https://github.com/zituitui/diffusionfisher
[ICML 2025] Official implementation of "Efficiently Access Diffusion Fisher: Within the Outer Product Span Space".
https://github.com/zituitui/diffusionfisher
aigc diffusion-model diffusion-models fisher-information icml icml-2025
Last synced: 3 months ago
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[ICML 2025] Official implementation of "Efficiently Access Diffusion Fisher: Within the Outer Product Span Space".
- Host: GitHub
- URL: https://github.com/zituitui/diffusionfisher
- Owner: zituitui
- License: mit
- Created: 2025-05-29T07:20:00.000Z (11 months ago)
- Default Branch: main
- Last Pushed: 2025-06-02T13:36:37.000Z (11 months ago)
- Last Synced: 2025-06-28T07:43:43.909Z (10 months ago)
- Topics: aigc, diffusion-model, diffusion-models, fisher-information, icml, icml-2025
- Language: Python
- Homepage:
- Size: 15.1 MB
- Stars: 8
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
# Fisher Information in the Diffusion Models
This repository is the official implementation of the **ICML 2025** paper:
_"Efficiently Access Diffusion Fisher: Within the Outer Product Span Space"_
> **Fangyikang Wang1,2, Hubery Yin2,, Shaobin Zhuang2,3, Huminhao Zhu1,
Yinan Li1, Lei Qian1, Chao Zhang1, Hanbin Zhao1, Hui Qian1, Chen Li2**
>
> 1Zhejiang University 2WeChat Vision, Tencent Inc. 3Shanghai Jiao Tong University
[](https://www.arxiv.org/abs/2505.23264)
[](https://opensource.org/licenses/MIT)
## 🆕 What's New?
### Analytical diffusion Fisher (DF)
We first derived the analytical formulation of [Fisher information](https://en.wikipedia.org/wiki/Fisher_information) in diffusion models.
Let us define the Fisher information of diffused distributions as follows:
```math
F_t(x_t, t) := - \frac{\partial^2}{\partial x_t^2} \log q_t(x_t, t)
```
We have the following analytical formulation for $F_t(x_t, t)$:
```math
F_t({x}_t, t) = \frac{1}{\sigma_t^2} {I} - \frac{\alpha_t^2}{\sigma_t^4} \left[
\int w({y}) {y} {y}^\top \, \mathrm{d}q_0
- \left( \int w({y}) {y} \, \mathrm{d}q_0 \right) \left( \int w({y}) {y} \, \mathrm{d}q_0 \right)^\top
\right]
```
where we define $v(x_t, t, y)$ as $\exp(-\frac{|x_t - \alpha_t y|^2}{2\sigma_t^2})\in \mathbb{R}$ and $w(x_t, t, y)$ as $\frac{v(x_t, t, y)}{\int_{\mathbb{R}^d} v(x_t, t, y)\textnormal{d} q_0(y)} \in \mathbb{R}$
### DF Trace Matching
We propose the DF-TM algorithm to learn the trace of diffusion Fisher and thus enabling efficient NLL evaluation.
#### Code: [Coming Soon]
### DF Endpoint Approximation
We propose the DF-EA algorithm to enable more accurate and efficient adjoint optimization.
#### Code: [Coming Soon]
### DF Optimal Transport
We design the first numerical verification experiment for the optimal transport property of the general PF-ODE deduced map.
#### Code: [Coming Soon]
## 🪪 License
This project is licensed under the MIT License - see the [LICENSE](LICENSE.txt) file for details.
## 📝 Citation
If our work assists your research, feel free to give us a star ⭐ or cite us using:
```
@misc{wang2025efficientlyaccessdiffusionfisher,
title={Efficiently Access Diffusion Fisher: Within the Outer Product Span Space},
author={Fangyikang Wang and Hubery Yin and Shaobin Zhuang and Huminhao Zhu and Yinan Li and Lei Qian and Chao Zhang and Hanbin Zhao and Hui Qian and Chen Li},
year={2025},
eprint={2505.23264},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={https://arxiv.org/abs/2505.23264},
}
```
## 📩 Contact me
My e-mail address:
```
wangfangyikang@zju.edu.cn
```