Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking that divides the generative dynamics into two distinct phases: 1) A linear steady-state dynamics around a central fixed-point and 2) an attractor dynamics directed towards the data manifold. These two "phases" are separated by the change in stability of the central fixed-point, with the resulting window of instability being responsible for the diversity of the generated samples. Using both theoretical and empirical evidence, we show that an accurate simulation of the early dynamics does not significantly contribute to the final generation, since early fluctuations are reverted to the central fixed point. To leverage this insight, we propose a Gaussian late initialization scheme, which significantly improves model performance, achieving up to 3x FID improvements on fast samplers, while also increasing sample diversity (e.g., racial composition of generated CelebA images). Our work offers a new way to understand the generative dynamics of diffusion models that has the potential to bring about higher performance and less biased fast-samplers.

翻译：生成扩散模型最近已成为生成高维数据的领先方法。在本文中，我们证明这些模型的动力学过程表现出一种自发对称性破缺，将生成动力学划分为两个不同的阶段：1）围绕中心不动点的线性稳态动力学，以及2）指向数据流形的吸引子动力学。这两个"相"由中心不动点稳定性的变化所分隔，由此产生的不稳定窗口负责生成样本的多样性。通过理论和实证证据，我们表明对早期动力学的精确模拟并不会显著贡献于最终生成，因为早期波动会回归中心不动点。为利用这一见解，我们提出一种高斯晚期初始化方案，该方案显著提升了模型性能，在快速采样器上实现了高达3倍的FID改进，同时增加了样本多样性（例如生成的CelebA图像中的人种构成）。我们的工作为理解扩散模型的生成动力学提供了一种新的视角，有望带来更高性能和更低偏差的快速采样器。