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本文隔离了降噪得分匹配训练损失中的不可约多余项，表明它等于沿扩散轨迹的Fisher-Rao度量的迹，连接了变分原理、潜在空间几何和信息论。
This paper introduces Fisher8, an output-layer gradient correction that uses Fisher geometry instead of Euclidean geometry to stabilize neural heteroscedastic regression, improving uncertainty calibration and likelihood-error tradeoffs.