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        "description": "Inherits DDIM and classical multistep/Runge–Kutta ideas. The high-density-manifold interpretation does not certify that finite learned-model trajectories stay on an exact data manifold. Speed and error orders require their stated schedule/smoothness conditions; no universal fixed-step quality guarantee.",
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      "statement": "# PNDM: pseudo-numerical diffusion sampling with nonlinear transfer\n\nSeparated numerical updates into estimated-gradient and transfer parts, combining multistep noise estimates with a DDIM-related nonlinear transfer to accelerate sampling from pretrained diffusion models.\n\n## Scientific scope\n\nInherits DDIM and classical multistep/Runge–Kutta ideas. The high-density-manifold interpretation does not certify that finite learned-model trajectories stay on an exact data manifold. Speed and error orders require their stated schedule/smoothness conditions; no universal fixed-step quality guarantee.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nLuping Liu; Yi Ren; Zhijie Lin; Zhou Zhao\n\nSource-listed authors or explicitly credited technical contributors for the cited versions. Family entries retain source-specific attribution; a combined list is not one original-paper byline or equal individual work. Names alone do not establish resolved identities.\n\n\n\n## Original sources\n\n- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://arxiv.org/abs/2202.09778v1)\n",
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