Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs
This work addresses a specific bottleneck in diffusion models for researchers and practitioners in generative modeling, offering incremental improvements to enhance likelihood-based performance.
The paper tackled the problem of improving likelihood estimation for diffusion ODEs, achieving state-of-the-art results such as 2.56 on CIFAR-10 and 3.43/3.69 on ImageNet-32 without variational dequantization or data augmentation.
Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs), which enables deterministic inference and exact likelihood evaluation. However, the likelihood estimation results by diffusion ODEs are still far from those of the state-of-the-art likelihood-based generative models. In this work, we propose several improved techniques for maximum likelihood estimation for diffusion ODEs, including both training and evaluation perspectives. For training, we propose velocity parameterization and explore variance reduction techniques for faster convergence. We also derive an error-bounded high-order flow matching objective for finetuning, which improves the ODE likelihood and smooths its trajectory. For evaluation, we propose a novel training-free truncated-normal dequantization to fill the training-evaluation gap commonly existing in diffusion ODEs. Building upon these techniques, we achieve state-of-the-art likelihood estimation results on image datasets (2.56 on CIFAR-10, 3.43/3.69 on ImageNet-32) without variational dequantization or data augmentation, and 2.42 on CIFAR-10 with data augmentation. Code is available at \url{https://github.com/thu-ml/i-DODE}.