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
this https URL

通过创新性地将逆扩散视为不同阶段的潜变量之间的最优传输（OT）问题，提出了 DPM-OT，一种用于快速 DPM 的统一学习框架，通过 OT 映射表示直接快速生成高质量样本，具有约 10 个函数评估内的优秀表现。大量实验证实了 DPM-OT 在速度和质量（FID 和模式混合）方面的有效性和优势，因此为生成建模提供了高效的解决方案。