We propose a new "Poisson flow" generative model (PFGM) that maps a uniform
distribution on a high-dimensional hemisphere into any data distribution. We
interpret the data points as electrical charges on the $z=0$ hyperplane in a
space augmented with an additional dimension $z$, generating a high-dimensional
electric field (the gradient of the solution to Poisson equation). We prove
that if these charges flow upward along electric field lines, their initial
distribution in the $z=0$ plane transforms into a distribution on the
hemisphere of radius $r$ that becomes uniform in the $r \to\infty$ limit. To
learn the bijective transformation, we estimate the normalized field in the
augmented space. For sampling, we devise a backward ODE that is anchored by the
physically meaningful additional dimension: the samples hit the unaugmented
data manifold when the $z$ reaches zero. Experimentally, PFGM achieves current
state-of-the-art performance among the normalizing flow models on CIFAR-10,
with an Inception score of $9.68$ and a FID score of $2.35$. It also performs
on par with the state-of-the-art SDE approaches while offering $10\times $ to
$20 \times$ acceleration on image generation tasks. Additionally, PFGM appears
more tolerant of estimation errors on a weaker network architecture and robust
to the step size in the Euler method. The code is available at
this https URL .

该研究提出了一种新的 “泊松流” 生成模型 (PFGM)，通过对高维半球面上的均匀分布进行映射来实现任何数据分布的生成，利用电荷在一个带有额外维度的扩展空间中的分布和电场可以生成高维电场及其在空间中的流动进行学习来实现这一目标，此模型在 CIFAR-10 数据集上表现出优秀的生成效果，并且在网络架构弱的情况下同样具有较好的鲁棒性和加速性。