Diffusion models have become the state-of-the-art for generative modeling in images, but there’s still much to uncover about their theoretical foundations. In collaboration with Anand Jerry George and Nicolas Macris, we dive into these aspects in our two latest preprints. In Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves, we analyse the time-reversed dynamics of denoising score matching in generative diffusion models, leveraging random feature neural networks to derive precise learning curves. In Analysis of Diffusion Models for Manifold Data, explore the behaviour of diffusion models when data lies on a manifold, under the assumption of an exact empirical score.