修正噪声干扰的朗之万采样法，只需单级噪声数据即可高效生成。
A noise-corrected Langevin algorithm and sampling by half-denoising
- 通过校正噪声数据梯度偏差，实现更准确的采样。
- 仅需单一噪声水平的噪声得分函数，降低计算复杂度。
- 可直观理解为‘加噪后去除一半’，适合生成模型研究者。
朗之万算法是实空间中从给定概率密度函数采样的经典方法，仅需对数密度的梯度（即得分函数）信息。在深度学习中，通常更容易学习所谓的‘噪声数据得分函数’，即添加高斯噪声后数据对数密度的梯度。然而，这种估计存在偏差，使朗之万方法的应用复杂化。本文提出一种噪声校正的朗之万算法，至少在首阶项上消除了噪声数据带来的偏差。与扩散模型不同，该算法仅需单一噪声水平下的噪声得分函数。此外，我们还提出一个简单特例，其具有直观解释：迭代地向数据加噪，再尝试去除一半噪声。
原文摘要 · Abstract (English)
The Langevin algorithm is a classic method for sampling from a given pdf in a real space. In its basic version, it only requires knowledge of the gradient of the log-density, also called the score function. However, in deep learning, it is often easier to learn the so-called "noisy-data score function", i.e. the gradient of the log-density of noisy data, more precisely when Gaussian noise is added to the data. Such an estimate is biased and complicates the use of the Langevin method. Here, we propose a noise-corrected version of the Langevin algorithm, where the bias due to noisy data is removed, at least regarding first-order terms. Unlike diffusion models, our algorithm only needs to know the noisy score function for one single noise level. We further propose a simple special case which has an interesting intuitive interpretation of iteratively adding noise the data and then attempting to remove half of that noise.
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