<ul><li>Recent advancements in Diffusion models (DMs) have explored incorporating the second-order diffusion Fisher information (DF) into various downstream tasks and theoretical analysis.</li><li>Diffusion Fisher can be accessed efficiently within a space spanned by the outer products of score and initial data, leading to two efficient approximation algorithms for trace and matrix-vector multiplication of DF.</li><li>These algorithms bypass the auto-differentiation operations and provide time-efficient vector-product calculations, with established approximation error bounds.</li><li>Experiments show superior accuracy and reduced computational cost of the proposed algorithms, along with the design of a novel numerical verification experiment for the optimal transport property of the general PF-ODE deduced map.</li></ul>

Efficiently Access Diffusion Fisher: Within the Outer Product Span Space

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