  Whereas diverse variations of diffusion models exist, extending the linear
diffusion into a nonlinear diffusion process is investigated by very few works.
The nonlinearity effect has been hardly understood, but intuitively, there
would be promising diffusion patterns to efficiently train the generative
distribution towards the data distribution. This paper introduces a
data-adaptive nonlinear diffusion process for score-based diffusion models. The
proposed Implicit Nonlinear Diffusion Model (INDM) learns by combining a
normalizing flow and a diffusion process. Specifically, INDM implicitly
constructs a nonlinear diffusion on the \textit{data space} by leveraging a
linear diffusion on the \textit{latent space} through a flow network. This flow
network is key to forming a nonlinear diffusion, as the nonlinearity depends on
the flow network. This flexible nonlinearity improves the learning curve of
INDM to nearly Maximum Likelihood Estimation (MLE) against the non-MLE curve of
DDPM++, which turns out to be an inflexible version of INDM with the flow fixed
as an identity mapping. Also, the discretization of INDM shows the sampling
robustness. In experiments, INDM achieves the state-of-the-art FID of 1.75 on
CelebA. We release our code at https://github.com/byeonghu-na/INDM.
