Diffusion Models with Deterministic Normalizing Flow Priors

For faster sampling and higher sample quality, we propose DiNof ($\textbf{Di}$ffusion with $\textbf{No}$rmalizing $\textbf{f}$low priors), a technique that makes use of normalizing flows and diffusion models. We use normalizing flows to parameterize the noisy data at any arbitrary step of the diffusion process and utilize it as the prior in the reverse diffusion process. More specifically, the forward noising process turns a data distribution into partially noisy data, which are subsequently transformed into a Gaussian distribution by a nonlinear process. The backward denoising procedure begins with a prior created by sampling from the Gaussian distribution and applying the invertible normalizing flow transformations deterministically. To generate the data distribution, the prior then undergoes the remaining diffusion stochastic denoising procedure. Through the reduction of the number of total diffusion steps, we are able to speed up both the forward and backward processes. More importantly, we improve the expressive power of diffusion models by employing both deterministic and stochastic mappings. Experiments on standard image generation datasets demonstrate the advantage of the proposed method over existing approaches. On the unconditional CIFAR10 dataset, for example, we achieve an FID of 2.01 and an Inception score of 9.96. Our method also demonstrates competitive performance on CelebA-HQ-256 dataset as it obtains an FID score of 7.11. Code is available at https://github.com/MohsenZand/DiNof.