DPM-OT: A New Diffusion Probabilistic Model Based on Optimal Transport
Zezeng Li ShengHao Li Zhanpeng Wang Na Lei Zhongxuan Luo Xianfeng Gu
Sampling from diffusion probabilistic models (DPMs) can be viewed as a
piecewise distribution transformation, which generally requires hundreds or
thousands of steps of the inverse diffusion trajectory to get a high-quality
image. Recent progress in designing fast samplers for DPMs achieves a trade-off
between sampling speed and sample quality by knowledge distillation or
adjusting the variance schedule or the denoising equation. However, it can't be
optimal in both aspects and often suffer from mode mixture in short steps. To
tackle this problem, we innovatively regard inverse diffusion as an optimal
transport (OT) problem between latents at different stages and propose the
DPM-OT, a unified learning framework for fast DPMs with a direct expressway
represented by OT map, which can generate high-quality samples within around 10
function evaluations. By calculating the semi-discrete optimal transport map
between the data latents and the white noise, we obtain an expressway from the
prior distribution to the data distribution, while significantly alleviating
the problem of mode mixture. In addition, we give the error bound of the
proposed method, which theoretically guarantees the stability of the algorithm.
Extensive experiments validate the effectiveness and advantages of DPM-OT in
terms of speed and quality (FID and mode mixture), thus representing an
efficient solution for generative modeling. Source codes are available at
https://github.com/cognaclee/DPM-OT