Likelihood-based deep generative models have recently been shown to exhibit pathological behaviour under the manifold hypothesis as a consequence of using high-dimensional densities to model data with low-dimensional structure. In this paper we propose two methodologies aimed at addressing this problem. Both are based on adding Gaussian noise to the data to remove the dimensionality mismatch during training, and both provide a denoising mechanism whose goal is to sample from the model as though no noise had been added to the data. Our first approach is based on Tweedie's formula, and the second on models which take the variance of added noise as a conditional input. We show that surprisingly, while well motivated, these approaches only sporadically improve performance over not adding noise, and that other methods of addressing the dimensionality mismatch are more empirically adequate.

本文提出使用高斯噪声来解决高维密度函数模拟低维结构数据时的维度不匹配问题，并基于 Tweedie's 公式和噪声方差为条件的模型提出了两种方法。研究结果表明，虽然这些方法在理论上有合理性，但在实践中表现不一，并不是解决维度不匹配问题的最佳方案。

去噪深层生成模型