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 https://github.com/Newbeeer/poisson_flow .
翻译:我们提出一个新的“ Poisson 流” 基因模型(PFGM ), 该模型将高维半球的统一分布映射到任何数据分布中。 我们将这些数据点解读为美元=0美元高空空间的电费, 增加一个维维度, 增加美元, 产生一个高维电场( Poisson 等式解决方案的梯度 ) 。 我们证明, 如果这些电费沿着电场线向上移动, 最初以 $=0 平面的分布将转换成半径美元( 美元) 的分布, 该半径的分布将统一到 $$\to\ intfty 的分布中。 为了了解双向直线转换, 我们估算扩大空间的平面平面平面的平面电费。 对于取样,我们设计了一个由具有实际意义的额外维度的维度支撑的后值值模式: 当美元达到零美元时, 样本将进入未加固的数据流。 试看, 私人GMFGM 10 的流量将显示为9.68美元, 和FID 美元的平流, 平面的平流将显示为美元。