{"id":29092570,"url":"https://github.com/zituitui/diffusionfisher","last_synced_at":"2026-02-03T16:34:50.746Z","repository":{"id":296675296,"uuid":"992454611","full_name":"zituitui/DiffusionFisher","owner":"zituitui","description":"[ICML 2025] Official implementation of \"Efficiently Access Diffusion Fisher: Within the Outer Product Span 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unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["aigc","diffusion-model","diffusion-models","fisher-information","icml","icml-2025"],"created_at":"2025-06-28T07:36:39.178Z","updated_at":"2026-02-03T16:34:50.707Z","avatar_url":"https://github.com/zituitui.png","language":"Python","readme":"# Fisher Information in the Diffusion Models\n\n\u003cdiv align=\"center\"\u003e\n\nThis repository is the official implementation of the **ICML 2025** paper:\n_\"Efficiently Access Diffusion Fisher: Within the Outer Product Span Space\"_ \n\n\u003e **Fangyikang Wang\u003csup\u003e1,2\u003c/sup\u003e, Hubery Yin\u003csup\u003e2,\u003c/sup\u003e, Shaobin Zhuang\u003csup\u003e2,3\u003c/sup\u003e, Huminhao Zhu\u003csup\u003e1\u003c/sup\u003e, \u003cbr\u003e Yinan Li\u003csup\u003e1\u003c/sup\u003e, Lei Qian\u003csup\u003e1\u003c/sup\u003e, Chao Zhang\u003csup\u003e1\u003c/sup\u003e, Hanbin Zhao\u003csup\u003e1\u003c/sup\u003e, Hui Qian\u003csup\u003e1\u003c/sup\u003e, Chen Li\u003csup\u003e2\u003c/sup\u003e**\n\u003e \n\u003e \u003csup\u003e1\u003c/sup\u003eZhejiang University \u003csup\u003e2\u003c/sup\u003eWeChat Vision, Tencent Inc. \u003csup\u003e3\u003c/sup\u003eShanghai Jiao Tong University  \n\n[![arXiv](https://img.shields.io/badge/arXiv%20paper-2505.23264-b31b1b.svg)](https://www.arxiv.org/abs/2505.23264)\u0026nbsp;\n[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)\u0026nbsp;\n\n\u003cimg src=\"assets/figure_icml_adjoint.jpg\" alt=\"Adjoint Improvement Results\" style=\"width: 85%;\"\u003e\n\n\u003cimg src=\"assets/nll_drawio.png\" alt=\"Adjoint Improvement Results\" style=\"width: 80%;\"\u003e\n\n\u003c/div\u003e\n\n\n\n\n## 🆕 What's New?\n### Analytical diffusion Fisher (DF)\nWe first derived the analytical formulation of [Fisher information](https://en.wikipedia.org/wiki/Fisher_information) in diffusion models.\n\nLet us define the Fisher information of diffused distributions as follows:\n```math\nF_t(x_t, t) := - \\frac{\\partial^2}{\\partial x_t^2} \\log q_t(x_t, t)\n```\nWe have the following analytical formulation for $F_t(x_t, t)$:\n```math\nF_t({x}_t, t) = \\frac{1}{\\sigma_t^2} {I} - \\frac{\\alpha_t^2}{\\sigma_t^4} \\left[ \n    \\int w({y}) {y} {y}^\\top \\, \\mathrm{d}q_0\n    - \\left( \\int w({y}) {y} \\, \\mathrm{d}q_0 \\right) \\left( \\int w({y}) {y} \\, \\mathrm{d}q_0 \\right)^\\top\n\\right]\n```\nwhere 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 $\\frac{v(x_t, t, y)}{\\int_{\\mathbb{R}^d}  v(x_t, t, y)\\textnormal{d} q_0(y)} \\in \\mathbb{R}$\n\n### DF Trace Matching\nWe propose the DF-TM algorithm to learn the trace of diffusion Fisher and thus enabling efficient NLL evaluation.\n#### Code: [Coming Soon]\n\n\n### DF Endpoint Approximation\nWe propose the DF-EA algorithm to enable more accurate and efficient adjoint optimization.\n#### Code: [Coming Soon]\n\n### DF Optimal Transport\nWe design the first numerical verification experiment for the optimal transport property of the general PF-ODE deduced map.\n#### Code: [Coming Soon]\n\n\n## 🪪 License\nThis project is licensed under the MIT License - see the [LICENSE](LICENSE.txt) file for details.\n\n\n## 📝 Citation\nIf our work assists your research, feel free to give us a star ⭐ or cite us using:\n```\n@misc{wang2025efficientlyaccessdiffusionfisher,\n      title={Efficiently Access Diffusion Fisher: Within the Outer Product Span Space}, \n      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},\n      year={2025},\n      eprint={2505.23264},\n      archivePrefix={arXiv},\n      primaryClass={cs.LG},\n      url={https://arxiv.org/abs/2505.23264}, \n}\n```\n\n## 📩 Contact me\nMy e-mail address:\n```\nwangfangyikang@zju.edu.cn\n```","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fzituitui%2Fdiffusionfisher","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fzituitui%2Fdiffusionfisher","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fzituitui%2Fdiffusionfisher/lists"}