A finite-sample perspective reveals that inexact likelihood approximations cause under- or over-estimation of posterior spread at intermediate timesteps, leading to early-stopping sensitivity, mode weighting errors, and hallucinations even from multimodal priors alone.
FunDiff: Diffusion models over function spaces for physics-informed generative modeling.Nature Communications, April 2026
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When, why, and how do diffusion posterior samplers fail? A finite-sample lens
A finite-sample perspective reveals that inexact likelihood approximations cause under- or over-estimation of posterior spread at intermediate timesteps, leading to early-stopping sensitivity, mode weighting errors, and hallucinations even from multimodal priors alone.