Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can potentially help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs with learnable transformations through experiments on standard image generation benchmarks, including CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood and produce high-quality samples.

翻译：扩散模型在众多生成任务中展现出卓越性能。尽管近期取得了成功，大多数扩散模型仍局限于仅允许数据分布的线性变换。相比之下，更广泛的变换族有助于更高效地训练生成分布，简化逆向过程并缩小真实负对数似然与变分近似之间的差距。本文提出神经扩散模型（NDMs），这是对传统扩散模型的泛化，能够定义和学习数据随时间的非线性变换。我们展示了如何在无需仿真的设置下，通过变分界对NDMs进行优化。此外，我们推导出NDMs的时间连续形式，可利用现成的数值常微分方程和随机微分方程求解器实现快速可靠的推理。最后，通过标准图像生成基准实验（包括CIFAR-10、降采样版ImageNet和CelebA-HQ），我们验证了具有可学习变换的NDMs的实用性。NDMs在似然度方面优于传统扩散模型，并生成高质量样本。