  Employing a forward diffusion chain to gradually map the data to a noise
distribution, diffusion-based generative models learn how to generate the data
by inferring a reverse diffusion chain. However, this approach is slow and
costly because it needs many forward and reverse steps. We propose a faster and
cheaper approach that adds noise not until the data become pure random noise,
but until they reach a hidden noisy data distribution that we can confidently
learn. Then, we use fewer reverse steps to generate data by starting from this
hidden distribution that is made similar to the noisy data. We reveal that the
proposed model can be cast as an adversarial auto-encoder empowered by both the
diffusion process and a learnable implicit prior. Experimental results show
even with a significantly smaller number of reverse diffusion steps, the
proposed truncated diffusion probabilistic models can provide consistent
improvements over the non-truncated ones in terms of performance in both
unconditional and text-guided image generations.
