform inversion data.<n>Our method achieves lower model error and better data fit at a substantially reduced computational cost.
  arXiv  Detail & Related papers  (2025-12-14T18:34:12Z)
• A Minimalist Method for Fine-tuning Text-to-Image Diffusion Models [3.8623569699070357]
  Noise PPO is a minimalist reinforcement learning algorithm that learns a prompt-conditioned initial noise generator.<n>Experiments show that Noise PPO consistently improves alignment and sample quality over the original model.<n>These findings reinforce the practical value of minimalist RL fine-tuning for diffusion models.
  arXiv  Detail & Related papers  (2025-05-23T00:01:52Z)
• Distributional Diffusion Models with Scoring Rules [83.38210785728994]
  Diffusion models generate high-quality synthetic data.<n> generating high-quality outputs requires many discretization steps.<n>We propose to accomplish sample generation by learning the posterior em distribution of clean data samples.
  arXiv  Detail & Related papers  (2025-02-04T16:59:03Z)
• Robust Representation Consistency Model via Contrastive Denoising [83.47584074390842]
  randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations.<n> diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples.<n>We reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space.
  arXiv  Detail & Related papers  (2025-01-22T18:52:06Z)
• On the Relation Between Linear Diffusion and Power Iteration [42.158089783398616]
  We study the generation process as a correlation machine'' We show that low frequencies emerge earlier in the generation process, where the denoising basis vectors are more aligned to the true data with a rate depending on their eigenvalues. This model allows us to show that the linear diffusion model converges in mean to the leading eigenvector of the underlying data, similarly to the prevalent power iteration method.
  arXiv  Detail & Related papers  (2024-10-16T07:33:12Z)
• Your Diffusion Model is Secretly a Noise Classifier and Benefits from Contrastive Training [20.492630610281658]
  Diffusion models learn to denoise data and the trained denoiser is then used to generate new samples from the data distribution. We introduce a new self-supervised training objective that differentiates the levels of noise added to a sample. We show by diverse experiments that the proposed contrastive diffusion training is effective for both sequential and parallel settings.
  arXiv  Detail & Related papers  (2024-07-12T03:03:50Z)
• Immiscible Diffusion: Accelerating Diffusion Training with Noise Assignment [56.609042046176555]
  suboptimal noise-data mapping leads to slow training of diffusion models. Drawing inspiration from the immiscibility phenomenon in physics, we propose Immiscible Diffusion. Our approach is remarkably simple, requiring only one line of code to restrict the diffuse-able area for each image.
  arXiv  Detail & Related papers  (2024-06-18T06:20:42Z)
• Boosting Diffusion Models with Moving Average Sampling in Frequency Domain [101.43824674873508]
  Diffusion models rely on the current sample to denoise the next one, possibly resulting in denoising instability. In this paper, we reinterpret the iterative denoising process as model optimization and leverage a moving average mechanism to ensemble all the prior samples. We name the complete approach "Moving Average Sampling in Frequency domain (MASF)"
  arXiv  Detail & Related papers  (2024-03-26T16:57:55Z)
• Adaptive Multi-step Refinement Network for Robust Point Cloud Registration [82.64560249066734]
  Point Cloud Registration estimates the relative rigid transformation between two point clouds of the same scene.<n>We propose an adaptive multi-step refinement network that refines the registration quality at each step by leveraging the information from the preceding step.<n>Our method achieves state-of-the-art performance on both the 3DMatch/3DLoMatch and KITTI benchmarks.
  arXiv  Detail & Related papers  (2023-12-05T18:59:41Z)
• Multi-scale Diffusion Denoised Smoothing [79.95360025953931]
  randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale. We present scalable methods to address the current trade-off between certified robustness and accuracy in denoised smoothing. Our experiments show that the proposed multi-scale smoothing scheme combined with diffusion fine-tuning enables strong certified robustness available with high noise level.
  arXiv  Detail & Related papers  (2023-10-25T17:11:21Z)
• Boosting Fast and High-Quality Speech Synthesis with Linear Diffusion [85.54515118077825]
  This paper proposes a linear diffusion model (LinDiff) based on an ordinary differential equation to simultaneously reach fast inference and high sample quality. To reduce computational complexity, LinDiff employs a patch-based processing approach that partitions the input signal into small patches. Our model can synthesize speech of a quality comparable to that of autoregressive models with faster synthesis speed.
  arXiv  Detail & Related papers  (2023-06-09T07:02:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.