流形上扩散模型的拟数值方法
Pseudo Numerical Methods for Diffusion Models on Manifolds
摘要：
去噪扩散概率模型（DDPM）可以生成高质量的样本，例如图像和音频样本。然而，DDPM需要数百到数千次迭代才能生成最终样本。几个先前的工作已经通过调整方差时间表成功地加速了DDPM（例如，改进的去噪扩散概率模型）或去噪方程（例如，去噪扩散隐式模型（DDIM））。然而，这些加速方法不能保持样本的质量，甚至引入新的噪声在高加速比，这限制了它们的实用性。为了加快推理过程，同时保持样本质量，我们提供了一个新的视角，DDPM应被视为解决流形上的微分方程。在此基础上，我们提出了扩散模型的伪数值方法。具体来说，我们弄清楚如何解决微分方程的流形上，并表明DDIM是伪数值方法的简单情况。将几种经典的数值方法转化为相应的伪数值方法，发现在大多数情况下伪线性多步法是最好的。根据我们的实验，通过直接使用Cifar10，CelebA和LSUN上的预训练模型，PNDM可以生成更高质量的合成图像，与1000步DDIM相比，仅需50步（20倍加速），显着优于250步的DDIM（FID中约为0.4），并且在不同的方差时间表上具有良好的泛化能力。我们的实现可以在https://github.com/luping-liu/PNDM上获得。
英文摘要：
Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multi-step method is the best in most situations. According to our experiments, by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules. Our implementation is available at https://github.com/luping-liu/PNDM.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
