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 radiusr that becomes uniform in the r limit. To learn the bijective transformation, we estimate the normalized field in the augmented space.

We propose a new "Poisson flow" generative model (PFGM) that maps a uniform

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for $N$ dimensional data by embedding paths in $N{+}D$ dimensional space while still controlling the progression with a simple scalar norm of the $D$ additional variables. The new models reduce to PFGM when $D{=}1$ and to diffusion models when $D{\to}\infty$. The flexibility of choosing $D$ allows us to trade off robustness against rigidity as increasing $D$ results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of $D$, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models ($D{\to} \infty$) to any finite $D$ values. Our experiments show that models with finite $D$ can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ $64{\times}64$ datasets, with FID scores of $1.91/2.43$ when $D{=}2048/128$. In class-conditional setting, $D{=}2048$ yields current state-of-the-art FID of $1.74$ on CIFAR-10. In addition, we demonstrate that models with smaller $D$ exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Generative AI models have made great strides in the past few years. Physics-inspired Diffusion Models have ascended to state-of-the-art performance in several domains, powering models like Stable Diffusion, DALL-E 2, and Imagen. Researchers from MIT have recently unveiled a new physics-inspired generative model, this time drawing inspiration from the field of electrodynamics. This new type of model - the Poisson Flow Generative Model (PFGM) - treats the data points as charged particles. By following the electric field generated by the data points, PFGMs can create entirely novel data. PFGMs constitute an exciting foundation for new avenues of research, especially given that they are 10-20 times faster than Diffusion Models on image generation tasks, with comparable performance. In this article, we'll take a high-level look at PFGM theory before learning how to train and sample with PFGMs. After that we'll take another look at the theory, this time perfoming a deep dive starting from first principles. Then we'll look at how PFGMs stack up to other models and other results before ending with some final words. Several families of generative models have evolved throughout the development of AI. Other approaches, like GANs, cannot explicitly calculate likelihoods, but can generate very high-quality samples.

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 .