深度生成模型在地震反演中易记忆训练数据，导致结果不可靠。
On the role of memorization in learned priors for geophysical inverse problems
- 用最大似然训练生成模型会使其记忆训练样本而非学习地质规律
- 记忆后先验退化为加权样本查找，后验呈高斯混合形式
- 扩散模型可解析推导后验结构，适合分析反演不确定性
基于深度生成模型的先验为地震反演提供了数据驱动的正则化，但其训练需代表性地下模型数据集——这在地球物理应用中本就稀缺。由于大多数生成模型的训练目标可表述为有限数据集上的最大似然，此类模型可能收敛至经验分布，即实质上记忆训练样本而非学习底层地质分布。我们证明，此类记忆先验下的后验退化为重加权的经验分布——即对存储训练样本的似然加权查找。针对扩散模型，记忆导致闭式解的高斯混合先验；线性化正向算子于每个训练样本附近，得到各分量宽度与偏移由局部雅可比矩阵决定的高斯混合后验。我们在一个简化反演问题上验证了这些预测，并通过扩散后验采样展示了记忆对全波形反演的影响。
原文摘要 · Abstract (English)
Learned priors based on deep generative models offer data-driven regularization for seismic inversion, but training them requires a dataset of representative subsurface models -- a resource that is inherently scarce in geoscience applications. Since the training objective of most generative models can be cast as maximum likelihood on a finite dataset, any such model risks converging to the empirical distribution -- effectively memorizing the training examples rather than learning the underlying geological distribution. We show that the posterior under such a memorized prior reduces to a reweighted empirical distribution -- i.e., a likelihood-weighted lookup among the stored training examples. For diffusion models specifically, memorization yields a Gaussian mixture prior in closed form, and linearizing the forward operator around each training example gives a Gaussian mixture posterior whose components have widths and shifts governed by the local Jacobian. We validate these predictions on a stylized inverse problem and demonstrate the consequences of memorization through diffusion posterior sampling for full waveform inversion.
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