Kavli Affiliate: Max Tegmark
| First 5 Authors: Yilun Xu, Ziming Liu, Max Tegmark, Tommi Jaakkola,
| Summary:
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 $r toinfty$ 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 $2.48$. It also performs
on par with the state-of-the-art SDE approaches while offering $10times $ 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 .
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