Diffusion models accurately recover mixture weights despite score insensitivity

A new paper from A. Dennehy, R. Muthukumar, R. Willett, and N. Chandramoorthy addresses a puzzling behavior of score-based generative models: they often appear to cover all modes of a multimodal distribution yet may fail to learn the correct relative amplitudes (mixture weights). The authors show this paradox is only apparent—even when the target score function is insensitive to mixture weights at the final noise level, the generated samples can still recover accurate weights if scores at intermediate noise levels contain relevant information. They define the Diffusion Score Sensitivity Index (DSSI) as the variation in the DSM loss relative to changes in a distribution parameter. The DSSI directly governs how accurately that parameter can be estimated from generated samples.

For Gaussian mixtures in arbitrary dimensions, they prove that mixture weight estimation errors are on the same order as the DSM loss under mild conditions. Empirically, they demonstrate that sensitivity emerges during the noising process for benchmark data distributions under typical schedules, and these sensitivity values predict weight recovery accuracy in well-trained models. Critically, they show that the choice of noise schedule can reduce diffusion sensitivity, leading to unintended mode amplification (over- or under-representation of certain modes). While the paper focuses on mixture weights, the DSSI framework applies to recovering any qualitative parameter of the target distribution, offering a principled way to diagnose and control generative model behavior.