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Poisson Flow Generative Models
Yilun Xu · Ziming Liu · Max Tegmark · Tommi Jaakkola

Thu Dec 08 05:00 PM -- 07:00 PM (PST) @
in Lightning Talks 6B-1 »
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 .
Keywords: generative model · poisson equation · ODE

Author Information

Yilun Xu (Massachusetts Institute of Technology)
Ziming Liu (MIT)
Max Tegmark (MIT)

Max Tegmark is a professor doing physics and AI research at MIT, and advocates for positive use of technology as president of the Future of Life Institute. He is the author of over 250 publications as well as the New York Times bestsellers “Life 3.0: Being Human in the Age of Artificial Intelligence” and "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality". His AI research focuses on intelligible intelligence. His work with the Sloan Digital Sky Survey on galaxy clustering shared the first prize in Science magazine’s “Breakthrough of the Year: 2003.”

Tommi Jaakkola (MIT)

Tommi Jaakkola is a professor of Electrical Engineering and Computer Science at MIT. He received an M.Sc. degree in theoretical physics from Helsinki University of Technology, and Ph.D. from MIT in computational neuroscience. Following a Sloan postdoctoral fellowship in computational molecular biology, he joined the MIT faculty in 1998. His research interests include statistical inference, graphical models, and large scale modern estimation problems with predominantly incomplete data.

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