Papers › Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs
Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs
Kaiwen Zheng, Cheng Lu, Jianfei Chen, Jun Zhu
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}.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Density Estimation | CIFAR-10 | i-DODE | NLL (bits/dim) | 2.42 | #1 of 15 | Archive leaderboard | report |
| Density Estimation | ImageNet 32x32 | i-DODE | NLL (bits/dim) | 3.69 | #2 of 5 | Archive leaderboard | report |
| Image Generation | ImageNet 32x32 | i-DODE | FID | 9.09 | #9 of 35 | Archive leaderboard | report |
| Image Generation | ImageNet 32x32 | i-DODE | bpd | 3.43 | #9 of 35 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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