通过（改进的）旋转对齐匹配点云扩散中的最优去噪器
Matching the Optimal Denoiser in Point Cloud Diffusion with (Improved) Rotational Alignment
AI总结：
该研究针对点云扩散模型训练中的旋转对齐问题，证明最优去噪器可由SO(3)上的矩阵Fisher分布表示，对齐是其小噪声下的零阶近似，并推导了更优近似器，实验验证对齐在关键噪声水平下是足够好的近似。
摘要：
扩散模型是一类流行的生成模型，其训练目标是逆转从目标数据分布出发的加噪过程。训练扩散模型的核心是学习如何在不同噪声水平下对含噪样本进行去噪。在针对分子、蛋白质这类点云数据训练扩散模型时，通常不存在可指定的规范朝向。为了捕捉这种对称性，真实数据样本通常会通过在$SO(3)$（三维特殊正交群）上均匀采样的随机旋转变换进行增强。随后，在计算损失之前，通常会通过Kabsch-Umeyama算法将去噪预测结果与真实样本进行旋转对齐。然而，这一对齐步骤的作用尚未得到充分研究。在本文中，我们证明最优去噪器可以用$SO(3)$上的矩阵Fisher分布来表示。对齐操作对应于对该分布的众数进行采样，并且在小噪声水平下是最优去噪器的零阶近似，这也解释了对齐策略的有效性。我们基于这一视角，推导出了小噪声极限下最优去噪器的更优近似器。我们的实验表明，对于训练扩散模型最为关键的噪声水平区间，对齐通常是一种“足够好”的近似。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
