We propose using a Gaussian Mixture Model (GMM) as reverse transition
operator (kernel) within the Denoising Diffusion Implicit Models (DDIM)
framework, which is one of the most widely used approaches for accelerated
sampling from pre-trained Denoising Diffusion Probabilistic Models (DDPM).
Specifically we match the first and second order central moments of the DDPM
forward marginals by constraining the parameters of the GMM. We see that moment
matching is sufficient to obtain samples with equal or better quality than the
original DDIM with Gaussian kernels. We provide experimental results with
unconditional models trained on CelebAHQ and FFHQ and class-conditional models
trained on ImageNet datasets respectively. Our results suggest that using the
GMM kernel leads to significant improvements in the quality of the generated
samples when the number of sampling steps is small, as measured by FID and IS
metrics. For example on ImageNet 256x256, using 10 sampling steps, we achieve a
FID of 6.94 and IS of 207.85 with a GMM kernel compared to 10.15 and 196.73
respectively with a Gaussian kernel.

使用高斯混合模型（GMM）作为 Denoising Diffusion Implicit Models（DDIM）框架中的反向转换操作符（核），通过约束 GMM 的参数来匹配 DDPM 前向边际的一阶和二阶中心矩。通过 FID 和 IS 度量，实验证明在采样步数较少时，使用 GMM 核能够显著提高生成样本的质量。