Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, which maps data to noise according to equations inspired by thermodynamics and can significantly impact performance. A widely held assumption is that the ELBO objective of a diffusion model is invariant to the noise process (Kingma et al.,2021). In this work, we dispel this assumption -- we propose multivariate learned adaptive noise (MuLAN), a learned diffusion process that applies Gaussian noise at different rates across an image. Our method consists of three components -- a multivariate noise schedule, instance-conditional diffusion, and auxiliary variables -- which ensure that the learning objective is no longer invariant to the choice of the noise schedule as in previous works. Our work is grounded in Bayesian inference and casts the learned diffusion process as an approximate variational posterior that yields a tighter lower bound on marginal likelihood. Empirically, MuLAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet compared to classical diffusion. Code is available at https://github.com/s-sahoo/MuLAN

翻译：扩散模型已成为合成高质量图像的有力算法。这些算法的核心是扩散过程，该过程根据热力学启发的方程将数据映射到噪声，并可能显著影响性能。一个广泛持有的假设是，扩散模型的ELBO目标对噪声过程具有不变性（Kingma等人，2021）。在本文中，我们推翻了这一假设——我们提出了多元学习自适应噪声（MuLAN），这是一种学习到的扩散过程，能够以不同速率对图像施加高斯噪声。我们的方法由三个组成部分——多元噪声调度、实例条件扩散和辅助变量——确保学习目标不再像先前工作中那样对噪声调度的选择具有不变性。我们的工作基于贝叶斯推断，并将学习到的扩散过程视为一个近似变分后验，从而产生边界更紧的边际似然下界。实验表明，与经典扩散方法相比，MuLAN在CIFAR-10和ImageNet上的密度估计中取得了新的最优结果。代码可在https://github.com/s-sahoo/MuLAN获取。