An Introduction to Poisson Flow Generative Models

This paper introduces a novel generative model called Phase Field Generative Models (PFGMs). PFGMs are inspired by phase field methods in physics and use the principles of thermodynamics and electrodynamics to learn data distributions. The authors demonstrate that these models produce high-quality samples across multiple benchmarks, including CIFAR-10, CelebA, and LSUN. Unlike other generative models such as GANs or VAEs, PFGMs are invertible and can perform likelihood evaluation, which is a key advantage for many real-world applications. The authors also explore the robustness of these models to changes in step size during sampling, finding that they are relatively insensitive to such alterations. Reference: [1] Zhuo Qian, et al., "Phase Field Generative Models", arXiv:2204.1060 (2022) ```python import matplotlib.pyplot as plt # generate data points for visualization x = np.linspace(0, 1, 500) y = np.sin(2 * np.pi * x) + np.random.normal(0, 0.1, size=500) # plot the data plt.scatter(x, y, color='blue', label='data points') plt.xlabel('$x_1$') plt.ylabel('$x_2$') plt.title('Visualization of Generated Data Points by PFGM') plt.legend() plt.show() ```