Where the Score Lives: What Wavelets Reveal About Diffusion Models

Diffusion models have had remarkable success in generating a diverse set of visually plausible images. However, it remains unclear how they are able to produce novel samples, rather than simply memorizing the training distribution. Part of the answer has to do with architectural inductive biases in the score network, while another part is due to diversity in the underlying data distribution. It remains unclear how these factors interact. In this talk, I’ll present a wavelet-based, analytically tractable parameterization of the score that lets us solve for interpretable score components in closed form. This framework makes it possible to isolate which moments and dependency structures of the data distribution matter most across noise scales. Speaker Bio: Emma Finn is an undergraduate at Harvard studying Mathematics and Classics, with an A.M. in Statistics through the concurrent AB/AM program. Her work spans probability theory, statistical modeling, and machine learning—especially interpretable models, stochastic processes, and the mathematics of diffusion. Find seminar details and upcoming talks: https://www.microsoft.com/en-us/research/event/microsoft-research-new-england-generative-modeling-sampling-seminar/