4 papers
Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data
Anand Jerry George, Nicolas Macris
We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifo…
Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves
Anand Jerry George, Rodrigo Veiga, Nicolas Macris
We theoretically investigate the phenomena of generalization and memorization in diffusion models. Empirical studies suggest that these phenomena are influenced by model complexity…
Analysis of Diffusion Models for Manifold Data
Anand Jerry George, Rodrigo Veiga, Nicolas Macris
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of…
Sampling in High-Dimensions using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations
Anand Jerry George, Nicolas Macris
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transp…