Semi-Implicit Denoising Diffusion Models (SIDDMs).

Despite the proliferation of generative models, achieving fast sampling during inference without compromising sample diversity and quality remains challenging. Existing models such as Denoising Diffusion Probabilistic Models (DDPM) deliver high-quality, diverse samples but are slowed by an inherently high number of iterative steps. The Denoising Diffusion Generative Adversarial Networks (DDGAN) attempted to circumvent this limitation by integrating a GAN model for larger jumps in the diffusion process. However, DDGAN encountered scalability limitations when applied to large datasets. To address these limitations, we introduce a novel approach that tackles the problem by matching implicit and explicit factors. More specifically, our approach involves utilizing an implicit model to match the marginal distributions of noisy data and the explicit conditional distribution of the forward diffusion. This combination allows us to effectively match the joint denoising distributions. Unlike DDPM but similar to DDGAN, we do not enforce a parametric distribution for the reverse step, enabling us to take large steps during inference. Similar to the DDPM but unlike DDGAN, we take advantage of the exact form of the diffusion process. We demonstrate that our proposed method obtains comparable generative performance to diffusion-based models and vastly superior results to models with a small number of sampling steps. The code is available at https://github.com/xuyanwu/SIDDMs.